--- title: "Sum Up Math 4" book: "xxxxx" category: "MA" publisher: "Ratan Prakashan Mandir Pvt. Ltd." type: "Educational Material" ---  ![](Sum up math-4_files/Sum20up20math-4-1.jpg)^ RATAN PRAKASHAN MANDIR PVT. LTD Educational & University Publishers 2nd Floor, Centre Plaza, Parinay Kunj, Lajpat Kunj Marg, Agra - 282002 Contact: 0562-4068152 | Mob.: 9068675302 Email: | Website: [www.ratanprakashan.com](http://www.ratanprakashan.com) # Bpm By Ved Prakash M.Sc (Math), B.Ed. ![](Sum up math-4_files/Sum20up20math-4-2.jpg)ISBN: 978-93-7899-560-6 MRP: ' 400 BRANCHES Agra Ahmedabad Bengaluru Gorakhpur Indore Jaipur Meerut Mumbai Nagpur Noida Patna Kanpur Kolkata Lucknow : 5/169/1, First Floor, Lata Kunj, Old Agra Mathura Road, Agra. Ph.: 0562-2650100, 2650109, Mob. : 9719004934 : Ground Floor, Dwarkesh Apartment, Nr. SBI, Punit Marg, Maninagar, Ahmedabad. Ph.: 079-65493027, Mob.: 9624094927 : No. 660, Freedom Fighter Colony, Nr. Leggere Bridge, Leggere, Bengaluru. Mob. :9964170120 : 25, 26 Pratibha Complex, Opp. Govt. Jublee Inter College, Baxipur, Gorakhpur. Ph.: 0551-2337178, Mob. : 9719004925,9451686798 : 504, M. G. Road, Opp Kothari Market, Indore. Ph.: 0731-2432479, Mob. : 9827233199, 9719004951 : 1632, Chordia Bhawan, Sonthliwalon Ka Rasta, Choura Rasta, Jaipur. Mob. : 9783358000, 9719004930 : Tilak Hall Lane, Meston Road, Kanpur. Mob.: 9336106323 : 129-A, Mukta Ram Babu Street, Kolkata. Ph. : 033-22193306, Mob. : 9830466360 : Indira Market, Opp. Mahila College, Aminabad, Lucknow. Mob. : 9719004924, 9450422840 - : Shop No.2, Sunil Complex, Western Kutchery Road, Meerut. Ph.: 0121-2641622, Mob. : 9719004929 - : Plot No. 124, D-2, Bhagyodaya C.H.S. Ltd. Swami Vivekanand Nagar, Nr Vasant Vihar Club, Pokhran Road No. 2, Thane (West), Mumbai. Ph. 022-21730175, Mob. : 9930537375 - : Shop No. GS-22, Shyam Palace, Opp. Shivaji Science College, Congress Nagar, Nagpur. Ph.: 0712-2452361, Mob. : 9822086148, 9823385600 - : D-159, Sector-7, Near Vasundhara Enclave Check Post, Noida. Ph.: 0120-4541101,02, Mob.: 9891179480 - : Chunni Lal Market, BM Dass Road, Patna. Ph.: 0612-6456562, Mob. : 9931568925 © All rights reserved with publishers. Revised Edition Printed by: Ravi Offset Printers & Publishers (P) Ltd. 5/169/1, Lata Kunj, Agra-Mathura Road, Agra-282002. Ph. : 0562-2650100, 2650109 ![](Sum up math-4_files/Sum20up20math-4-3.jpg) Typeset & Illustrated at : Typeface ![](Sum up math-4_files/Sum20up20math-4-4.jpg)We all like to play. When we indulge ourselves into an activity, and if it is interesting, we concentrate and put all our attention in it. Suppose the same principle is applied to Mathematics! "Sum Up Mathematics" brings to you the subject in easy-to-understand way. The contents are from everyday life and so children will grasp the matter quickly. We can safely say-Children will play with mathematics. This series redefines the concepts of Mathematics. Close attention has been paid to present the topics in an innovative and lucid way. The chapters are well illustrated with solved examples and numerous problems for better comprehension and ample of practice. Main Features of this Series - • Learning by Doing is the essence of the text - • Illustrations and exercises are tastefully done - • The text is designed to generate and build comprehension of the learner This series also fosters a positive attitude among children and encourages them to be friendly with mathematics so that the values of the subject can be enjoyed. Author ^CONTENTS ![](Sum up math-4_files/Sum20up20math-4-5.jpg) No. Chapters 1\. Number and Number names 05 2\. K Roman Numerals 20 3\. Addition 24 4\. Subtraction 33 5\. Multiplication 42 6\. Division 54 7\. Problems on Four Fundamental Operation 65 8\. Factors and Multiples 68 9\. Composite Numbers 73 10\. Common Fraction 80 11\. Money 99 12\. Measurement of Weight 107 13\. Measurement of Capacity 115 14\. Measurement of Length 122 15\. Measurement of Time 136 16\. Geometry 148 17\. Patterns 166 18\. Data Handling 176 19\. Examination Time 181 Formative Assessment Papers 189 Answers 193 ![](Sum up math-4_files/Sum20up20math-4-6.jpg) ![](Sum up math-4_files/Sum20up20math-4-7.jpg) ![](Sum up math-4_files/Sum20up20math-4-8.jpg) NumbeR5 And NvmbeR Names ![](Sum up math-4_files/Sum20up20math-4-9.jpg) Previously we have already learnt that:- The greatest (Largest) 1-digitnumberis 9 The greatest (Largest) 2-digit number is 99 The greatest (Largest) 3-digit number is 999 The greatest (Largest) 4-digit number is 9999 We also obtained the smallest number by adding one (1) to the greatest number as below:- The smallest The smallest The smallest The smallest The smallest 1-digitnumberis 2-digit number is 3-digit number is 4-digit number is 5-digit number is 1 10(i.e9 + 1) 100 (i.e 99 + 1) 1000(i.e999 + 1) 10000 (i.e 9999 + 1) So, we see that 10000 is obtained by adding 1 to 9999. The number name for 10,000 is "Ten Thousand". Now, let us study the following:- [Oneten + one =11](#bookmark6) [One hundred + one =101](#bookmark7) [One thousand + one =1001](#bookmark8) [Seven thousand + one =7001](#bookmark9) [Ten thousand + one =10001](#bookmark10) 10001 stands for 1 ten-thousand, 0 hundreds, 0 tens and 1 ones. The number name for 10001 is "ten thousand one." 10010 stands for 1 ten-thousand, 0 hundreds, 1 tens and 0 ones. The number name for 10010 is "ten thousand ten". 10100 stands for 1 ten-thousand, 1 hundred, 0 tens and 0 ones. The number name for 10100 is "ten thousand one hundred". 11000 stands for eleven thousand, 0 hundred, 0 tens and 0 ones. The number name for 11000 is "eleven thousands and" 95000 is "ninety five thousand". 99999 is "ninety nine thousand nine hundred ninety nine". 99999 is the greatest number of five digits. Let us see, what number shall we get by adding 1 to 99999. 99999 + 1 = 90000 + 9000 + 900 + 90 + 9 + 1 = 90000 + 9000 + 900 + 90+10 (adding ones) = 90000+ 9000+ 900+ 100 (adding tens) = 90000 + 9000+ 1000 (adding hundreds) = 90000 +10000 (addingthousands) = 100000 (adding ten thousands) 100000 stands for 100 thousand and its number name is "one lakh" 100000 has six digits. It is one more than 99999. 100000 is the smallest number of six digits. REPRESENTATION OF NUMBERS ON SPIKE ABACUS Previously, we have already learnt the representation of 4-digits numbers on a spike abacus in standard III. 15015 a five digit number is represented on the spike abacus as shown here. Now, study the following examples. Example 1 : Write the number represented on each of the spike abacus. T-ThTh H T O 15 0 15 T-ThTh H T O T-ThTh H T O T-Th Th H T O Solution : (a) 42513 (b) 25134 (c) 51342 Example 2 : Write the following numbers. (a) 1 more than 100 - (c) 1 more than 9 (b) 1 more than 1000 - (d) 1 more than 999 (e) 1 more than 4999 Solution : "X (a) 101 (b) 1001 (c) 10 (d) 1000 (e) 5000 Example 3: Write the next five numbers starting from. ![](Sum up math-4_files/Sum20up20math-4-10.jpg) ###### EXERCISE 1 ![](Sum up math-4_files/Sum20up20math-4-11.jpg) - 1\. Write the numbers given on each of the following spike abacus: ![](Sum up math-4_files/Sum20up20math-4-12.jpg)(b) (c) (a) - 2\. Write the following numbers : - (a) 1 more than 11 (b) (d) 1 more than 22399 (e) 1 more than 1100 1 more than 9999 (c) (f) 1 more than 25400 1 more than 10000 - 3\. For each of the following, write the next four numbers starting from: (a) 57465 (b) 24567 (c) 35125 (d) 15459 - 4\. Write all the numbers between : (a) 14525 and 14530 (b) 37875 and 37880 - 5\. Fill in the blanks by observing the pattern carefully : - [(a) 34320, 34322, 34324, ,,](#bookmark19) - [(b) 22215,22220,22225, ,,](#bookmark20) - [(c) 15410,15420,15430, ,,](#bookmark21) - [(d) 555115,556115,557115, ,,](#bookmark22) - [(e) 67917, 67817, 67717, ,,](#bookmark23) - 6\. Write in ascending order the numbers from : - (a) 67279 to 67284 (b) 78439 to 78445 - 7\. Write in descending order the numbers from : - (a) 15439 to 15435 (b) 99235 to 99231 - 8\. Counting by fives, write the numbers from : - (a) 13615 to 13635 (b) 27441 to 27461 - 9\. Counting by tens, write the numbers from : - (a) 28310 to 28340 (b) 87516 to 87546 - 10\. Counting by hundreds, write five numbers starting from : - (a) 68110 (b) 37371 - 11\. Counting by thousands, write four numbers starting from : - (a) 84221 (b) 65997 - 12\. Write the smallest number of 5 digits : - 13\. Write the smallest number of 6 digits : - 14\. How many thousands are there in one lakh? Writing the numbers in words and figures Lakhs (L) Ten-Thousands (T-Th) Thousands (Th) Hundreds (H) Tens (T) Ones (O) (i) 2 3 4 5 (ii) 7 8 1 1 6 (iii) 8 1 2 3 4 (iv) 1 1 0 0 0 0 \-- The first number has 2 thousands, 3 hundreds, 4 tens and 5 ones. In figures it is written as '2345' and in words it is written as "two thousand three hundred forty five". The second number has 7 ten-thousands, 8 thousands, 1 hundred, 1 tens and 6 ones. In figure it is written as '78116' and in words as "seventy eight thousand one hundred sixteen". The third number has 8 ten-thousands, 1 thousand 2 hundreds, 3 tens and 4 ones. It figure it is written as '81234' and in words as "eighty one thousand two hundred thirty four". The fourth number has 1 lakhs, 1 ten-thousands, 0 thousands, 0 hundreds, 0 tens and 0 ones. In figure it is written as '110000' and in words as "one lakh ten thousand". 1\. Write the correct numeral in the table : ![](Sum up math-4_files/Sum20up20math-4-13.jpg) (a) (b) (c) 5 ten-thousands, 3 thousands, 0 hundreds, 5 tens, 4 ones. 3 ten-thousands, 6 thousands, 2 hundreds, 5 tens, 0 ones. 7 ten-thousands, 5 thousands, 3 hundreds, 4 tens, 3 ones. Fill in the box with correct numeral : - (a) 3578 = L - (b) 8532 = □ - (c) 47685 = □ - (d) 97483 = □ j thousands, 5 hundred, 7 tens, 8 ones. 3 thousands, \[ \] hundred, 3 tens, 2 ones. n ten-thousands, \[ | thousands, \[ \] hundreds, 8 tens, 5 ones. "I ten-thousands, \[ \] thousands, \[ \] hundreds, 8 tens, \[ \] ones. (e) 84567 = □ ten-thousands, thousands, hundreds, tens, \] ones. - 3\. Write the number names for the following numbers : (a) 45362 (b) 94865 (c) 24359 (d) 77499 (h) 88090 (e) 20059 (f) 40004 (g) 3 7000 - 4\. Write the following numbers in figures : - (a) Five thousands seven hundred twenty five. - (b) Fifty thousand four hundred thirty nine. - (c) Eighty five thousand eighty five. - (d) Ninety thousand ninety. - (e) Thirty nine thousand seven hundred. ![](Sum up math-4_files/Sum20up20math-4-14.jpg)(f) Sixty seven thousand five hundred three. (g) Seventy thousand. (h) Twenty two thousand forty eight. PLACEVALUE Previously, we have already learnt that the place value of a digit depends on its position in the number. Here we shall extend the idea in respectof a number of 5 digits. - Example 1: Find the place value of each digit in 34502 in figures and words. [Solution:,](#bookmark13) Number 3 4 5 0 2 Value In words Two Zero Five Hundreds Four Thousands Thirty Thousands In figures [2 ones2](#bookmark26) [0 tens0](#bookmark27) [5 hundreds500](#bookmark28) [4 thousands4000](#bookmark29) 3 ten-thousands 30000 Note-Face value of a digit remains unchanged. - Example 2: Find the place value of 7 and 7 in 57574. Solution: Tricky method 5 7 5 7 4 ▼ ▼ ▼ ▼ 10 0 0 7 appears at the thousands place in 57574. . The place value of 7 is 7 thousands, i.e 7000. - 7 appears at the tens place in the given number. The place valueof 7 is 7 tens i.e 70. - Example 3: Find the sum of the place values of 5's in the number 53505. Solution: In 53505, the place valueof: - 5 in ten-thousand place is 50000 - 5 in hundred place is 500 ![](Sum up math-4_files/Sum20up20math-4-15.jpg) - 5 in ones place is 5 .-. Sum ofthe place values = 50000 + 500 + 5 = 50505 Get Set Go With Sum Up Mathematics-4 ###### . EXERCISE 3 f - 1\. Write the place value of : (a) 5 in 65422 - (d) 9 in 14609 (g) 5's in 45257 (b) 9 in 94708 - (e) 6 in 85056 (h) 8's in 85875 (c) 6 in 34678 (f) 0 in 60594 - 2\. Write the place value oftwo 5's in 65452 in words: - 3\. Here is the meter reading of Chandra's car. Answer the fol lowing questions : - (a) If 1000 km more is travelled. Which digit will change? - (b) To make the digit 5 changed to 6 other digit do not change, how many km will have to be travel led? (c) How many times greater is the 6 on the left than the 6 on the right? - 4\. Underlinethecorrectplace valueof 7 in each number: Number Place Value (a) 37681 70 7000 700 7 (b) 46728 70 7000 700 7 (c) 78352 70 70000 7000 700 (d) 22471 70 70000 7000 700 (e) 93447 70 70000 700 7 - 5\. Write the place value of two 4's in the number 64435. Is one value ten times the other? - 6\. Find the sum of the place values of the coloured digits: (a) 39435 (b) 65545 (c) 45424 (d) 72707 - 7\. Rewrite the following numbers interchanging the digits of the thousands and ones places: Example: 27405 -------> 25407 (a) 27085 (b) 17621 (c) 95047 (d) 55800 - 8\. Rewrite the following numbers interchanging the digits at the tens and ten-thousands places: (a) 85715 (b) 38618 (c) 42416 (d) 85905 EXPANDED FORMS We know the method of writing 4-digit numbers in the expanded form. Now, here we shall learn howto write 5-digit numbers in the expanded form. - Example 1: Write 7546 in the expanded form. Solution: '.' 7546 has 7 thousands, 5 hundreds, 4 tens and 6 ones. /. 7546 = 7000 + 500 + 40 + 6 Examples 2: Write 98437 in the expanded form. Solution: 98437 has 9 ten-thousands, 8 thousands, 4 hundreds, 3 tens and 7ones. .-. 98437 = 90000 + 8000 + 400 + 30 + 7 - Example 3: Write in short form : - (a) 9000 + 700 + 50 + 3 (b) 80000 + 6000 + 400 + 70 + 5 (c) 60000 + 4000 + 40 + 4 Solution: - (a) 9000 + 700 + 50 + 3 = 9 thousands 7 hundred 5 tens 3 ones = 9753 - (b) 80000 + 6000 + 400 + 70 + 5 = 8 ten-thousands 6 thousands 4 hundreds 7 tens 5 ones = 86475 - (c) 60,000 + 4000 + 40 + 4 = 6 ten thousands 4 thousands 0 hundreds 4 tens 4 ones = 64044 - Example 4: How many hundreds are there in 8967? Solution: 8967 = 8000 + 900 + 60 + 7 = eighty hundreds + 9 hundreds + 6 tens + 7 ones = 89 hundreds + 6 tens + 7 ones .•. There are 89 hundreds in 8967 ###### . EXERCISE 4 1\. Write the following in expanded form : (a) 4848 (b) 77345 (c) 88880 (d) 63047 (e) 80505 (f) 30748 2\. Write the following in short form: (a) 60000 + 4000 + 300 + 40 + 5 (b) 90000 + 7000 +60+5 (c) 70000 + 8000 + 500 + 60 (d) 20000 + 900 + 30 + 9 (e) 80000 + 2000 + 30 (f) 50000 + 500 + 2 (g) 40000 + 80 + 7 (h) 5 ten-thousands 8 thousands 3 hundreds 7 tens 2 ones (i) 86 thousands 5 hundreds 7 ones - 3\. Which one of the following is the expanded form of 68704: - (a) 60000 + 8000 + 70 + 4 (b) 60000 + 8000 + 700 + 4 (c) 60000 + 800 + 70 + 4 (d) 60000 + 8000 + 700 + 40 - 4\. Find that correct break up (expanded form) from the following for 88088: - (a) 80000 + 8000 + 800 + 8 (b) 80000 + 800 + 80 + 8 (d) 80000 + 8000 + 80 + 8 (b) Thousands in 82471 ? (d) Tens in 865? (c) 80000 + 8000 + 800 + 80 + 8 - 5\. How many are: - (a) Hundreds in 3809? - (c) Hundreds in 27607? (e) Tens in 4475? ORDER RELATION We have learntthe method of findingthe greater of the two given 4-digit numbers. To compare 5-digit numbers, we follow the same rule. We also know that: Rule : A number containing more digits is greater than the number containing less digits. For example, 18 > 9,1 78 > 45, 3525 > 888 Example 1: Which is greater: 75842 or 8958. Solution: The number 75842 has more digits than the number 8958. /. 75842 > 8958 We also know that: Rule : If two number contain the same number of digits, we compare them by their left most digits. If the left most digits are also the same, we compare them by their next digits to the right and so on. Example 2: Which is smaller 76451 or 88475? Solution: 76451 has 7 ten thousands 88475 has 8 ten-thousands But we know that 7 ten-thousands are less than 8 ten thousands. Therefore, 76451 in smallerthan 88475 or 76451 < 88475 Example3: Which is greater 85439 or 85654? Solution: 85439 has 8 ten-thousands and 5 thousands, 85654 also has 8 ten-thousands and 5 thousands. Since both the numbers have same digits at the ten-thousands and thousands places, so we compare the digits at the hundreds places. 85439 hasthedigit4 atthe hundreds place 85654 has thedigit 6 atthe hundreds place Since 6 is greater than 4. .•. 85654 is greater than 85439 or85654 > 85439 ASCENDING-DESCENDING ORDER Ascending order means the increasing order. While writing the given group of numbers in the ascending order, we first-write the smallest number and then the next greater number. Like this we keep on writing the next greater number and lastly, we write the greatest number. Descending order means the decreasing order. While writing the given group of numbers in descending order, we first write the greatest number and then the next smaller number. Like this we keep on writing the next smaller number and lastly, we write the smallest number. Example 4: Arrange the following numbers in ascending order 18735,18389,27505,2967, 539. Solution: Here the smallest number is 539. The next number greater than 539 is 2967. The other number greater than 2967 in orderare 18389,18735 and 27505. Therefore, the given numbers when arranged in ascending order are: 539, 2967, 18389,18735,27505. Examples: Arrange the following numbers in descending order using symbols: 6047, 36505,1 712, 28284, 35602. Solution: Here the greatest number is 36505 the next number smaller than 35602. The other number less than 35602 in order are 28284, 6047 and 1 712. Therefore, the given numbers when arranged in descending order are : 36505 > 35602 > 28284 > 6047 >1712. FORMATION OF GREATEST AND SMALLEST NUMBERS Now, we know how to form the greatest and the smallest number of 3 digits with the given digits. We will adopt the same procedure in case of numbers of 4 or 5 digits. We adopt the procedure below. Case 1: When the digits are not repeated. For the greatest number of 4 digits write the greatest digit out of the given digits in the thousands place, the next smaller digit in the hundreds place next smaller digit in the tens place and the smallest digit in the ones place. For Example: If the given digits are 8, 9,2 and 6, then the greatest number of 4 digits is 9862. For the greatest number of 5 digits, write the greatest digit in the ten-thousands place nextsmallerdigit in the thousands place and soon. For Example: If the given digits are 6,8,9, 2 and 3 then the greatest number of 5 digits is 98632. For the smallest number of 4 digits, write the smallest digit out of the given digits in the thousands place, the next greater digit in the hundreds place, still greater digit in the tens place and the greatest digit in the ones place. ![](Sum up math-4_files/Sum20up20math-4-16.jpg) Get Set Go With Sum Up Mathematics-4 For Example: If the given digits are 6, 4, 2 and 8, then the smallest number of 4 digits is 2468. For the smallest number of 5 digits, write the smallest digit in the ten-thousands place, next greater digit in the thousands place and so on. For Example : If the given digits are 8, 6, 4, 2 and 3, then the smallest number of 5 digits is 23468. Note, when the given digits are 7 1 2 0 and 3 then the smallest number of 5 digits is 10237. 01237 is actually 1237, which is a4 digit number. Example6: Write the greatest and the smallest 4-digit number with the digits 4, 8, 3 and 6 (digits not to be repeated). Solution: The greatest 4-digit number = 8643 The smallest 4-digit number = 3468 - Example 7: Write the greatest and smallest 5-digit numbers with the digits 7, 6, 4, 8 and 0 (digits not to be repeated) Solution: The greatest 5-digit number = 87640 The smallest 5-digit number = 40678 Case 2: When the digits are repeated. For the greatest 4-digit or 5-digit number, write the smallest digit at the ones place, with the next greater digit at the tens place and so on. Till all the digits are used. Repeated the greatest digit at the remaining places. For Example: If the given digits are 3, 2, 9 then the greatest number of 4-digits is 9932. The greatest number of 5-digits is 99932. For the smallest 4-digit or 5-digit numbers, write the greatest digit at the ones place, write the nextsmallerdigitatthetens place and soon. Till all thedigitsare used. Repeatthe smallest atthe remaining places. For Example: If the given digits are 3, 7,6, then the smallest 4-digit number is 3367. The smallest 5-digit numbers is 33367 Example8: - •J Write the greatest and the smallest 4-digit number using all the digits 8,2,4. ![](Sum up math-4_files/Sum20up20math-4-17.jpg)Solution: The greatest 4-digit number = 8842 The smallest 4-digit number = 2248 Example 9: Write the greatest and the smallest 5-digit numbers by using all the digits 4,0,6, 7. Solution: The greatest 5-digit number = 77640 The smallest 5-digit number = 40067 ###### J. EXERCISE 5 f '10 Put > or < or = in the blanks to make the sentences true : (a) 2532 829 (b) 888 8880 (c) 6420 4602 (d) 78041 7781 (e) 65236 80686 (f) 28080 28808 (g) 40421 Forty thousand four hundred twenty one (h) 38482 30000 + 8000 + 400 + 80 + 2 (i) 27503 Twenty seven thousand five hundred three 2\. Find the greatest and the least numbers in each group of numbers (a) 24202 24220 22402 22204 (b) 80808 80088 88008 88800 (c) 25008 25800 25000 25080 (d) 51766 51667 51776 51676 - 3\. Rearrange the following numbers in ascending order: - (a) 20600, 26200, 3048, 844, 6072 - (b) 4400, 40044, 6602, 985, 360 - (c) 7001, 244, 18036, 44232, 45602 - (d) 80808, 88008, 80088, 80008, 88000 ![](Sum up math-4_files/Sum20up20math-4-18.jpg) - 4\. Rearrange the following number in descending order: - (a) 24612, 8887, 1 7612, 27612, 4041 - (b) 14212, 884, 1780, 22002, 2 7416 - (c) 1 7616, 15412, 38244, 60203, 44072 - (d) 8808, 88088, 80888, 88808, 88008 - 5\. Say which of the following groups of numbers are arranged in descending or ascendingorder: - (a) 2400, 24001, 25601, 52000, 52500 - (b) 1011, 11101, 21212, 23007, 27119 - (c) 25221, 25000, 25817, 19282, 17021, 1421 - (d) 22001, 22208, 18097, 1 5612, 12028, 841 7 - 6\. Write the greatest and smallest 4-digit numbers using al I the digits from the following: - [(a) 8, 3, 4, 2 (b) 5, 7,2,4](#bookmark58) - [(c) 9, 5, 1,8 (d) 3, 1,8,6](#bookmark59) - 7\. Write the greatest and smallest 5-digit numbers using al I the digits from the following: - [(a) 4, 2, 1,5, 8 (b) 8, 3, 9,2, 5](#bookmark60) - [(c) 6, 4, 8, 0, 2 (d) 2, 5, 0,7, 3](#bookmark61) - 8\. Write the greatest and smallest 4-digit numbers using all the digits (repetition allowed) from the following: - (a) 3,6,5 (b) 1,4,0 (c) 2,5 - 9\. Write the greatest and the smallest 5-digit number using all the digits (repetition allowed) from the following: - (a) 2, 6, 5, 7 (b) 4, 0, 3, 5 (c) 5,0,2 - 10\. Change the positions of the digits, if necessary, to get the smallest 5-digit number: - (a) 12 765 (b) 6443 7 - (c) 20564 (d) 40206 11\. Change the position of the digits, if necessary to get the greatest 5-digit number: (a) 61342 (b) 43484 (c) 8405 3 (d) 60402 Get Set Go With Sum Up Mathematics-4 ![](Sum up math-4_files/Sum20up20math-4-19.jpg) - 12\. Write the greatest 4-digit number using : - (a) only one digit - (b) all different digits - (c) all different digits but 3 in hundreds place - 13\. Write the smallest 5-digit number using: - (a) all different digits - (b) 2 different digits - (c) only two different digits with 3 in the ten-thousands place. - (d) 3 different digits with 6 in tens place. - (e) 3 different digits with 4 in the thousands place and 1 in the tens place. - 14\. Write all possible 3-digit number using each of the digits 3, 9Z 6 (only once) and then arrange them in ascending order. - 15\. Write all possible 3-digit numbers using each ofthe digits 4,0, 3 (only once) and them arrange them in descending order: - 16\. Which has greater value: - (a) 43968 one-rupee coins or forty three thousand six hundred ninety eight one-rupee notes? - (b) 86752 one-rupee notes or eight-thousand six hundred seventy five-ten rupee notes? ![](Sum up math-4_files/Sum20up20math-4-20.jpg) ![](Sum up math-4_files/Sum20up20math-4-21.jpg) Roman NvmeRcib ![](Sum up math-4_files/Sum20up20math-4-22.jpg) We have already learnt the method of writing numbers up to ten thousand. We used ten numerals i.e 0, 1,2, 3, 4, 5, 6, 7, 8 and 9 for writing these numbers. These numerals were first used by Hindus and the by Arabians. So there numerals are called Hindu Arabic numerals. These numerals are now used all over the world and are thus called international numerals. In India people speak different regional languages and so use different regional numerals for writing numbers. For example, the numeral used for writing the number four in Hindi (Devnagri) island in Urdu it is written asT . ROMAN NUMERALS Romans used other symbols for writing numbers. They used only seven basic symbols. They are I, V, X, L, C, D and M. Their respective values are given in the following 1 5 10 50 100 500 1000 At present, we shall learn the use of only first three symbols i.e. I, V and X. With the help of these three symbols we can write numbers upto thirty nine. According to the convention the compound symbols are formed by the rules given below: - (a) Repetations of I and X means addition, e.g. II =1+1=2 III = 1 + 1 + 1 = 3 XX = 10+10 = 20 XXX = 10+10 + 10 = 30 Note : I and X can be repeated at the most three times. V is never repeated. - (b) If a smaller number is written to the right of a larger one, then smaller is added to the largere.g. VI = 5+ 1=6, XII = 10 + 1 + 1 = 12, XV=10 + 5 = 15 - (c) If I is written to the left of V or X, it is subtracted e.g. IV = 5-1 = 4, IX = 10-1 = 9 Note : V is never written to the left of X. I is written only once to the left of V and X. - (d) For numbers between 10 and 40, we first write the number in groups of tens and -^ ones and then write the Roman Numeral e.g. 22 = 10 + 10 + 2 = XXII, 39 = 10 + 10 + 10 + 9 = XXXIX Get Set Go With Sum Up Mathematics-4 Write the Hindu-Arabic numerals for the following : (a) IX (b) XVI (d) XIV (e) XXXV Solution : (c) XIX (f) XXXVII - (a) IX = 9 - (c) XIX = 10 + 9 = 19 - (e) XXXV = 30 + 5 = 35 (b) XVI = 10 + 6 = 16 (d) XIV= 10 + 4= 14 (f) XXXVII = 30 + 7 = 37 Example 2 : Write the following in Roman Numerals. (a) 7 (b) 15 (e) 21 (f) 17 Solution : (c) 28 (d) 32 (g) 23 (h) 24 (a) 7 = VII (b) 15 = 10 + 5 = XV (c) 28 = 10 + 10 + 8 = XXVIII (d) 32 = 10+10 + 10 + 2 = XXXII (e) 21 = 10 + 10 + 1 = XXI (g) 23 = 10 + 10 + 3 = XXIII (f) 17= 10+7 = XVII (h) 24 = 10 + 10 + 4 = XXIV Example 3: Correctthe following by changingthe place of one matchsticks only. ![](Sum up math-4_files/Sum20up20math-4-23.jpg)Example 1 : ![](Sum up math-4_files/Sum20up20math-4-24.jpg) ![](Sum up math-4_files/Sum20up20math-4-25.jpg) ![](Sum up math-4_files/Sum20up20math-4-26.jpg) ![](Sum up math-4_files/Sum20up20math-4-27.jpg) Solution : ![](Sum up math-4_files/Sum20up20math-4-28.jpg) ![](Sum up math-4_files/Sum20up20math-4-29.jpg) ![](Sum up math-4_files/Sum20up20math-4-30.jpg) ![](Sum up math-4_files/Sum20up20math-4-31.jpg) ![](Sum up math-4_files/Sum20up20math-4-32.jpg) ![](Sum up math-4_files/Sum20up20math-4-33.jpg) ### XV Note : There may be more than one solution. ###### Q. EXERCISE 6 g 1\. Write the Hindu-Arabic numerals for the following Roman numerals : (a) (e) VII (b) XII XXV (f) XXXI (c) XXVII (g) XVIII (d) (h) XXXVI XXIII 2\. Fill in the boxes by using >,< or = to make a correct sentence : (a) VIII Ol5 (b >) xix O21 (c) XXIV 019 (d) XXIX O 29 (e ) XXXV O 23 (f) XXXI O 21 3\. Read and match the time on the following watches: ![](Sum up math-4_files/Sum20up20math-4-34.jpg) (d) ![](Sum up math-4_files/Sum20up20math-4-35.jpg) - 1\. 8 p.m. - 2\. 5 p.m. - 3\. 9 p.m. - 4\. 3 p.m. Join the correct numerals by arrow : (a) XXVI (i) 22 (b) XXII (ii) 34 (c) XXXIV (iii) 19 (d) XIX (iv) 26 ![](Sum up math-4_files/Sum20up20math-4-36.jpg)4\. Write the following in Roman numerals : ![](Sum up math-4_files/Sum20up20math-4-37.jpg) (a) 2 (b) 11 (c) 13 (d) 26 (e) 32 (f) 34 (g) 39 (h) 37 Which of the following are correct statements : (a) IXX = 19 (b) VX = 5 (c) XXIX = 29 (d) XXXIV = 34 (e) XXIV = 24 (f) XIIV=17 (g) VW = 15 (h) IIV = 3 - 7\. Using two matchsticks, we can make the following Roman numerals: ### II V X - (a) Make as many Roman numerals as possible by using - (i) 3 matchsticks (ii) 5 matchsticks - (b) How many matchsticks will be needed to write the following in Roman numerals? - (i) 29 (ii) 33 (iii) 18 (iv) 36 - 8\. Correct the following by changing the place of one matchsticks only in each equation: ![](Sum up math-4_files/Sum20up20math-4-38.jpg) ![](Sum up math-4_files/Sum20up20math-4-39.jpg) Previously, we have learnt the addition of 3-digit and 4-digit numbers (without carrying) and the addition of 3-digit numbers with carrying in this chapter, we shall learn the addition of 5-digit numbers (without carrying) and the addition 4-digit or 5-digit numbers with carrying or regrouping. The result obtained after addition is called sum. ADDITION WITHOUT CARRYING We know the method of addition of two or three 4-digit numbers without carrying. In the same way we add number of 5-digits. - Example 1: Add 16465 and 62302 Solution: We write the given number in columns and add. ![](Sum up math-4_files/Sum20up20math-4-40.jpg)![](Sum up math-4_files/Sum20up20math-4-41.jpg)Start with ones, then move to tens, go to hundreds, then reach thousands and lastly go one step further-add ten-thousands. .-. 16465 + 62302 = 78767 ADDITION WITH CARRYING (REGROUPING) We have learnt the addition of 3-digit numbers (with carrying). Same rule will apply foradding4-digitand 5-digit numbers. - Example 2: Add 4576 and 3855 ![](Sum up math-4_files/Sum20up20math-4-42.jpg)Solution : Putting numbers in the column. ![](Sum up math-4_files/Sum20up20math-4-43.jpg) Explanation: Adding ones 6 + 5 = 11 = 1 T + 1 ones Carried to tens 4........................................1 — Addingtens 1+7 + 5 =13 Remember to regroup 10 ones - 1 ten 10 tens - 1 hundred 10 hundred - 1 thousand 10 thousands - 1T-thousand = 1 H + 4 tens Carried to hundreds ■\*................................1 Adding hundreds 1+5 + 8 = 14 = 1 TH + 3 hundreds Carried to thousands ◄........... Addingthousands 1+4 + 3 = 8 thousands .-.4576 + 3855 = 8431 - Example 3: Add together: 38456 and 32475 Solution: Putting numbers in column form and adding: T-ThTh H T O [o00](#bookmark82) [3 8 4 56](#bookmark83) [+ 3 2 4 75](#bookmark84) [7 0 9 31](#bookmark85) ![](Sum up math-4_files/Sum20up20math-4-44.jpg) Explanation^ Adding ones 6 + 5 = 11 ones = 1 T + 1 ones Carried tötens « Addingtens 1+5 + 7 = 13 tens = 1 H + 3 tens Carried to hundreds < Adding hundreds Addingthousands 1 + 4 + 4 = 9 hundreds 8 + 2 = 10 thousands = 1 T-th + 0 thousands Carried to T-thousands + ■ AddingT-thousands 1+3 + 3 = 7T-thousands .-. 38456 + 32475 = 70931 - Example 4 : Add together 34652, 52483 and 5815. Write the sum in words. Solution : Putting numbers in column form and adding: [o o oo](#bookmark88) [3 4 6 52](#bookmark89) [+ 5 2 4 83](#bookmark90) [+ 5 815](#bookmark91) [9 2 9 50](#bookmark92) .-. 34652 + 52483 + 5815 = 92950 92950 = Ninety two thousand nine hundred fifty. U- EXERCISE 7 ^------------- - 1\. Add : [(¡) T-Th Th H TO](#bookmark93) [2 5 0 22](#bookmark94) [+ 2 2 9 67](#bookmark95) [(¡¡) T-Th Th H TO](#bookmark96) [3 6 7 28](#bookmark97) [+ 4 3 0 61](#bookmark98) [(¡¡¡) 4 5 6 30](#bookmark99) [+20149](#bookmark100) [(iv) 5 0 8 29](#bookmark101) [+ 4 3 0 61](#bookmark102) [(v) 3 4 0 56](#bookmark103) [+ 3 2 9 31](#bookmark104) [+ 12 012](#bookmark105) (vi) 2 \+ 1 3 0 4 5 16 2 1 [+ 4 2 32](#bookmark106) (vii) Th H T O (viii) Th H T O (¡x) Th H T O 4198 5734 6308 \+ 2964 +1879 +2943 (x) 5 3 9 7 (xi) 4 3 6 4 (xii) 6 8 3 5 \+ 2823 +2698 +1784 (xiii) 2 4 7 3 (xiv) 3 0 6 8 (xv) 8 5 9 4 \+ 6189 +2052 + 687 (xvi) 6 8 7 4 (xvii) 6 5 2 9 (xviii) 8 8 9 4 \+ 7639 +4688 +3456 (xix) 5 8 1 5 (xx) 4 3 0 9 (xxi) 16 8 1 \+ 723 +2982 +6352 \+ 2541 +2543 +2281 (xxviii) 4 6 2 5 9 (xxix) 4 5 4 6 7 + 1 8 8 3 2 + 6 6 9 3 + 2 4 1 7 5 (xxx) 2 7 4 9 5 (xxxi) 2 3 4 6 9 + 1 8 9 3 9 + 5 3 6 0 8 + 2 4 4 7 5 + 2 4 7 9 2 ![](Sum up math-4_files/Sum20up20math-4-45.jpg) (xxii) T-Th 5 Th 3 H 7 T 7 o 5 + 2 1 8 2 9 (xxiv) 8 5 8 5 3 + 2 5 6 9 8 (xxvi) 5 4 8 0 9 + 4 6 7 8 6 (xxiii) T-Th 2 Th 5 H 6 T 2 o 9 \+ 2 7 9 9 5 (xxv) 2 4 6 9 7 \+ 5 7 0 2 8 (xxvii) 2 3 8 7 6 \+ 6 3 9 8 5 [(xxxü) 3 4 6 82](#bookmark107) [+ 2 8 3 33](#bookmark108) [+ 3 6 2 28](#bookmark109) 2\. Write in columns and add : (a) 5439 + 273 (b) (d) 3 7829 + 4567 (e) 3\. Add and write the sum in words : (a) 5608 + 1719 + 318 (b) 4808 + 2696 (c) 3003 + 884 + 426 49739 + 2648 (f) 48769 + 19873 53937 + 18078 + 697 WORD PROBLEMS The concept of addition is used in many daily life situations. We should read the problem and find outwhat isto bedonethen solve it. Let us considerthe following examples: - Example 1: A factory produced 2545 bulbs on Monday and 2869 on Tuesday. How many bulbs are produced altogether in two days? Write the number sentence and the solution sentence. Solution: o o o [Bulbs produced on Monday = 2 54 5](#bookmark114) [Bulbs produced on Tuesday = + 2 86 9](#bookmark115) [Bulbs produced in two days = 5 414](#bookmark116) NumberSentence: 2545 + 2869 = 5414 Solution sentence: 5414 bulbs are produced in 2 days. - Example 2: Boy scouts sold 13874 stickers. Girl guides sold 29239 stickers. How many stickers did they sell? Write the solution sentence. Solution: o o o [Stickers sold by scouts = 1 38 7 4](#bookmark117) [Stickers sold by guides = + 2 92 3 9](#bookmark118) [Total stickers sold = 4 3113](#bookmark119) Solution sentence: They sold 43113 stickers. ![](Sum up math-4_files/Sum20up20math-4-46.jpg) ![](Sum up math-4_files/Sum20up20math-4-47.jpg) ###### . EXERCISE 8 - 1\. There are 4089 bags of wheat and 2236 bags of sugar in a store. Find the total number of bags in the store. Write the number of sentence and the solution sentence. - 2\. A factory produced 5385 cakes on Sunday and 3897 cakes on Tuesday. How many cakes were produced in two days? - 3\. A shopkeeper bought 4583 nuts and 2836 bolts. How many pieces did he buy in all? Write the numbers sentence and solution sentence. - 4\. There are 3786 men, 2983 women and 3508 children in a village. What is the total population ofthis village ? - 5\. There are 2872 cows, 3428 buffaloes and 1283 other cattle in a village. How many total cattle are in that village? - 6\. In an election Abdul got 3825 votes and Vimal got 1309 votes more than Abdul. How many votes did Vimal get? How many votes did both of them get altogether? - 7\. A postman delivered 28753 letters in January and 12391 letters in February. How many letters did he deliver in two months? - 8\. Kumar has 12539 stamps and Rita has 34818 stamps in their albums. How many stamps do they have altogether? - 9\. Reena subtracted 23789 from a number. The remainder was 9805. What was the number she started with? Write the number sentence. - 10\. Neha lost a diamond ring. Her husband bought has another diamond ring that cost 5896 more than the previous one. If the cost of the old ring was 3429, find the cost of the new ring. Write the number sentence and the solution sentence. - 11\. The male population of a village is 830 more than the female population. Find the male population and the total population if the females population is 23512. - 12\. The cost of a scooter is 5685 more than the cost of a T.V. If the cost of the T.V. is 22643, find thetotal cost of scooter and T.V. - 13\. The number of person who visited a zoo in January, February and March 2008 was 12332, 28407 and 25116 respectively. How many persons visited the zoo in three months? - 14\. A milk booth sold 25802, 22729 and 29083 liters milk in the last quarter of 2008. How much total milkare sold in the lastquarter? - 15\. Two ropes are 52381 metres and 5912 metres long respectively. Find the total length of these ropes. Write the number of sentence. - 16\. A school library has 25035 books in English, 48509 books in Hindi and 12999 books in other languages. How many books are there in the library? Write the solution sentence. - 17\. Rajesh spent 68935 during the year on food and clothing. He paid 24840 as rent forthe house in thatyear. He saved 5350. How much did he earn duringtheyear? ESTIMATING THE SUM We have learnt in standard III the method of roundingoff a numbertothe nearest tens or hundreds. It the same way, to round off a number to the nearest thousands or ten-thousands, we consider the number at the hundreds place or thousands place respectively and move up or move down. \-- - Example 1: Round off each ofthe fol lowing to the nearest (a) thousands (b) ten-thousands. - (a) 13880 (b) 25318 Solution: - (a) 13880 is rounded off to the nearest thousand as 14000. 13880 is rounded off to the nearest ten-thousands as 10000. - (b) 25318 is rounded off to the nearest ten-thousands as 25000. 25318 is rounded off to the nearest ten thousands as 30000. - Example 2: Kunal bought a shirt for 482 and a trouser for 947. Estimate the cost he has to pay to the shopkeeper and then compare with the actual cost. Solution: [Estimated cost of shirt =500](#bookmark124) [Estimated cost of trouser =900](#bookmark125) Total estimated cost = (500 + 900) [=1400](#bookmark126) Actual cost = (482 + 947) [=1429](#bookmark127) Estimated cost is very close to the actual cost. - 1\. Round off to the nearest thousands: (a) 8312 (b) 12605 Round off to the nearest ten-thousands: (a) 23809 (b) 78114 - 3\. Find the actual estimated sum by rounding off to the nearest thousands: Actual Estimated - (a) 3 2 8 1 \+ 4 9 3 0 Actual (b) 18 3 12 \+ 24109 Estimated - 4\. Find the actual and estimated sum by rounding off to the nearest: Actual Estimated Actual Estimated - (a) 7 8 5 1 5 (b) 3 2 9 7 8 \+ 13290 +35103 - 5\. Abhay spent 2310 on shoes and 1872 on books. Estimate the total cost he has to pay. - 6\. Rohan bought the fol lowing: An old car = 71819 A new scooter = 22010 Estimate the total cost = FRAMING WORD PROBLEM OR STORY WRITING We have learnt the method of framing word problem when a number sentence is given. Different word problems can be framed for a single number sentence. We take up an example : For the number sentence 7380 + 7638 = ? We can frame following word problems : - (a) A milk booth sold 4380 litres milk on Monday and 7638 litres on Tuesday. How much milk was sold in two days? - (b) A shop has 4380 pairs of gents shoes and 7638 pairs of ladies shoes. How many pairs of shoes are in the shop? - (c) There are 4380 girls and 7638 boys in a school. What is the total strength of the school? ###### J. EXERCISE 10 ^------------ - 1\. Frame a word problem (write a story) of your own for each of the following : - (a) 86 + 78 = ? (b) 512 + 689 = ? (c) 1849 + 7439 = ? (d) 21715 + 49486 = ? ![](Sum up math-4_files/Sum20up20math-4-48.jpg) ![](Sum up math-4_files/Sum20up20math-4-49.jpg) In standard III, we have learnt the subtraction of the 3-digit and 4-digit number (without borrowing) and the subtraction of 3-digit numbers (with borrowing). In this chapter, we shall learn the subtraction of 5-digit numbers and (without borrowing) the subtraction of 4-digit numbers ordecomposing. SUBTRACTION WITHOUT BORROWING We know the method of subtraction of 4-digit numbers without borrowing (decomposing). The same method is applied when we subtract numbers of 5-digits. Example 1: Subtract 25632 from 48756 and write the number sentence. Solution: Putting the digits of given numbers in columnsand subtracting: T-thTh H T O - 4 8 7 5 6 - \- 2 5 6 3 2 2 3 12 4 Number sentence 48756 — 25632 = 23124 Note - In a subtraction question, the number from which we subtract the other number is called minuend, the number which is subtracted is called subtrahend and the result which we get after subtraction is called difference. In the above example 48756 is minuend, 25632 is subtrahend and 23124 is difference. ###### . EXERCISE 11 B - 1\. Subtract: - (a) T-Th Th H T O [8 6 5 68](#bookmark140) [- 6 3 0 22](#bookmark141) - (b) T-Th Th H T O [8 8 8 88](#bookmark142) [- 6 6 8 35](#bookmark143) - (C) T-Th Th H T O [6 8 6 49](#bookmark144) [- 4 5 3 25](#bookmark145) ![](Sum up math-4_files/Sum20up20math-4-50.jpg)(d) T-Th Th H T O (e) T-Th Th H T O (f) T-Th Th H T O 98756 62738 89035 -87632 -40417 -34021 (g) 7 5 9 7 2 (h) 8 4 8 6 5 (i) 3 7 5 6 2 -45720 -10731 -36340 - 2\. Write in columns form and find the difference : - (a) 38726 -27305 (b) 49389 - 37108 (c) 57985 - 14281 88528 - 35203 - (d) 86844 -42310 (e) 88088 -44044 (f) - 3\. Find the difference when : - (a) Subtrahend = 28246; minuend = 58268 - (b) Minuend = 86525; subtrahend = 43112 - 4\. Fill in the blanks : - [(a) 8 7 6 5 3 (b) 4 58](#bookmark146) 6 5 2 2 - [- 13 0 -0](#bookmark147) [6 3 23](#bookmark148) SUBTRACTION WITH BORROWING (DECOMPOSING) We have learnt the subtraction of 3-digit numbers (with borrowing). Same rule will apply for subtracting 4-digit and 5-digit numbers. Let us recall decomposing. - 1 ten =10 ones - 1 hundred = 10 tens - 1 thousand = 10 hundreds - 1 T-thousand = 10 thousands - Example 1: Decompose and fill in the blanks: - (a) 8 hundreds + 7tens = 7 hundreds + tens - (b) 6 hundreds + 2 tens = 5 thousands + hundreds + 12 tens - (c) 9 thousand + 3 tens = 8 thousands + hundreds + 12 tens + ones ![](Sum up math-4_files/Sum20up20math-4-51.jpg)Solution: - (a) 8 hundreds + 7tens = 7 hundreds + 10tens + 7tens = 7 hundreds + 17 tens - (b) 6 thousands + 2 tens = 5 thousands + 10 hundreds + 2 tens = 5 thousands + 9 hundreds + 12 tens - (c) 9 thousands + 3 tens = 8 thousands + 10 hundreds + 3 tens = 8 thousands + 9 hundreds + 13tens = 8 thousands + 9 hundreds + 12 tens + 10 ones. - Example 2: Subtract: - (a) 36 thousands from 68 thousands. - (b) 45 hundreds from 8 thousands. - (c) 7 thousands 9 hundreds from 9 thousands. Solution: - (a) 68 thousands - \- 36 thousands 32 thousands - (b) 8 thousands = 80 hundreds - \- 45 hundreds = - 45 hundreds 35 hundreds - (c) 9 thousands - 7 thousand 9 hundreds = 8 thousands 10 hundreds - 7 thousands 9 hundreds = 1 thousand 1 hundred. - Example 3: Subtract 3678 from 8163 Solution: Putting numbers in column form. ![](Sum up math-4_files/Sum20up20math-4-52.jpg)Subtract ones 8 > 3, Borrow 1 ten ten + 3 ones = 1 3 ones 13-8 = 5 ones ![](Sum up math-4_files/Sum20up20math-4-53.jpg)Subtract tens 7>5Z borrow 1 hundred 1 hundred + 5 ten = 15 tens 15-7 = 8 tens ![](Sum up math-4_files/Sum20up20math-4-54.jpg) G=-- Th H T O To 15 7 X X 13 6 3 \- 3 6 7 8 4 8 5 Subtract hundreds, 6>0, Borrow 1 thousand, 1 thousand + 0 hundreds = 10 hundreds 10-6 = 4 hundreds /. 8163 - 3678 = 4485 Th H T O 10 15 7 //13 8 1 6 3 — 3 6 7 8 0 4 4 8 5) Subtract thousands 7-3 = 4 thousands - Example 4: Find the difference between 9423 and 6734 Solution: Write the greater of the two numbers on the top and then subtract the other number from it. Th H T O 13 11 8 % X 13 9 4 2 3 \- 6 7 3 4\* 2 6 8 9 Since addition and subtraction are related, you can add to check your answer [\* 6 7 34](#bookmark151) [>+ 2 6 89](#bookmark152) [9 4 23](#bookmark153) Examples: Subtract 67039 from 92403 Solution: Afterwritingthedigitsofthegiven numbers in columnsand subtracting. T-ThTh H T O - 8 12 3 9 13 >------After decomposing - 9 2 4 0 3 - \- 6 7 0 3 9 2 5 3 6 4 ![](Sum up math-4_files/Sum20up20math-4-55.jpg) ###### EXERCISE 12 J - 1\. Subtract: (a) (b) (c) 39 thousands from 47 thousands. 49 tens from 5 hundreds. 63 hundreds from 16 thousands. G=-- (d) 14 hundred 6 tens from 3 thousands. (e) 3 thousands 15 hundreds from 12 thousands. 2\. Subtract: (a) 9 8 6 4 \- 2 4 2 0 (b) 8 8 6 4 (c) 6 5 8 5 -4412 -5124 (d) 7 8 6 5 \- 6 5 8 9 (e) 6 8 3 2 (f) 5 8 2 4 -2825 -4643 (g) 8 8 3 0 \- 5 3 4 6 (h) 8 5 2 3 (i) 8 5 3 4 -1529 -2983 (j) 8 6 18 4 \- 2 7 8 4 8 (k) 8 6 5 2 4 (I) 6 5 4 8 3 -68792 -48539 (m) 8 8 6 3 8 \- 3 8 9 4 9 (n) 8 7 4 0 5 (o) 8 6 0 0 1 -69568 - 8396 3\. Write in column and subtract : (a) 8846 - 3429 (b) (d) 60038 - 52 78 (e) 7208 - 3838 (c) 9000- 1234 63028 - 1 7938 (f) 90500 - 65342 Find the difference between : (a) 8810 and 3425 (b) (c) 6 2 3 (d) \- 1 3 8 213 6 7 and 76001 8 5 0 (e) 9 4 3 2 2 8 4 - 5 6 1 6 7 1 6 6 3 6 WORD PROBLEMS - Example 1: Mary made 9326 candles for Christmas festival. She sold 6836 candles and used the remaining candles to decorate the Christmas tree at home. How many candles did she use? Write the solution sentence. Z" ![](Sum up math-4_files/Sum20up20math-4-56.jpg)Solution : Candles made = 9326 Candles = 6836 Remaining candles = 2490 Solution sentences : She used 2490 candles to decorate the tree. ADDITION AND SUBTRACTION - Example 2: Solve 6834 - 1142 + 624-3211 Solution: Here some numbers have ' + ' sign or no sign (first number only) before them and there are some which have'-' sign before them. 1\. Th H T O [6 8 34](#bookmark160) [+ 6 24](#bookmark161) [7 4 58](#bookmark162) 2. Th H T O 114 2 \+ 3211 4 3 5 3 3. Th H T O 7 4 5 8 \- 4 3 5 3 3 10 5 Adding numbers with ' +' sign or no sign before them Adding numbers with '-' sign before them Now subtract the second sum from the first sum /. 6834-1142 + 624-3211 = 3105. Note : If there is no sign before the first number, its sign is always taken as plus. - Example 3 : A factory produced 12306 and 20825 scooter parts in two months. It was noticed that 8729 parts were defective. How many parts were not defective? Solution : Parts produced in first month Parts produced in second month = [Total parts produced=](#bookmark168) [Tota I pa rts p rod u ced=](#bookmark169) [Defective parts=](#bookmark170) [Parts not defective=](#bookmark171) = 12306 \+ 20825 Add here 33131 33131 \- 8729 Just subtract 24402 ###### J. EXERCISE 13 ^------------ - 1\. Ramesh had 8845 in his bank account. If he with draw 4535 for buying a carpet. How much money was left in his account? - 2\. Ajay is a good cricket player. He requires 185 more runs to score a total of 4846 runs. How many runs has he scored so far? Write the number sentence. - 3\. There are 3 540 seats in a cinema hall. One day 1948 persons saw the movie. How many seats remained vacant? - 4\. There are 5125 students in a school. If the number of boys is 3809, find the number of girls. Write the solution sentence. - 5\. The sum oftwo numbers is48385. Ifoneofthem is 3843 7, find the other. - 6\. Seema added 11 780 to a number. She got the sum as 18035. What was the number she started with? - 7\. A factory produced 13285 T.V sets in April and 20302 T.V sets in may find the increase in the number of T.V sets. - 8\. 43742 persons came to see a football match on Sunday 27936 persons came on Monday. How many more persons visited on Sunday ? Write the number sentence. - 9\. Deepika bought a motorcycle for 40000 and a scooter for 28560. How much did she pay more for the motor cycle. - 10\. Solve the following: - (a) 4523-2312 + 684 (b) 52485-12857-32242 - 11\. Rohit collected 20815 stamps, 936 were from U.S.A and 18390 from India. How many are from other countries? - 12\. Rohan has 29815 oranges. He sold 11435 on Monday and 9806 on Tuesday. How many oranges does he have now? - 13\. From 88015m long wire, two pieces measuring 37362 m and 22826 m wire cut off. Find the length ofthe remaining wire. - 14\. The population of a town in 78415. If 40215 are men, 24245 are women and the remaining are children, find the number of children. ![](Sum up math-4_files/Sum20up20math-4-57.jpg)ESTIMATE THE DIFFERENCE We have learnt estimation in addition. Applying the same rule, we estimate the difference. - Example 1: Find the actual and estimated difference of 34424 and 16756 by rounding of the nearest thousands. Solution : Actual 3 4 4 2 4 - 1 6 7 5 6 1 7 6 6 8 Estimated [3 4 0 00](#bookmark174) [- 1 7 0 00](#bookmark175) [1 7 0 00](#bookmark176) - Example 2: A fruit-seller has 38210 bananas. Out of these he sold 21799 bananas. Estimate the unsold bananas. Solution: Estimatingto ten thousands Total bananas = 40000 Bananas sold out = 20000 Bananas unsold = 20,000 FORMATION OF WORD PROBLEM (STORY WRITING) As in case of formation of word problems on addition, we can form different word problems for each number sentence. For example: Forthe number sentence 48915 - 36100 = ? Some of the word problems are : - (a) A fruit-seller has 48915 fruits in his shop. It 36100 are only bananas, how many are otherfruits? - (b) A carpenter has 48915 nails. He used 36100 nail in making some desks. How many nails are left? - (c) The population ofavillage is 4891 5. Ifthe number of males is 36100, how many are females? ###### ... EXERCISE 14 - 1\. Find the actual and estimated difference by rounding off to the nearest thousands: (a) Actual 5 8 19 \- 3 2 9 5 Estimated (b) Actual 16 19 0 2 9 7 9 Estimated - 2\. Find the actual and estimated difference by rounding off to the nearest ten thousands: (a) Actual 3 9 5 0 6 \- 2 2 9 1 8 Estimated (b) Actual 7 3 0 1 2 \- 2 8 7 9 0 Estimated - 3\. Mona bought a computer for 25392 and a laptop for 30915. Estimate, how much did she pay more for laptop? - 4\. A bakery shop has an order to supply 6705 packets of biscuit. There are only 4920 packets in the shop. Estimate the number of packets, needed to complete the supply. - 5\. Write a word problem (a story) for each of the following: (a) 86510-79842 = ? (b) 10000-8975 = ? ![](Sum up math-4_files/Sum20up20math-4-58.jpg) ![](Sum up math-4_files/Sum20up20math-4-59.jpg) In standard lllz we have learnt the multiplication of a number by a one or two-digit number. We also learnt some properties of multiplication. In this class, we shall make use of the procedure learnt there and learn the multiplication of a number by a two or three-digitnumber. Let us first-review the properties of multiplication learnt earlier. - 1\. The product of two numbers does not change when we change the grouping of the numbers. For example, 25x13 = 13x25 - 2\. The product of three numbers does not change when we change the groupings of the numbers. For example, 20 x (8x4) = (20x8) x4 = (20x4) x 8 - 3\. The product of a number by 1 is the number itself. For example, 143x1 = 143 and 12535x1 = 12535 - 4\. The product of a number by zero is always zero. For example, 563x0 = Oand 6984x0 = 0 - 5\. The productof a number by thesum of two numbers is the same as the sum of the products of that number by the two numbers sepertaly. For example, 25x (45 + 38) = 25x45 + 25x38 Note : In a multiplication question, the numbers to be multiplied is called multiplicand; the number by which we multiply is called multiplier and the result of multiplication is called product. For example: (251 x ED x \[250\] Multiplicand Multiplier Product MULTIPLICATION BY 1-DIGIT NUMBER - (a) Column Method (without carrying or regrouping) We have already done in previous class the multiplication of a 3-digit or 4-digit number by a 1-digit number without carrying. In this class we shall multiply a 5-digit number by 1-digit number using the same method. - Example 1: Multiply 10201 by 4 and write the product in words. Solution: T-thTh H T O 1 0 2 0 1 x 4 4 0 8 0 4 /. 10201 x4 = 40804 Product = Forty thousand eight hundred four 2\. (a) 13041 x3 (b) 34214x2 (c) 10416x4 (d) 11011x5 (e) 11032x3 (e) 20131 x3 Multiply and write the product in words: (a) 12043 x 2 (b) 11202 x 4 (c) 21022 x 3 - (b) Column method (with carrying or regrouping) - Example 1: 2578 by 6 Solution: Th H T O © 2 5 7 8 x 6 8 Multiply ones 8x6 = 48 ones = 4 tens 8 ones carry 4 tens to tens column ![](Sum up math-4_files/Sum20up20math-4-60.jpg) Th H T O © © 2 5 7 8 x 6 6 8 Multiply tens 7x6 = 42 tens 42 tens + 4 tens = 46 tens = 4 hundreds 6 tens carry 4 hundreds to hundreds column Th H T O © © © 2 5 7 8 x 6 4 6 8 Th H T O © © © 2 5 7 8 x 6 15 4 6 8 Multiply hundreds 5x6 = 30 hundreds 30 hundreds + 4 hundreds = 34 hundreds = 3 thousand 4 hundred carry 3 thousands to thousands column Multiply thousands 2x6 = 12 thousands 12 thousands + 3 thousands = 15 thousands /. 2578 x 6 = 15468 Verification by standard multiplication algorithm. Write 2 5 78 in expanded form then multiply 2 5 78 by 6 Expanded form 2000 500 70 8 6 12000 3000 920 48 2578x8 = 12000 + 3000 + 420 + 48 = 15468 Example 2: Multiply 26742 by 3 Solution: © © O 2 6 7 4 2 x 3 8 0 2 2 6 26742 x 3 = 80226 ###### . EXERCISE 16 f 1\. 182 x 8 2\. 741 x 6 3\. 638 x 8 4\. 804 x 7 5\. 1138 x 7 6\. 1368 x 7 7\. 2245 x 4 8\. 1211 x 8 (9. 1207 x 8 10\. 1312 x 9 11\. 1332 x 6 12\. 1164 x 8 13\. 5221 x 5 14\. 4879 x 7 15\. 7236 x 4 16\. 6236 x 8 17\. 11612 x 5 18\. 12341 x 4 19\. 13365 x 5 20\. 10417 x 9 MULTIPLICATION BYTENS - (a) 4x 10 = 4x 1 tens = 4 tens =40 (b) 4x20 = 4x2 tens = 8 tens =80 (c) 4x30 = 4x3tens = 12tens =120 (d) 4x80 = 4x8 tens = 32 tens = 320 MULTIPLICATION BY HUNDRED (a) 3 x 100 = 3 x 1 hundreds = 3 hundreds = 300 (b) 3x400 = 3 x4 hundreds = 12 hundreds = 1200 (c) 3x500 = 3x5 hundreds = 15 hundreds = 1500 (d) 3 x 700 = 3x7 hundreds = 21 hundreds = 2100 Example 1: Multiply. (a) 4 by 60 (b) 45 by 40 (c) 210x40 Solution • 6 0 4 5 2 1 0 (a) 4x60 = 240 x 4 x 4 0 x 4 0 (b) 45x40 = 1800 (2 4 0J (1 8 0 O) 8 4 0 0) (c) 210x40 = 8400 - Example 2: Multiply. - (a) 4 by 300 (b) 215 by 400 (c) 80 by 600 ® [2 1 56 0 0](#bookmark190) [x 4 0 0x 8 0](#bookmark191) [860004800](#bookmark192) Solution: 3 0 0 - (a) 4x300 = 4x3 hundreds x 4 = 12 hundreds = 1200 „ ~ 12 0 0 - (b) 215x400 = 86000 Multiply 1\. (a) 4x2 (b) 4x20 (c) 4x200 2\. (a) 10x5 (b) 10x50 (c) 10x500 3\. (a) 13x4 (b) 13x40 (c) 13x400 4\. (a) 16x7 (b) 16x70 (c) 16 x 700 5\. (a) 18x6 (b) 18x60 (c) 18 x 600 6\. (a) 25x3 (b) 25x30 (c) 25x300 7\. Rohan has 95 hu ndred-rupee notes. How much money does he have? 8\. There are 186 mangoes in a box. How many mangoes will be there in 300 boxes? 9\. 845 pencils can be packed in a box. I have to pack pencils in 80 boxes. How many penci Is do need to pack? - 10\. Manormahas 135 fifty-rupee notes in her purse. How much money is in her purse? - 11\. Ranjan got 85 hundred-rupee notes from the bank. How much money did he get from the bank? - 12\. Ramu bought a motorcycle and gave 95 hundred rupee notes and 135 fifty-rupee notes. How much did the motorcycle cost him? MULTIPLICATION BY 2-DIGIT NUMBER - Example 1: Multiply 283 by 35 ![](Sum up math-4_files/Sum20up20math-4-61.jpg)Solution : In practice it is arranged as follows: 283 = 200 + 80 + 3 and 35 = 30 + 5 We use standard multiplication algorithm 200 80 3 6000 2400 90 30 1000 400 15 5 Sum of partial products = 6000+1000 + 2400 + 400 + 90+15 [2 83](#bookmark197) [x 35](#bookmark198) [14 15 <-- 283 x5](#bookmark199) [8 4 9 0 <--- 283 x30](#bookmark200) [9 9 0 5 <--- 283 x35](#bookmark201) = 9905 283x35 = 9905 - Example 2: Multiply 2015 by 47 and write the number names of the product. Solution: 47 = 40 + 7 - 2 0 15 [x 47](#bookmark202) [14 105](#bookmark203) - [8 0 6 00](#bookmark204) - [9 4 7 05](#bookmark205) /. 2015x47 = 94705 Number name- Ninety fourthousand seven hundred five. LAB ACTIVITY We can find the product of two numbers by lattice multiplication algorithm in mathmatics lab as follows: Let us find 2015x47 Take a white chart paper and prepare a box write 2015 on the top and 47 on the side as shown: Multiply 5 by 4 and write the product 20 under the column headed by 5. Similarly, multiply 1 by 4, 0 by 4 and 2 by 4 and write the products under respective columns. ![](Sum up math-4_files/Sum20up20math-4-62.png) ![](Sum up math-4_files/Sum20up20math-4-63.jpg) ![](Sum up math-4_files/Sum20up20math-4-64.jpg) ![](Sum up math-4_files/Sum20up20math-4-65.jpg)Multiply ###### EXERCISE 18 a 1\. 85x45 4\. 381x34 7\. 415x55 - 10\. 411 x42 - 13\. 2201 x37 16\. 6516x15 - 19\. 2041 x57 - 2\. 69x65 5\. 462x42 8\. 281x78 11\. 717x25 14\. 4792x19 17\. 3423x23 20\. 1217x32 - 3\. 118x38 - 6\. 817x38 - 9\. 785x27 12\. 1135x22 15\. 3117x23 18\. 3839x17 MULTIPLICATION BY 3-DIGIT NUMBER Example 1 : Multiply 56 by 234 Solution : 234 = 200 + 30 + 4 5 6 x 2 3 4 2 2 4 + 56 x 4 56 x 4 56 x 30 56 x 200 1 6 8 0 + 1 1 2 0 0< 13104\* 56 x 234 = 13104 - Example 2: Multiply 226 by 220 Solution: 2 2 6 x 2 2 0 [4 5 2 0 «----226 x20](#bookmark220) [4 5 2 0 0 <----226 x200](#bookmark221) [4 9 7 2 0<---226 x220](#bookmark222) /. 226 x 220 = 49720 - Example 3: Multiply 634 by 134 Solution: 6 3 4 x 1 3 4 [2 5 36](#bookmark223) - [1 9 0 20](#bookmark224) - [6 3 4 00](#bookmark225) - [8 4 9 56](#bookmark226) /. 634x134 = 84956 - Example 4: 4x68x125 Solution: 4x68x125 = 68x125x4 = 68x500 = 34000 ![](Sum up math-4_files/Sum20up20math-4-66.jpg) ![](Sum up math-4_files/Sum20up20math-4-67.jpg) Note : In the above example we have changed the grouping to make the task of multiplication easier. ![](Sum up math-4_files/Sum20up20math-4-68.jpg) ###### . EXERCISE 19 Multiply 1\. 35x140 - 4\. 334x130 7\. 367x135 10\. 144x507 13\. 362x242 16\. 260x225 19\. 71x4x125 2\. 47x301 - 5\. 352x250 8\. 238x227 11\. 447x147 14\. 341x107 17\. 383x237 20\. 4x89x25 3\. 89x313 - 6\. 203x455 - 9\. 321 x242 12\. 403x174 15\. 585x131 18\. 563x147 21\. 4x325x50 WORD PROBLEMS ON MULTIPLICATION - Example 1: A box contains 381 apples. Find the 4 number of apples in 187 such boxes. Solution: - [3 81](#bookmark233) [x 1 87](#bookmark234) - [2 6 67](#bookmark235) - [3 0 4 80](#bookmark236) - [3 8 100](#bookmark237) - [7 1 2 47](#bookmark238) Total number of apples = 71247. - Example 2: A box containing 285 mangoes. Find the number of mangoes in 215 such boxes. Solution: 2 8 5 x 2 1 5 14 2 5 2 8 5 0 5 7 0 0 0 Total mangoes = 61275. 6 12 7 5 ###### J. EXERCISE 20 ^------------ - 1\. A box contains 247 mangoes. Find the number of mangoes in 345 such boxes. - 2\. A bus can carry 45 passengers in one trip. How many passengers will it carry in 215 trips? - 3\. 65 passengerscan sit in a bus. How many passengers will sit in 515 buses? - 4\. The water capacity of a tank is 1635 litres. Find the total capacity of such 67 tanks. - 5\. In a village there are 1225 farmers. Each farmers has 259 sheep. How many sheep are there in all? - 6\. Rajesh reads 15 pagesofa book in one hour. How many pages are there in that book if he reads 5 hours in a day and finishes the book in 25 days? - 7\. A weaving machine makes 1062m cloth in a day. How much cloth will it make in 55 days? - 8\. The monthlyfee of a student is 465. There are 163 students in aclass. How much fee is collected from that class? - 9\. There are 135 troops of soldiers in a cantonment. If there are 515 soldiers in each troop. Find the total number of soldiers in the cantonment. - 10\. The price of a book is 212. Find the price of such 245 books. - 11\. A shopkeeper has 735 tins of ghee in stock. If each tin contains 17 kg ghee, find the total weight of ghee in stock. - 12\. Fill in the blanks: - [(a) 8 7 2 (b)9 6 3](#bookmark245) [Xx 6 □](#bookmark246) 7 [□□□□0□□□□0](#bookmark247) 7 □□ 7 6 6 □□□ 4 Example 1 : A shopkeeper put 46 pencils in a packet. Estimate by rounding off to the nearest tens the numberof pencilsthe will put in 175 boxes. Find the actual numberof pencilsalso. x- Solution : Actual 1 7 5 x 4 6 10 5 0 7 0 0 0 8 0 5 0 Estimated 1 8 0 x 5 0 9 0 0 0 FORMATION OF WORD PROBLEMS (STORY WRITING) We have learnt earlier that different stories can be narrated for a given number sentences. A few stories for the number sentence 154x95 = ?are: - (a) A packet contains 154 balloons. How many balloons these are in the 95 packets? - (b) Rashmi earns 154 a day. She worked for 95 days. Find the amount she earned. - (c) A packet contains 95 pencils. How many pencils will be needed for 154 such packets? ###### J. EXERCISE 21 ^------------ 1\. Find the actual and estimated product by rounding off to the nearest tens. (a) Actual 2 3 8 x 6 8 Estimated (b) Actual Estimated 1111 x 7 7 - 2\. Roshni saves 45 in a day. How much money will she save in 165 days. Estimate by rounding off to the nearest tens. Actual Estimated 1 6 5 x 4 5 ![](Sum up math-4_files/Sum20up20math-4-69.jpg) - 3\. Sohan runs 2418 m everyday. Estimate by rounding off to the nearest tens, the distance he runs in the month of march 2009: Actual 2 4 18 x 3 1 Estimated 2 4 2 0 x 4 0 - 4\. Write a story for each of the following: (a) 288x50 = ? (b) 1318x15 = ? (c) 6865x7 = ? - 5\. Complete the story for each number sentence: - (a) 619x20 = ? A basket contains 619 mangoes. How many ? - (b) 2240x22 = ? A truck carries 2240 kg wheat How much ? ![](Sum up math-4_files/Sum20up20math-4-70.jpg) We have already learnt in standard III the division of 3 and 4-digit number by 1-digit number. In this class, we shall learn the division of a 5-digit number by a 1-digit number and the division of 3,4 and 5-digit number by a 2-digit number. Let us recall the relation between multiplication and division. We know that every multiplication fact with two distinct factors gives us two distinct division facts. For example 6x4= 24, gives us 24 = 4 = 6 and 24 4- 6 = 4 We also know that if the multiplication fact has both similar factors, then we get only one division fact. For example, 5x5 = 25 gives us 25 = 5 = 5 Note : 0x8 = 0 gives us 0 = 8 = 0 (only), since division by 0 is not possible. ###### J. EXERCISE 22 ^------------ - 1\. For each of the following, write al I possible division facts: - (a) 6x7 = 42 (b) 34x2 = 68 (c) 99x3 = 297 - (d) 4x4 = 16 (e) 7x7 = 49 (f) 12x12 = 144 - 2\. Write the multiplication factforeach ofthe followingdivision facts: - (a) 35 = 5 = 7 (b) 55 = 11=5 (c) 72 = 9 = 8 DIVISION BY 1-DIGIT NUMBER We know that in a division sum, the number we divide is called dividend, the number by which we divide is called divisor and the answer is called quotient. If any number is leftover, then the number left is called remainder. For example, Divisor------> 3 4 <---- 4JTT7- \- 1 2 1 7 1 6 1 Quotient Dividend ##### G~ The above defined four terms are connected as below: Dividend = Quotientx Divisor+Remainder When the divisor is 1, the quotient will be the same number as the dividend. For example: 6 = 1 = 6, 18 = 1 = 18, 315 = 1= 315 When the divisor is the same number as the dividend, the quotient will be 1. Forexample: 8 = 8 = 1,35 = 35 = 1, 99 = 99 = 1 When the dividend is 0 and the divisor is any number (other than zero), the quotient will beO. Forexample: 0 = 9 = 0, 0 = 47 = 0, 0 = 55 = 0 Note : The students are advised to revise the multiplication tables learnt earlier. While dividing a 5-digit number by 1-digit number, the process adopted will be the same as used in previous class. Example: 75747 by 8. Check your answer. Solution: 9 4 6 8 8J 7 5 7 4 7 \- 7 2 3 7 3 2 5 4 -48 6 7 -64 3 Quotient = 9468, Remainder = 3 We know that Dividend = Quotient x Divisor + Remainder 9 4 6 8 <----- Quotient X g <\_\_\_\_\_ Divisor 7 5 7 4 4 \+ 3 ^----- Remainder ![](Sum up math-4_files/Sum20up20math-4-71.jpg)###### (J. EXERCISE 23 s 1\. Find the quotient and remainder: (a) 6284-7 (b) 8114-5 (c) 9500-8 (d) 27908-5 (e) 25713-7 (f) 85317-3 (g) 71825-8 (h) 92518-7 (i) 53409-7 (j) 21315-4 (k) 73514-6 (I) 14005-9 2\. Divide and check yo ur answer: (a) 23813 by 5 (b) 17518 by 9 (c) 55129 by 8 DIVISION BY 10 AND 100 Let us find the method of dividing a given number by 10,100 etc. and establish some rule to get quotient and remainder. - Example 1 : Divide: (a) 7800by 10and Solution : - (a) 7 8 0 ioJtToT - \- 7 0 8 0 8 0 0 Quotient = 780 Remainder = 0 - (b) 87835 by 10. - (b) 8 7 8 3 ioj8"78”Tir - \- 8 0 7 8 7 0 8 3 8 0 3 5 3 0 5 Quotient = 8783 Remainder = 5 From the above example, we conclude : When we divide a number by 10, the digit at the units place in the dividend is the remainder and the number formed by the digits after removing the units digit in the dividend is the quotient. \-- To find the quotient and remainder when a number is divided by 100, let us study the following patterns. We know that: - (a) 18 x 100 = 1800 .'. 1800 4-100 gives us quotient 18 and remainder 00 (simply 0). - (b) 30 x 100 + 95 = 3000 + 95 = 3095 /. 3095 4-100 gives us quotient 30 and remainder 95 - (c) 17x100+11 = 1700+11 = 1711 /. 1711 4-100 gives us quotient 17 and remainder 11 from the above pattern, we conclude: When we divide a number by 100, the number formed by the remaining digits is the quotient. ###### g. EXERCISE 24 “^------------- Find the quotient and remainder: - 1\. 708 -10 - 4\. 2817 - 10 5. - 7\. 17527 - 10 8. - 10\. 700 - 100 11. - 13\. 3700 - 100 14. 2\. 611 - 10 3. 717 - 10 4817 - 10 6. 7011 - 10 18087 - 10 9. 85555 - 10 909 - 100 12. 717 - 100 5101 - 100 15. 8056 - 100 16\. 21617 - 100 17. 34004 - 100 DIVISION BY 2-DIGIT NUMBER We explains the division of a given number by 2-digit number by solving a few example. - Example 1: Divide 525 by 15 Solution: Stepl : The divisor consists of two digits. The two digits on the extreme left of the dividend make a number 52 which is greater than 15. We know that 15x4 = 60 and 15x3=45. But 60 is greater than 52 and 45 is less than 52. 3 5 - 15 goes into 52, three times. 15^)5 2 Write 3 in the quotient (above 2) and subtract45 from 52. ----- Step 2: Bring down 5 and write on the right side of the remainder, thus ^ makingthe new dividend 75. ---- Step3: Divide 75 by 15. 15 goes into 75, 5 times. Write 5 on the right side of 3 in the quotient and subtract 75 from 75. The remainder is 0. /. Quotient = 35, Remainder = 0 - Example 2: Divide 1107 by 17 [Solution:](#bookmark46) [Step 1 : The divisor consists of two digits. On the extreme left of the 17) 1 10 7 dividend is 11 which is less than 1 7. So we take 3-digit number which is -10 2 110and divide by 17.8 7](#bookmark278) [We know that:](#bookmark279) 17x7 = 119and17x6 = 102 119>1 Wand 102 <110 .'. 17 goes into 102, six times Write 6 in the quotient (above) and subtract 102 from 110. Step2 : Bring down 7 and write on the right side of the remainder, thus making the newdividend 87. Step 3: Divide 87 by 1 7. Now 17x6 = 102and17x5 = 85 But102787and85<87 /. 17 goes in 87, three times Write 5 on the right side of 6 in the quotient and subtract 85 from 87. The remainder is 2. Quotient = 65, Remainder = 2. Note : We know that Dividend = quotientxdivisor-i-remainder By using the above relation, we can check the answer 2 as below. quotientxdivisor+remainder = 65 x 1 7 + 2 = 1105 + 2 = 1107 = dividend Note : For practical purpose, we do not use arrows to bring down the digits from the dividend. Example3: Divide 87021 by 63 and check your answer. Solution: 63 goes into 87onetime. Subtract 63 from 87 and write 1 in the quotient. Bring down 0 from the dividend. The new dividend becomes 240. 63 goes into 240 three time. Subtract 189 from 240 and write 3 on the right side of1 in the quotient. Bring down next digit 2 from the dividend and write on the right side of 51. The new dividend is 512. 63 goes in 512, eight times, write 8 on the right of 13 in the quotient and subtract 504 from 512. Bring down 1 from the dividend and the new dividend becomes 81,63 goes into 81 onetime. Write 1 on the right of 138 in the quotient and subtract 63 from 81. The remainder is 18. Quotient x divisor + remainder = 1381 x63 + 18 = 87003 + 18 = 87021 13 8 1 10)8 7 0 2 ’ - \- 6 3 I 2 4 0 - 1 8 9 v - 5 1 2 - 5 0 4 i 8 1 - 6 3 1 8 = dividend ###### J- EXERCISE 25 s Divide, find the quotient and the remainder : 1\. 1738 by 13 - 4\. 1387 by 11 - 7\. 8212 by 19 - 10\. 1992 by 17 13\. 18977by77 - 16\. 3 7485 by 63 - 2\. 907 by 17 - 5\. 2283 by 16 - 8\. 2672 by 12 11\. 2565by23 14\. 23773by63 17\. 67507by47 - 3\. 811 by 15 - 6\. 7618 by 16 - 9\. 18672 by 982 12\. 8007by37 - 15\. 52055 by 75 18\. 52166by66 ![](Sum up math-4_files/Sum20up20math-4-72.jpg)WORD PROBLEMS ON DIVISION Example 1: A packet contains 135 balloons. How many packet will be needed for 2025 balloons? Solution: Divide 2025 by 135 1 5 135)2 025 \- 1 3 5 6 7 5 6 7 5 0 /. 15 packets will be needed. Example 2: A farmer produced 27600 kg rice. How many bags will be buy to store the rice if one bag can hold 80 kg rice? Solution: Divide 2 7600 by 80 3 4 5 80)2 7 6 0 0 \- 2 4 0 3 6 0 \- 3 2 0 4 0 0 -400 0 .•. 345 bags will be purchased. - Example 3: 78 crates of Limca can be loaded in a truck will be required to load 1475 crates? How many crates will be left unloaded? -- Solution: To find the required numberoftrucks, wedivide 1475 by 78. 1 8 78JTTTT - 7 8 6 9 5 - 6 2 4 7 1 /. 18 trucks will be required and 71 creates will remain unloaded. - Example 4: What least number should be subtracted from 4320 so that the remainder is exactly divisible by 47? Solution: Divide 4320 by 47 and find the remainder. 9 1 47jm-o" - 4 2 3 9 0 4 7 4 3 Remainder 43 is to be subtracted from 4320. ###### (J. EXERCISE 26^------------- - 1\. There are equal number of students in each section in a school. In 26 sections there are 6162 students. Find the numberof students in each section. - 2\. A train had 21 compartments. If each compartment had an equal number of passengers and there were 1008 passengers in the train, find there number in each compartment. - 3\. The price of 28 copies is 1568. Find the price of one copy. - 4\. Thecostofl 5 motorcycle is 87675. Findthecostofonemotorcycle. - 5\. 35 trucks can carry 10920 kg rice. How much rice can be carried in 18 trucks? - 6\. 88 water tanks can hold 18832 litres water. Find the capacity of each tank. - 7\. What least number should be subtracted from 4825 so that the remainder is exactly divisible by 43? - 8\. 4418 oranges were divided equally among 36 persons. How many maximum number of oranges did each one get and how many remained undivided? - 9\. The wages of 17 labours is 1836. Find the wagesofa labour, ¡fall are paid equally. - 10\. There are 8496 stones in 18 heaps. Find the number of stones in one heap if each heap contains the same number of stones. - 11\. The product oftwo numbers is 3190. If one of them is 22 find the other. - 12\. 36 packets weight 2592 kg. Find theweightofone packet ¡fall are ofthe same weight. - 13\. Write the greatest number of six digits. Find the quotient and the remainder if it is divided by 28. - 14\. 12705 persons visited in the cinema hall in aweek. If same numberof persons visited everyday, how many did visit in a day? - 15\. There are equal number of students in each section in a school. In 28 sections there are 2352 students. Find the numberof students in each section. - 16\. 40 studentscan sit in a room. How many roomswill accommodate 560 students. - 17\. 60 water tanks, can hold 43080 litres water. Find the capacity of each tank. ESTIMATING THE QUOTIENT We estimate the quotient while dividing. It is useful when given number is divided by a2-digit number. - Example 1: Estimate the quotient. (a) 52-21 (b) 64 - 32 (c) 155-27 (d) 5 73 - 68 (e) 5 79 - 58 (f) 789 - 78 Solution: - [(a) 52-21 rounds offto 80-204](#bookmark291) [Tosolvethiswethinkof8-22j) 8](#bookmark292) [/. The estimated quotient is 4.](#bookmark293) #### G=-- - (b) 64^-32 rounds off to 60 ¿-30 To solve this we think of 6 4-3 /. The estimated quotient is 2 - (c) 155 4-2 7 round off to 160 4-30 Tosolvethis wethinkof 164-3 /. The estimated quotient is 5 - (d) 5 73 4-68 rounds off to 600 4-70 Tosolvethis wethinkof 604- 7 /. The estimated quotient is 8 - (e) 5 79 4-58 rounds off to 600 4-60 Tosolvethis wethinkof 604-6 /. The estimated quotient is1 0 - (f) 789 4-78 roundsoffto800 4-80 Tosolvethis wethinkof 804-8 The estimated quotient is 10 2\_ 3\) 6 \- 6 0 5 3\) 1 6 \- 1 5 1 8 Remainder 7\) 6 0 \- 5 6 4 is ignored while estimating the quotient 1 0 6)6 0 \- 6 0 0 1 0 8)8 0 \- 8 0 0 Note : Some times it is better to round off the dividend to tens. 789 rounded off to tens is 790 9 .-. 789 -78 rounds off to 790 4-80 8) 7 9 Tosolvethis,wethinkof79 4-8 ~ 7 2 7 The estimate quotient is 9, which is the same as the actual quotient. - Example 2: Estimate the quotient when 4831 is divided by 19. Solution: 4831 rounds off to 5000 to the nearest hundred 19 rounds off to 20 (to the nearest ten). /. 4831 4-19 rounds off to 5000 4-20 To solve this, wethinkof 5004-2 /. The estimated quotient is 250. 2 5 0 2J 5 0 0 ![](Sum up math-4_files/Sum20up20math-4-73.jpg) ![](Sum up math-4_files/Sum20up20math-4-74.jpg) STORY WRITING Here we shall write a story for the given number sentence. For example a few stories for the sentence 525 - 25 = ?are: - (a) The price of 25 books is 525. Find the price of one book. - (b) The wages of 25 labours is 525. Find the wage of a labour, if all are paid equally. - (c) There are equal number of students in each section in a school. In 25 section, there are 525 students. Find the number of students in each section. ![](Sum up math-4_files/Sum20up20math-4-75.jpg) ###### . EXERCISE 27 1\. Find the estimated quotient for the fol lowing: (a) 76-17 (b) 58-26 (c) 78-19 (d) 83-27 (e) 186-28 (f) 183-21 (g) 418-51 (h) 387-27 (i) 929-37 (j) 601 -29 (k) 598-32 (I) 641-78 (m) 6588-79 (n) 3837-61 (o) 6862-59 - 2\. Write a story for each ofthe fol lowing sentences: (a) 620-10 = ? (b) 4535-165 = ? (c) 51431-81=? ![](Sum up math-4_files/Sum20up20math-4-76.jpg) problems on Pour fundamental OpeRdtions ![](Sum up math-4_files/Sum20up20math-4-77.jpg) The four fundamental operations in mathematics are addition, subtraction, multiplication and division. Now we shall solve some problems which involve these operations. Before taking actual problems, let us study the fol lowing: - 1\. Before starting writing we sharpen our pencils - 2\. Before starting reading, we open our books. - 3\. After getting up in the morning, we go to the toilet, brush ourteeth, take bath and eat our breakfast. Can you change the order of operations and get the same result in the above statements? Similarly in mathematics when all the fundamental operations are given in a sum, the order of operations is as follows: First we do the operation of division, then multiplication and lastly addition and subtraction. Example 1: Simplify 2721 5-1181 7+19036-20718 Solution: We add separately the numbers having ( + ) sign before them the number having (-) sign before them. Then we subtract the second sum from the first sum. Step 1 : [2 7 2 15](#bookmark306) [+ 1 9 0 36](#bookmark307) [4 6 2 51](#bookmark308) Step 2 : 118 17 \+ 2 0 7 1 8 3 2 5 3 5 Step 3 : 4 6 2 5 1 \+ 3 2 5 3 5 13 7 16 Example 2: Simplify: 45-40-^20 Solution: 45-40-^20 = 45-2 (after dividing 40 by 20) = 43 (after subtracting) Example 3: Simplify: 115x12 + 1235 Solution: 115x12 + 1235 = 1380 + 1235 = 2615 Example 4: Simplify: 34x 12 75 1 5 + 78 7 Solution: 34x1275-15 + 787 = 34x85 + 787 = 2890 + 787 = 3677 Examples: Simplify: 8816-15120-35+ 5415 Solution: First we divide 15120 by 35 8816-15120-35 + 5415 = 8816-432 + 5415 = 14231-432 = 13799 (after multiplying 115 by 12) (after adding) (afterdividing 1275 by 15) (after multiplying 34 by 85) (after adding) 4 3 2 35JTTTT0 - 1 4 0 1 1 2 1 0 5 7 0 7 0 0 ###### J. EXERCISE 28 s Simplify: 1\. 35248-18335 + 24612-38615 - 3\. 39600-18702-32468 + 32615 - 5\. 615x11 +6415-6235 - 7\. 215x16-4 + 210 - 9\. 14212 + 630-42x2 - 11\. 515 + 210x66-33-401 - 2\. 38674 + 22468-18322-16844 - 4\. 680-440-10 - 6\. 3825-45 + 6832-6410 8\. 435x65-585-13 - 10\. 410 + 312x44-22-262 MENTAL PROBLEM 1\. 680divisibleby 10 ? 2\. What is 435x100? - 3\. What is 1800+ 3200? - 4\. What is the difference between 1400 and 700? - 5\. What is 3 9000-19000? - 6\. Isthesmallestnumberof5-digitsdivisibleby 100 ? - 7\. Fill in the blanks: - (a) 6 x (65 + 19) = 6 x 65 + - (b) 29 x (75-25) = 29 x 75 + - (c) (44 x 31) x 11 = 44 x 11 x - (d) 80 x 6 = 70 x 6 + x 6 - (e) (44 x 28) x 18 = 44 x (28 x ) - (f) 228 x 12 = 100 x +28 x 12 - (g) 0^45 = - (h) 2417 = 1 = - (¡) 48-48 = - 8\. Complete the sentences: - (a) Divisionfactsfor5x7 = 35are and. - (b) Division facts for 7x 7 = 49 is . - (c) Every multiplication fact with two distinct factors gives us two - (d) Dividend = quotientxdivisor+ . - (e) When 628 is divided by 10 the remainder will be ![](Sum up math-4_files/Sum20up20math-4-78.jpg) ![](Sum up math-4_files/Sum20up20math-4-79.jpg) FACTORS Let us considerthe number 35. We know that 35 = 7x5. Each of 7 and 5 is called factor of 35. Let us considerthe another number, say, 42. 42 = 1 x 42, 42 = 6 x 7 42 = 2 x 21, 42 = 3 x 14 (1,42), (2,21), (3,14), (6, 7) are all factors of 42. All factors of 42, when arranged in ascending order are: - 1,2, 3, 6, 7,14,21,42. Let us divide 42 by its factors e.g. 42 = 1 = 42, 42 = 2 = 21, 42 = 3 = 14 42 = 6 = 7, 42 = 7 = 6, 42 = 14 = 3 etc. Thus each factors divides the given number (with no remainder). Hence, A factor is an exact dividor of the number. Remember we can have more than two factors of a number. 48 = 2 x4x 6, so 2,4, 6 are factors of 42 105 = 3 x 5 x 7, so 3, 5, 7 are factors of 105 From above, we see that. A number is a factor of another number if on dividing the second number by the first numberthe remainder iszero. METHOD OF FINDING FACTORS We can find factors of a number by two methods-multiplication and division. Finding Factors Using Multiplication In this method, we try to find the numbers whose product is the given number. Let us fi nd the factors of 16 : 1,16 are factors of 16 •.• 2x8=16 ?. 2,8 are factors of 16 •\_• 4x4 =16 /. 4,4 are factors of 16 !\*^/ All factors of 16 are 1,2,4,8,16. Get Set Go With Sum Up Mathematics-4 ![](Sum up math-4_files/Sum20up20math-4-80.jpg) ![](Sum up math-4_files/Sum20up20math-4-81.jpg)Finding Factors Using Division In this method, we try to find a number which divides the given number without remainder. Let us try to find the factors of 18 by this method. . 16-1 =16 ?. 1,16 are factors of 16 \_ 16-2 =8 /. 2, 8 are factors of 16 16-4=4 /. 4,4 are factors of 16 All factor of 16 are 1,2,4, 8,16. PROPERTIES OF FACTORS Every number can be written as a product of 1 and the number itself. For example, 24 = 1 x24, 38 = 1 x 38, 45 = 1 x45, 107 = 1 x 107. Thus, 1 is a factor of every number and every number (other than zero) is a factor of it self. The number zero can be written as a product of 0 and any number, e.g., 0 = Ox 3,0 = 0x24,0 = 0x47, 0 = Ox 105, Thus, Every number is a factor of zero. Let us write al I the factor of 15 15 = 1x15,15 = 3x5 /. 1,3, 5,15 are al I factors of 15. Let us write al I the factors of 36 36 = 1 x36, 36 = 2x18,36 = 3x12,36 = 4x9,36 = 6x6 /. 1,2, 3,4,6,9,12,18, 36 are all factors of 36. From the above example we see that A factor of a number (other than zero) is either less than or equal to the number. What is the smallest factor of a number? 1 What is the greatest factor of a number? The number itself. Every number (exceptl) has at least two factors For example: Factors of 3 are 1 and 3 Factors of 8 are 1,2,4 and 8 Let us solve a few examples ![](Sum up math-4_files/Sum20up20math-4-82.jpg)Example 1: Is 7 a factor of 91 ? Solution: 1 3 7)9 1 \- 7 2 1 -2 1 0 Since 91 is exactly divisible by 7, therefore 7 is a factor of 91. Example 2: Is 7 a factor 92 ? Solution: 1 3 7)9 2 \- 7 2 2 2 1 1 Since there is a remainder when 92 isdivided by 7, so 7 is not a factor of 92. Example 3: Find all the factors of 36. Solution: 1 x 36 = 36, 2 x 18= 36 3 x 12 = 36, 4 x 9 = 36 /. All the factors of 36 are 1,2, 3,4, 9,12,18, 36. Example 4: Find the factors of 19. Solution: 19-1 = 19 There is no other number which divides 19 without a remainder. /. 1 and 19 are the only two factors of 19. ACTIVITY METHOD OF FINDING FACTORS Let us find the factors of 28. ^^^^^è^ 4k 4k Ik Ik Ik Ik Ik '\*^7 ’ '\*^7 ' ^27 ^&7 ' ^ ^ ' ^ Take 28 marbles and arrange then in the form a rectangle. One such arrangement is done for you. There are 4 rows of 7 marbles in each row. /. 4 and 7 are factors of 28 Similarly, you can arrange the marbles as follows: 2 rows of 14 marbles i n each row. 1 rowof 28 marbles in each row. The factors of 28 are: (1,28), (2,14), (4,7) ###### (g. EXERG1SE 29 - 1\. Is 7afactorof 847 ? - 2\. Is 13q factorof 143 ? - 3\. Is25afactorif 125 ? - 4\. Is 1 7afactorof2125 ? - 5\. Listali thèfactorsof 36. - 6\. Listali thèfactorsof48. - 7\. Find all thèfactorsof 124. - 8\. Find all thèfactorsof 140. - 9\. What is thè smallestfactorof 24? - 10\. Whatisthègreatestfactorof48? - 11\. Write for the fol lowing statement in true or false: - (a) 4 is a factor of 16 - (b) 4, 5, 8 is a factor of 40 - (c) 3 is a factor of 50 - (d) 0 is the smallest factor of 10 - (e) 1,2, 3, 5, 6 are factor of 18 - (f) 1 is a factor of every number - (g) 3 isafactorof 9 but9 is notdivisibleof9. ![](Sum up math-4_files/Sum20up20math-4-83.jpg) - 12\. A gardener wants to arrange 42 flowerpots in rows, each having same number of flowerpots. Find the different number of rows he can make. - 13\. Mohan has a collection of 28 stamps. He wants to paste them in the album in how many different rows, having same number of stamps. He can do that? - 14\. Monika has 60 beads. How many different number of necklaces she can make, using al I the beads, such that each necklace has the same number of beads? PRIME NUMBERS Let us find all the factors 2, 3, 5, 7,11,1 3. 2 = 1x2, 3=1x3, 5 = 1x5, 7=1x7, 11 =1x11, 13 = 1x13. Al I the factors of 2 are 1 and 2. Al I the factors of 3 are 1 and 3. All thefactorsof 5 are 1 and 5. Al I the factors of 7 are 1 and 7. Al I the factors of 11 are 1 and 11. Al I the factors of 13 are 1 and 13. From the above we see that each of the number 2, 3, 5, 7, 11 and 13 has only two factors, i.e. 1 and itself. These are prime numbers. A number greater than one (1) is a prime number if it has only two factors i.e. 1 and itself. Do You Know? A Russian mathematician named Goldbach said "Every even number greater than 2 can be expressed as the sum of two primes. For example: 4 = 2 + 2, 6 = 3 + 3 8 = 3 + 5, 16 = 5 + 11 ![](Sum up math-4_files/Sum20up20math-4-84.jpg)Let us see al I the factors of 4,6,8, 4=1x4, 4 = 2x2 All the factors of 4 are 1,2,4 6 = 1x6, 6=2x3 .-. All the factors of 6 are 1,2, 3, 6 8 = 1x8, 8 = 4x2 .-. All the factors of 8 are 1,2,4,8 Each of the numbers 4,6 and 8 has more than two factors. All are composite numbers. A composite number has more than two factors. Note : 1 is neither a prime number nor a composite number. Even Numbers - Numbers which aredivisibleby 2 are called even numbers. Example: 2,4, 6, 8,10,12 are even numbers. Note : 0 is an even number. Odd Number - Numbers that are not exactly divisible by 2 are called odd numbers. There will always be a remainder 1 when an odd number is divided by 2. For example, 1,3, 5, 7, 9,11 are odd numbers. Example: Separate the prime numbers and composite numbers from the numbers. 5,13,15 and 32. Solution: 5= 1 x5 .-. All the factors of 5 are 1 and 5 13 = 1x13 .-. All the factors of 13 are 1 and 13 15 = 1x15, 15 = 3x5 .-. Al I the factors of 15 are 1,3, 5 and 15 ![](Sum up math-4_files/Sum20up20math-4-85.jpg) 32 = 1 x32, 32 = 2x16, 32 = 4x8 .-. All the factors of 32 are 1,2,4,8,16 and 32. From above, the numbers having only two factors are 5 and 13. .-. The prime numbers are 5 and 13. The numbers having more than 2 factors are 1 5 and 32. .-. Composite numbers are 15 and 32. - Example 2: Write 30 as a sum of 2 prime numbers. Solution: 30 = 11 + 19 - Example 3: Find the sum and say whether it is even or odd. - (a) 3 + 3 = - (c) 4+7 = - (d) 5 + 10 = - (b) 3 + 5 = 8 even (d) 5 + 10 = 15 odd - (b) 3 + 5 = Solution: - (a) 3 + 3= 6 even - (c) 4 + 7 = 11 odd ###### {J. EXERCISE 30 ^-------- - 1\. Write all prime numbers less than 25. - 2\. Write all prime numbers between 60 and 100. - 3\. Write down all the composite numbers between 10 to 20. - 4\. Which of the following numbers are primes and which are composite? - 102, 104, 105, 106, 109, 112, - 113, 122, 128, 127, 132, 133. - 5\. Write two prime numbers whose difference is 8. - 6\. Write five numbers which are prime as well as odd. - 7\. Write two pairs of prime numbers which differ by 2. - 8\. Write 22 as a sum of two prime numbers. How many such pairs of prime number are possible? - 9\. Express the smallest prime number greater than each of the following numbers. - 3, 8, 25, 39, 55, 77, 84, 90. - 10\. Write the greatest prime number less than each of the following numbers. - 7, 15, 21, 48, 56, 69, 90, 100. - 11\. Find outtheeven and odd numberfrom following given numbers. - 24, 31, 43, 48, 62, 67, 3 79, 182 - 294, 498, 1043, 90926. - 12\. Write the smallest number that should be subtracted from an odd number to make it even. - 13\. Tell whether the given sum will beeven or odd without adding. (a) 42 + 84 (b) 41+72 (c) 123 + 345 (d) 782 + 5043 Common Factors - Common factor is a factor of 2 or more numbers. Let us take two numbers 20 and 10. We find the factors of 20 and 10. 20 = 1 x20, 10 = 1 x10, 20 = 2 x 10, 10 = 2x5 20 = 4x5 The factors of 20 are = 1 2 4 5 5 The factors of Ware = 1 2 The numbers 1,2, 5 in both the lists of factors. .-. The common factors of 20 and Ware 1,2, 5. T h e g reatest facto r i s 5. The common prime factor of 20 and 16 is 2. Now see the factors of 4 and 20 4 = 1x4, 20 = 1 x 20, The factors of 4 are 4 = 2x2 and 20 = 4 x 5 = 12 4 The factors of 20 are = 12 4 5 Here, the greatest prime factor is 5. ![](Sum up math-4_files/Sum20up20math-4-86.jpg) (J. EXERCISE 31 ^--------- List the common factors and the greatest common factor of the following: - 1\. 8,12 2. 12,16 3. 8,32 4. 7,13 - 5\. 18,21 6. 15,35 7. 10,14 8. 9,15 MULTIPLES Let us see 4x5. You know that 4x5 = 20 20 is called a multiple of 4. The multiples of 4 are 4, 8,12,16................ because4x 1 = 4, 4x2 = 8, 4x3 = 12, 4x4 = 16and soon The smallest multiple of a number is the number itself. Lab Activity We can see any multiple of a number in mathematics lab as follows: Let us see the 4th multiple of5. Take 5 drinking straws of equal length and paste them on a card board with fevistick and l5 as shown in the figure. ![](Sum up math-4_files/Sum20up20math-4-87.jpg) ![](Sum up math-4_files/Sum20up20math-4-88.jpg) Take 3 more straws and fix them horizontally with help of drawing pins. Label these straws as t1z t2, t3. Countthe number of drawing pins used They are 15 in numbers 5x3 = 15 .-. Thethird multipleof 5 is 15. - Example 1: Find the first 4 multiples of 5. Solution: 5x1=5 5x2 = 10 5x3 = 15 5x4 = 20 .-. The first four multiples of 5 are 5,10,15 and 20. - Example 2: Find the 7th multiple of 7. Solution: To find the 7th multipleof 7 we multiply it by 7. 7x7 = 49 - Example 3: - (a) Is 1 + 7 a multiple of 7? Solution: - (a) Divide 147 by 7 2 1 7)1 4 7 \- 1 4 7 7 0 3 3 - (b) Is23 ismultipleof4? Note: Every number is a multiple of 1. Every number is multiple of itself. 0 is multiple every number. .-. Since remainder isOso 147 isthe multipleof 7. - (b) 5\_\_\_\_\_\_ 4)2 3 - \- 1 4 3 Since remainder is notO. So 23 is not a multiple of 4. ![](Sum up math-4_files/Sum20up20math-4-89.jpg) ###### EXERCISE 32 Find the first three multiples of 4. Find thefirstfour multiples of 5. ![](Sum up math-4_files/Sum20up20math-4-90.jpg) - 3\. Find the first five multiples of 8. - 4\. Find the tenth multiple of 15. - 5\. Findthe8th multipleof 19. - 6\. Is 52 a muItiple of 4 ? - 7\. Is83amultipleof7? - 8\. Write whether the fol lowi ng statements is true or false: - (a) 1,2,4,6,8 are multiples of 2 - (b) 6, 9,12,18, 21 are multiples of 3 - (c) 8,12,16, 20,23 are multiples of 4 - 9\. Find the multiples of 5 which are greater than 25, but less than 40. COMMON MULTIPLES A number which is a multiple of 2 or more number is called a common multiple of these numbers. Let us seethe multiples of4 and 6 : The multiples of 4 are The multiples of 6 are 4 8 6 12 12 16 20 24 28 18 24 30 32 36 36 The number 12, 24, 36 etc. are present in both 4 and 6. .-. Common multiples of 4 and 6 are 12,24, 36 and.............. In all these common multiples 12 is the least multiple number. It means the least common multipleof4and 6 is 12. Examplel: Search few common multiples of 3 and 9 and also find their least common multiple. Solution: The multiplesof 3 are 3, 6, 9,12,15,18,21,24, 27etc. The multiplesof 9are9,18, 27, 36,45, 54, 63, 72, 81 etc. The common multiplesof 3 and 9 are 9,18,27............ The least common multiples of 3 and 9 = 9. - ###### B. EXERCISE 33 J - 1\. Round 0 the multiples of 2 and cross (x) the multiple of 3 in the following grid. Then list the smallest common multipleof2 and 3. [12345678910](#bookmark353) [11 12 13 14 15 16 17 1819 20](#bookmark354) [21 22 23 24 25 26 27 2829 30](#bookmark355) - 2\. Listthefirstfive multiplesof 9. - 3\. Find the multipleof 6 between 13 and 37. - 4\. Find the first four common multiples ofthefollowing: - (a) 2,3 (b) 3,4 (c) 5,4 (d) 6,4 - 5\. List the first three common multiples and also find the least common multiples of the following: - (a) 3,4 (b) 6,9 (c) 12,18 MENTAL PROBLEMS 1\. 4\. Is 1 a composite number? 2. Islapr The smallest prime number is .......... Find a pair of prime numbers whose difference is 1 ? Is 0 an even number? 6. Is 3 an c Find the factor of 16. 8\. Is 7 a factor of 51 ? Is29amultipleof4? Is 1 isamultipleofall numbers? 12\. Iseverynumbera multiple of itself? Is 1 the smallest multiple of a number? Write true orfalseforthe following statements: (a) (b) (c) (e) The least common multipleof2 and 3 is9? The least common multiples of 3 and 5 is 15? Is 12acommon multipleof4and8? (d) Is 1 an even number? (f) Is 18acommon multipleof6and 7 Is 3 an odd number? ( ![](Sum up math-4_files/Sum20up20math-4-91.jpg) io: Common Exaction ![](Sum up math-4_files/Sum20up20math-4-92.jpg) First revise what we have learned in previous class. Fraction of a Whole In the figures given below each is divided into equal number of parts. Some parts of each figure are coloured. The coloured part is represented by fraction which is given below. ![](Sum up math-4_files/Sum20up20math-4-93.jpg) ![](Sum up math-4_files/Sum20up20math-4-94.jpg) 1 2 shows that an object is divided into two equal parts and one part is taken. ■I shows that an object is divided into four equal partsand one part is taken. -^ shows that an object is divided into four equal part and three parts is taken. Fraction of a Collection ![](Sum up math-4_files/Sum20up20math-4-95.jpg) There are a collection of similar figures, given below. In each collection some figures are coloured. ![](Sum up math-4_files/Sum20up20math-4-96.jpg) A 3 5 7 ÿ show that one figure out of 3 similarfigures iscoloured. 3 5 4 7 shows that three figures out of 5 similar figures are coloured. show that four figures out of 7 similar figures are coloured. Note : Each fraction has two numbers. One number is written above and the other is below which is separated by line. Above the line the number is called numerator and below the line is called denominator. 3 —» numerator Example- 11 —\* denominator ![](Sum up math-4_files/Sum20up20math-4-97.jpg)2\. Fill in the blanks in the following sentence: - (a) —, is numerator, is denominator. □ 4 - (b) —, is numerator, is denominator. - (c) Tpp, is denominator, is numerator. Write the fraction to following given number. The first number indicates the numerator and second number indicates the denominator. (a) 4,7 (b) 7,9 (c) 8,11 (d) 5,16 Finding Objects Equal to Fractions - (a) To find one-half There are six toffees. Two friends want to divide these toffees equal ly. Each friend gets half of the total. How many does each of them get? Each friend gets 3 toffees. .-. — of6 = 3 - (b) To find one third. There are nine marbles. Those marbles are divided into 3 equal groups. Each part shows y . How many marbles are in each group? Each group has 3 marbles .-. y of9 = 3 - (c) To find one fourth There are 16 crayons Sahil wants to putthem equally in 4 boxes. Each box will have one fourth of the crayons. How many crayons will be there in each box? Each box wi 11 have 4 crayons. .-. y of 16 = 4. ![](Sum up math-4_files/Sum20up20math-4-98.jpg) To find y divide by 2. ![](Sum up math-4_files/Sum20up20math-4-99.jpg)divide by 3. ![](Sum up math-4_files/Sum20up20math-4-100.jpg) To find y divide by 4. (d) To find three fourths There are 12 strawberries. 3 Sonam use y th of these strawberries for making shake. She divides the strawberries into 4 equal parts and then takes 3 parts. — of 12 = 9 4 ![](Sum up math-4_files/Sum20up20math-4-101.jpg) #### ea\*a ea\*a 'of is converted into ' x ' sign - Example 1: 3 What is — of1 kilogram? Solution: 3 3 — of1 kilogram = —x 1000 gram = 750 gram - Example 2: If 1 kg mangoes costs 24, find the cost of: [13](#bookmark375) - (a) kg of mangoes (b) -^kg of mangoes Solution: Cost of 1 kg mangoes = 24 [11](#bookmark378) - (a) Cost ofkg mangoes = — x24 = 12. [33](#bookmark379) - (b) Cost of — kg mangoes = — x24 = 18. ###### Q. EXERCISE 35 v - 1\. In which ofthe fol lowing col lections one-fourth offigures are coloured? ![](Sum up math-4_files/Sum20up20math-4-102.jpg) ![](Sum up math-4_files/Sum20up20math-4-103.jpg) (c) ![](Sum up math-4_files/Sum20up20math-4-104.jpg) ![](Sum up math-4_files/Sum20up20math-4-105.jpg) ![](Sum up math-4_files/Sum20up20math-4-106.jpg) - 5\. If 1kg oranges costs of 42, how much will — kg cost? - 6\. If 1kg tomatoes costs 21, how much will y kg cost? 3 - 7\. If 1 kg capsicum costs 20, how much will — kg cost? - 8\. If 1 litre milk costs 28, how much will — litre cost? 3 - 9\. If 1 litre refined oil of costs 72, how much will — litrecost? ![](Sum up math-4_files/Sum20up20math-4-107.jpg) - (b) y of 1 litre 1 - (d) yof 1 m ![](Sum up math-4_files/Sum20up20math-4-108.jpg)Equivalent fractions (Renaming a Fraction) Each figure is divided into equal number of parts. ![](Sum up math-4_files/Sum20up20math-4-109.jpg)10 10 10 10 10 10 10 10 10 10 Study the upper figure and given the answer. 1 1 How many — will make — ? ![](Sum up math-4_files/Sum20up20math-4-110.jpg) • 1=2. "24 1 1 How many will make—? 5 A 2 “ 10 2 5 1 y and y are other names of the fraction y 2 = 4 = 10 These fractions are equivalent fractions. ![](Sum up math-4_files/Sum20up20math-4-111.jpg) 1 1 How many — will make — ? 2 1-2 5 “ 10 2 1 — is another name for — 1 2 5 “ 10 These fractions are equivalent fractions. 3 4 5 10o - ■ s — = — = — = — = — < Yes 15 2 3 4 5 10 ' Lab Activity We can find equivalent fractions to a given fraction in mathematics lab as follows: Let us see fractions equivalent to — . Take a rectangular piece of chart paper and fold it into two halves. Press the fold so that crease is formed as shown by dotted lines in the figure. Unfold the paper and colour one part. (m) ![](Sum up math-4_files/Sum20up20math-4-112.jpg) Fold the whole rectangular piece again to get 4 equal parts. Press the fold to get crease. Then unfold the paper. Each part shows 4 ' (n) ![](Sum up math-4_files/Sum20up20math-4-113.jpg) Coloured parts of fig (m) and fig (n) are equal = • "2 4 Similarly, by folding the rectangular piece once more, we will find that ![](Sum up math-4_files/Sum20up20math-4-114.jpg) ###### Q. EXERCISE 36 v 1\. Write 'Yes' ifthe fractions are equivalent and 'No' ifthe fraction are not equivalent. ![](Sum up math-4_files/Sum20up20math-4-115.jpg)Write two equivalent fractions for the shaded parts in each figure given below: ![](Sum up math-4_files/Sum20up20math-4-116.jpg) ![](Sum up math-4_files/Sum20up20math-4-117.jpg) ![](Sum up math-4_files/Sum20up20math-4-118.jpg) ![](Sum up math-4_files/Sum20up20math-4-119.jpg) 3\. Colourthefollowingtoshowequivalentfractions: ![](Sum up math-4_files/Sum20up20math-4-120.jpg) (c) ![](Sum up math-4_files/Sum20up20math-4-121.jpg)3 4 ![](Sum up math-4_files/Sum20up20math-4-122.jpg) 9 12 2 4 14 (d) To find a fraction equivalent to a given fraction. 12 5 In previous lesson you have seen that — = — = — 1 5 1x5 .5 5-5 1 \_\_\_\_\_\_\_\_\_\_ And \_\_= \_\_\_\_\_\_= \_ 2 10 2x5 1010-52 When you multiply or divide the numerator and denominator of a fraction by the same (non-zero) number, you get one equivalent fraction. Examplel: Write next two fractions equ ivalent to- (b) 5 6 Solution: (a) \] 1 x 2 3x2 2 6 ' 2 3 1 x 3 3x3 ##### (b) 4 6 5x2 6x2 12\. 12' 5 6 5x3 6x3 \_3\_ 9 15 18 Example2: Fill in the blanks: , . 5 9 (a) T=~ <b) = 7 Z J 3 Solution : 3\_ = 3j£2 = JL 5 5x3 15 (b) 15 25 15^53 25 5 5 ###### {J. EXERCISE 37 %•-- - 1\. Write a fraction equivalenttoeach ofthe following: (a) é b 49 (c) \_9\_ 27 - 2\. Write nexttwofractionsequivalenttoeach ofthefollowing: - a — b — c — d — 4 6 5 7 - 3\. Fill in the blanks: - (a) y = (b) W T = - 3 5 o - 4\. Fill in the blanks: W T= <» J = (C) T = Like and Unlike Fractions View the following groups of fractions. (a) 2 3 5 6 7' 7' 7' 7 11111 n 1111 3' 4' 6' 7' 8 C 9 5 6 T1 In the fraction of (a) group, the denominator of each fraction is same. This is called like fractions. In the fraction of (b) and (c) group, the denominators are different. This is called unlike fractions. UNIT FRACTIONS A fraction which have 1 asanumeratoriscalledaunitfraction. —, —are unitfraction. 3'7'9 Examplel: Which ofthe following groups of fractions are like fractions ? (a) 2 3 9 ' 9 ' ± 9 ' 9 ..1234 (b) 9' 7' 5' 6 Solution : (a) 2 3 9 ' 9 ' 5 6 -¿p -^-have the same denominators 9. These are like fractions. (b) 1 9 ' 2 3 4 —, —, —have different denominators. 7 3 0 These are unlike fractions. Example2 : 12 3 4 Write the next three like fractions -p, -p, “¿p ”9 Solution : । 1\*1 f \* 5 6 7 Next three I ike fractions are y y y 1\. Which ofthefollowingare groups of like fractions : (a) (d) 1 1 1 A 10'10'10'10 1111 (b) 2 ' 3 ' 6 ' 7 (e) 7' 2\_ 9' 2 7' 2 5' 2\_ 7' 7 4 7 4 (c) 8' 6 (f) 2 7 2 9 3 4 9 1 9 6 9 4 6 2 9 2\. Write the next three like fractions in the blanks: 1 2 (a) 6 6 1 2 (b) ÏTÏÎ (c) \_2\_ 12 \_3\_ 12 3\. Which ofthefollowingare unitfractions : 5 5 4 ' 2 z 11 ' ![](Sum up math-4_files/Sum20up20math-4-123.jpg)ORDER RELATION IN FRACTIONS You have learnt previous how to compare two whole numbers. While comparing two whole numbers you found out whether they were equal or unequal if unequal, then which is greater than the other. Previously, you have learnt that if two fractions are equal then the numerator and the denominator of one can be obtained by multiplying or dividing the numerator and the denominator of the other by the same number (other than zero). For example: -y and y are equal when you multiply the numerator and the denominator of — by 2. You get the fraction = \_6\_ 4 4x28 Unequal fraction can be divided into the followingtwo categories. - (a) Like Fractions (b) Unlike Fractions Now you can learn more about like fractions COMPARISON OF LIKE FRACTIONS [47](#bookmark415) Now compare two fraction y and y. \_\_\_\_\_\_ 4 7 ------ ------ [In the adjoining figures the fraction — and — have been ------- . ](#bookmark416) [9 9 \_\_\_](#bookmark417) [shown by coloured portions of two equal strips. ------- $ 9](#bookmark418) Clearly y > y or y y You also know that means, 7 parts have been taken out of 9 equal parts of an 4 object. And -77 means, 4 parts have been taken out of 9 equal parts of the same object, y Hence 7>4 A A A A 9 > 9 or 9 < 9 LAB ACTIVITY Compare y and 4 • Take 2 equal circle pieces ofa chart paper ![](Sum up math-4_files/Sum20up20math-4-124.jpg) Fold the paper into 2 halves and then into fourths. Press the folds to get creases. 1 Unfold the paper. Each part shows y colour as shown in figure (a). ![](Sum up math-4_files/Sum20up20math-4-125.jpg) ![](Sum up math-4_files/Sum20up20math-4-126.jpg) Fold the other piece of paper also in the same manner and colour 3 parts as shown in the figure (b). ![](Sum up math-4_files/Sum20up20math-4-127.jpg) Put figure (a) and over figure (b) 3 The coloured part of figure (a) is less than the coloured part of — figure (b) 1 3 Hence, Y T Hence, If the fractions are like you compare their numerators. Note : In two like fractions, the fraction with greater numerator is greater than the fraction with smaller numerator. - Example 1: Compare and write > or < into make correct. Solution : ![](Sum up math-4_files/Sum20up20math-4-128.png) ![](Sum up math-4_files/Sum20up20math-4-129.png) ![](Sum up math-4_files/Sum20up20math-4-130.png) ![](Sum up math-4_files/Sum20up20math-4-131.png) Example: Which fraction in each of the following pairs of fractions is greater ? 1 2 (a) A' 3 Solution : A A z A A A A (b) 7'7 (C) 11'11 (d) 13' 13 Comparing numerators, we get. (a) •.• 2 > >1, A y> y (b) v 5>2, y> y (c) ... 7 >5 . A > A (d) .. 11 > 7, . 11 > A •• 11 11 • •• 13 13 Example: Arrange the fol lowing fractions in - (a) Ascending order and (b) Descending order ![](Sum up math-4_files/Sum20up20math-4-132.jpg) A A A A 12' 12' 12' 12 ![](Sum up math-4_files/Sum20up20math-4-133.jpg)Solution: - 2, 5, 3, 7 when written in ascending order are 2, 3, 5, 7. - (a) The ascending order of fraction is: \_2\_ \_3\_ 5 7 12' 12' 12' 12 - (b) The descending order of fraction is: A A A A 12' 12' 12' 12 ###### J. EXERCISE 39 । ![](Sum up math-4_files/Sum20up20math-4-134.jpg)A A 12 12 ![](Sum up math-4_files/Sum20up20math-4-135.jpg) 2\. Find the greater fraction in the following: z x 2 7 2 8 , A <a> y- y (b> t (c) 13 17' \_£ 17 (d) 7 13 5 13 3 Find the smaller fraction in the following: (a) T'T (b) n' n (c) 3 24' 6 24 (d) 11 18 5 18 4\. Arrange the fol lowing fraction in ascending order : / x 1 7 4 /,x 9 2 3 / x i 3 \\ J 1 i 1 5 \_8\_ 4 U 18' 18' 18 13' 13' 13 21' 21' 21 5 Arrange the fol lowing fraction in descending order : 2 11 A A A 12 3 \_9\_ 7 ( } 9'9'9 1 7' 1 7' 1 7 ( } 11' 11' 11 6 Fill in the blanks by using >,< or = iAt A A zm A A zr\\ 7\_ 5 11 15 ( ) 8'8 b 11'11 12' 12 (O) 18 18 ADDITION OF LIKE FRACTIONS Let us see, the sum of two fractions anj- . ![](Sum up math-4_files/Sum20up20math-4-136.jpg) In the first figure a triangle is divided into 9 equal parts. [42](#bookmark431) First colour y ofthe figure and then -y ofthefigure. 6 9~ ' Total coloured part of the figure represents = £ \_2\_ = 4 + 2 = \_6\_ [9 9 99 ‘](#bookmark432) ![](Sum up math-4_files/Sum20up20math-4-137.jpg) ![](Sum up math-4_files/Sum20up20math-4-138.jpg) [23](#bookmark433) When we add — and — you get, \_£ 3 = 2 + 3 = 5 [12 12 1212‘](#bookmark434) Similarly, coloured part of the circle show : - 1 \_2\_ \_3\_ = 1+2 + 3 = \_6\_ 8 8 8 8 8 ’ To add two or more like fractions, add the numerators of the given fractions to get the numerator of the sum and the denominator remains unchanged. Examplel : 3 2 Add y and -y. Solution : A + A = 3 + 2 = 5 9 9 9 9 ![](Sum up math-4_files/Sum20up20math-4-139.jpg) Example2 : 5 6 Add —, and 9 29 • Solution : 5 6 9 \_ 5 + 6 + 9 20 29 29 29 29 29~ ###### J. EXERCISE <0 %• - 1\. Write a fraction for each coloured part and add : ![](Sum up math-4_files/Sum20up20math-4-140.jpg) ![](Sum up math-4_files/Sum20up20math-4-141.jpg) ![](Sum up math-4_files/Sum20up20math-4-142.jpg) 2\. Add : (c) (f) —— and —— 14 14 (a) (d) 4 10 \_8\_ 18 and2 , 7 and yy (b) (e) 6 IT \_8\_ 21 and , 9 and yy 5 11 , 4 and yy (g) 1 6 ' 2 j 1 TandT (h) \_2\_ 13' —and — 13 13 (i) 5 12 -And 12 12 (j) \_2\_ 8 ' A and A 8 8 (k) \_3\_ 25' -^-and -^- 25 25 (I) 5 17 ^-and — 17 17 SUBTRACTION OF FRACTIONS For example A cake is divided into 12 equal parts. Each part shows yy of 9 the whole cake. Anmol took 9 parts or yy of the whole and out of 6 these 9 parts he ate 6 parts or yy of the whole. Now he is left with 3 3 parts or yy of the whole cake. ![](Sum up math-4_files/Sum20up20math-4-143.jpg) Th — - — = 9 ~ 6 = A = ± US/ 12 12 12 12 4 A piece of cloth is divided into 7 equal parts. Each part 1 4 shows -y of the whole. A tailor took 4 parts or — of the 2 cloth and from this he makes a dress with 2 parts or — of the 4 Tailor had — ![](Sum up math-4_files/Sum20up20math-4-144.jpg) whole. 4 Thus, — = 4 ~ 2 \_ 2 7 7 7 2 7 To subtract a fraction from a like fraction subtract the smaller numerator from the greater numerator to get the difference of the numerators and the denominator remains unchanged. ![](Sum up math-4_files/Sum20up20math-4-145.jpg) Example! : ###### Subtract ^- ^ Solution : 9\_\_\_7\_= 9-7 = 2 15 15 15 15 ###### (g. EXERCISE 41 f Subtract : (a) \_2\_ 6 from 6 (b) 6 TT 9 from —— 11 (c) 6 , 10 —— from —— 12 12 (d) 8 18 from 4t I 8 (e) 7 17 r 11 from (f) 9 12 from —— 14 14 (g) 13 21 19 from y (h) \_2\_ 5 , 3 from —7 5 (i) 6 z 11 y from y (j) \_8\_ 15 , 13 from -771 5 (k) \_3\_ 9 r 7 from -7— 9 (1) 11 , 17 y from y WORD PROBLEM ON FRACTIONS Example! : 6 3 Anurag spent part of his salary on food and part on travelling. What part of salary did he spend total ? Solution: 6 Salary part spent on food = -y 3 Salary partspentoftravelling = y [T t । । .6 3 6 + 39](#bookmark451) [y H 13 13 1313](#bookmark452) - Example 2: [74](#bookmark453) In a packet there are -y kg of rice, y kg of rice is used. How much rice is left? Convert it into gram. Solution : Rice is packet = -^ kg Rice used = -^ kg [Remaining rice =—— —— kg 6 1010 ](#bookmark456) = 7-4 = 3 [1010](#bookmark457) — kg = — of 1000 g = 300 gram. [1010](#bookmark458) - Example 3: [44](#bookmark461) Convert — litres into mililitres. Also, find the cost of — litres milk if a litre costs 28. Solution: - [44](#bookmark464) — litre = — of 100 ml = 70 ml Costof^ litre milk = ^■°f 26. ![](Sum up math-4_files/Sum20up20math-4-146.jpg)![](Sum up math-4_files/Sum20up20math-4-147.jpg)You have already known about Indian currency in previous classes. You have seen coins and note both form of currency, which is available in India. But some coins of 1-paisa, 2-paisa, 5-paisa, 10-paisa, 20-paisa, 25-paisaare not in circulation. 50-paisa, 1 -rupee, 2-rupee, 5-rupee coins and 10-rupee coins and 5-rupee, 10-rupee, 20-rupee, 50-rupee, 100-rupee, 500-rupee and 1000-rupee notes are in circulation and easily available in the market. 1000 rupee note is rarely used. You have learnt that 7-rupee 75 paise is written as 7.75. But 11 rupees 5 paise in terms of rupees is written as 11.05 paise. It is always written in two digits as explained in previous classes. Separate paisa from rupees, by putting a dot (.) between them. You know that 1 rupee = 100 paise. Note : 50 p = 16 of 1, 25 = % of 1, 75 p = % of 1, where P stands for paise and Re stands for rupee. ###### J. EXERCISE 43 ^------------ - 1\. How many 25-paisa coins make a rupee ? - 2\. How many 50-paisa coins make a rupee ? - 3\. How many 10-rupee notes exchange of a 50-rupee note ? - 4\. Suman got seven 50-paisa and four 2 rupee coins from his father. How much money did she get ? - 5\. Anand has seven 10-rupee notes and four 20-rupees note with him. How much money does he have ? - 6\. Meena bought a dress. She gave four 100 rupee, one 50 rupee and three 5 rupee notes to the shopkeeper. How much total cost of the dress ? - 7\. Bheem bought a packet of chips and a packet of chocolate costing 60. He gave one 100 rupees note to the shopkeeper and got back 2 notes. What notes are these ? - 8\. Exchange the following in paise: - (a) 126.40 (b) 23 rupees 5 paise Z" - 9\. Exchange in rupees : - (a) 14 rupees 9 paise (b) 84 rupees 65 paise (c) 156 rupees 7 paise - 10\. How many rupeesand paisewill Sonam get in exchange of: (a) 515.40 P (b) 470.00 P ADDITION OFMONEY Examplel: Add 15 rupees 40 paise and 13 rupees 5 paise. Solution: Express in terms of rupees and then add 15 rupees40paise- 15.40 \+ 13 rupees05 paise- + 13.05 Total = 28.45 Sum = 78.45 Example2: Add 131.35, 92.81 and 277.50 Solution: 131.35 92.81 \+ 277.50 501.66 Sum = 501.66. Examples: Rishi bought copy for 80.00, book for 124.00 and pen for 15.2 5. How much money did he pay to the shopkeeper? Solution: Price of Copy = 80.00 Price of Book = 124.00 Price of Pen = + 15.25 Total = 219.25~ Rishipaid 219.25 to the shopkeeper. ![](Sum up math-4_files/Sum20up20math-4-148.jpg)SUBTRACTION OF MONEY Examplel: Subtract 35.15 from 89.40 Solution: 89.40 \- 35.15 54.25 Difference = 54.25 Example2: Sonam had one 100-rupee note. She bought a comb for 24.50 and a talcum powder for 56.50. How much money has she now? Solution: Comb = 24.50 Talcum powder = \+ 56.50 Total Cost = 81.00 She had one 100-rupee note = 100.00 Spent amount = \- 81.00 Difference 19.00 Left amount = 19.00 1\. Add: (a) 325.42 and 224.75 (b) 2 77.58and 167.50 (c) 435.50and 339.15 (d) 289.34and 3 76.75 (e) 93.40, 149.25 and 276.15 (f) 545.75, 360.30and Item Price (In Rs.) Item Price (In Rs.) Trousers 475.50 Jeans 546.99 Shirt 324.00 Belt 199.00 Jacket T-shirt 771.75 241.90 Shoes ; 823.00 110.50 101 ![](Sum up math-4_files/Sum20up20math-4-149.jpg) Read the price ¡¡stand find the amount each person paid : - (a) Rohan boughtapairofshoes and one belt. - (b) Rahul bought a trouser and a shirt. - (c) Aman bought a Jeans and a T-shirt and a belt. - 3\. Subtract : (a) 74.65 from 120.99 (b) (c) 520.05 from 747.50 (d) 4\. Roshan bought sweets for 220.60, 55.00. He gave one 500-rupee note t returned to him ? 158.40 from 265.75 725.50 from 949.00 Namkin for 125.25, cold drinks for ) the shopkeeper. What did shopkeeper - 5\. Shruti spends 275.50 on shopping and Kirti spends 533.75 on shopping. How much does Kirti spend more than Shruti ? - 6\. Raj bought a bat for 341.50 , ball for Rs. 65.70 and a carom board for 459.00. He gave two notes of 500-rupee each to the shopkeeper. What balance did he get ? - 7\. Radhika bought a dress for 324.50 and some make-up kit for 241.60. She had one 500-rupee note and one 100-rupee note. Now she has how much money? - 8\. Rahul sold some old newspapers, books and iron pieces for 90.95, 22.50 and 290.25 respectively. After that he bought atta for 75.50 and rice for 80.50. Calculate theamount left with him. Calculate total amountalso. MULTIPLICATION OF MONEY - Example 1: If a pen costs 19.50 Find the cost of 5 pens. Solution: Here we multiply 19.50 by 5 19.50 x 5 97.50 Costof 5 pens is 97.50. ![](Sum up math-4_files/Sum20up20math-4-150.jpg) #### G=-- - Example 2: Sony bought 10 towels at the rate of Rs. 1 75.00 per towel. How much did she pay to the shopkeeper? Solution: In this we multiply 175.00by10. 175 x 10 1750 Cost of 10 towels is 1750.00 - Example 3: If you purchase 4 pens for. 12.20 each, 5 books for 72.50 each and a geometry box for 5 5.00 and you gave a note of 500.00 to the stationary shopkeeper, what amount did you get back? Solution: Multiply 12.20by4 12.20 x 4 48.80 Multiply 72.50 by 5 72.50 x 5 362.50 Multiply 55.00 by 1 55.00 x 1 55.00 Add them to find the total cost 48.80 362.50 ![](Sum up math-4_files/Sum20up20math-4-151.jpg)Now subtract to find the balance 500.00 466.30 33.70 You will get 33.70 back. Example: Pankhuri purchased 8 dresses at 1215.00 per dress and sold them at 1320.00 per dress. Calculate the money she earned. Solution: Multiply 1215.00by8 1215.00 x 8 9720.00 Multiply 1320.00 by 8 1320.00 x 8 10560.00 Amount paid for 8 dresses = 9720.00 Amount received for 8 dresses = 10560.00 Pankhuri earned (10560.00-9720.00) 840.00 DIVISION OFMONEY Example5: Babloo bought 9 metres of cloth for 1846.80. Calculate the cost of 1 metre of cloth. Solution: 2 0 5.2 0 9)1 8 4 6.8 0 \- 1 8 4 6 4 5 1 8 1 8 Cost of 1 metre of cloth is 205.20 0 Example6: Ravi bought 4 dresses for 1250.00. Sonam bought 2 dresses of same type gave a 100-rupee note to the shopkeeper. How much change did she get back? Solution: Cost of 4 dresses = 1250.00 Costofl dress = 1250.00 -^4 = 312.50 Costof 2 dresses = 312.50x2 = 625.00 Change got by Sonam = (1000-62 5.00) = 375.00 ###### EX&RG1S& 45 । ![](Sum up math-4_files/Sum20up20math-4-152.jpg) Multiply: (a) 215.00by2 - (c) 90.48 by 1 7 Divide: (a) 509.95 by 5 (c) 1312.40 by 17 (b) 891.30 by 5 (d) 83.13 by 76 - (b) 981.20 by 5 (d) 1515.60 by 24 - 3\. If 1 kg of wheat costs 24.95, how much will 17kg ofwheat cost? - 4\. Ramu bought 8 packets of biscuits. If 1 packet of biscuit costs 12.10, how much did Ramu pay to the shopkeeper? - 5\. Rana bought 3 pairs of trousers each costing 190.75 and 4 shirts each costing 210.25. He gave 2000.00 to the shopkeeper. What balance will he get back? - 6\. Ramesh bought 5 books, each costing 27.50 and 2 pens, each costing 1 7.20. He gave one 100-rupee note and two 50-rupee note to the bookseller. What balance did the shopkeeper return him back? - 7\. Renuka bought 4 packs of perfume each costing 328.70, two packs of dress, each coasting 412.20 and two pens each coasting 29.1. She had only 2000.00 rupees with her. How much more money did she needs to pay the bill? - 8\. Rohit bought two dresses and each costs 412.50. He sold them to Amit each for 478.20. How much did he earn? - 9\. Rohit bought 12 types of colour at 1 7.20 per colour, 3 books at 92.50 each, 5 pencils at the rate of 7.20 per pencil. He sold them to the other students and got 600.00 How much rupees did he earn? - 10\. Raju bought 5 kg of tomato at the rate of 16.20 per kg and 20 kg of rice at the rate of 27.50 per kg from the whole sale market. He sold tomato at 19.10 per kg and rice at the rate of 31.50 kg per kg to the people. How much did he earn? - 11\. Anju bought 5 books for 765.50. How much did one book cost her? - 12\. Ramesh paid 2510.25 fordinner in a restaurant with hisfriends. How much did one dinner cost if Ramesh went for dinner with 14 friends? - 13\. John purchased 12 tickets to visit a planetorium. He paid total of 493.80 for tickets. How much did he spend on one ticket? - 14\. If cost of 25 books is 2550.00, calculate the cost of one book. - 15\. Anmol purchased 4 books for 4200.40 and Asmit bought same type of 3 books. How much money Asmit has to pay? - 16\. A shopkeeper sells 3 pairs of shoes to a customer in 5167.50. He sells 5 pairs of shoes of same kind to Rohit. Rohit gave eight 1000-rupee notes to the shopkeeper. How much more money Rohit has to pay to the shopkeeper? ![](Sum up math-4_files/Sum20up20math-4-153.jpg)![](Sum up math-4_files/Sum20up20math-4-154.jpg) 12 teu^ment of Weight ![](Sum up math-4_files/Sum20up20math-4-155.jpg) In earlier classes you learnt that the standard unit of weight (mass) is kilogram (kg). To weight heavy things we use kilogram and to weight lighter ones we use gram. We weight - (a) Asackof rice in kilogram - (b) A packet of biscuits in gram - (c) A packet of kurkure or potato ch ips i n gram - (d) Wheat, sugar, pulse etc. in kilogram - (e) A person in kilogram - (f) A packet of chocolates i n gram You knowthat- 1 kilogram = 1000 gram Some standard weights used for weighing things are shown below: ![](Sum up math-4_files/Sum20up20math-4-156.jpg)W kg ![](Sum up math-4_files/Sum20up20math-4-157.jpg) ![](Sum up math-4_files/Sum20up20math-4-158.jpg) ![](Sum up math-4_files/Sum20up20math-4-159.jpg) ![](Sum up math-4_files/Sum20up20math-4-160.jpg) ![](Sum up math-4_files/Sum20up20math-4-161.jpg) ![](Sum up math-4_files/Sum20up20math-4-162.jpg) 500 g 200 g 100 g You also know that Two 500 g weights make 1 kg •■■ 500 g kg Five 200 g weights make 1 kg ■■■ 200 g 4 5 kg Ten 100 g weights make 1 kg .• . 1 oo g = -4g 0 10 Twenty 50 g weights make 1 kg 508 25 = kg ADDITION AND SUBTRACTION OF WEIGHTS You have already learntthe addition and subtraction of small quantities of weights in previous class. In this class you will learn the addition and subtraction of large quantities of weights using same methods. ![](Sum up math-4_files/Sum20up20math-4-163.jpg)Example 1: Add 35 kg 25 g and 20 kg 20 g. Solution: Write the quantities in column form and add. kg g 35 025 Write grams in 3 digits. For example write 20g as 020. \+ 20 020 55 045 .-. Sum = 55 kg 45 g. - Example 2: Add 35 kg 250 g and 55 kg 850 g. Solution: kg g 00\*1 35 250 \+ 55 850 91 ©100 Add ones to ones, tens to tens, hundreds to hundreds etc. Like whole numbers - Example 3: Subtract 36 kg 750 g from 48 g 350 g Solution: Write the digits in column form and subtracts kg g 48 350 -36 750 11 600 .-. Difference = 11 kg 600 g. - Example 4: Subtract 58 kg 500 g from 76 kg 150 g Solution: Write their in column form and subtract, kg g 76 150 ![](Sum up math-4_files/Sum20up20math-4-164.jpg) -58 500 Difference = 17kg 650 g. 17 650 Example5: Rajan purchased 5 kg 250 g potatoes, 2 kg 500 g rice and 15 kg of brinjals. He put all of them in a bag. Calculatethe weight of bag. Solution: Write in column form and add. kg g 5 250 2 500 +15 000 22 750 Total weight of bag = 22 kg 750 g. - Example 6: Railway allows 50 kg weight free of cost with one passenger. Amit has only 32 kg 200 g weight with him. How much more weight can he carry free of cost? Solution: Write them in column form and subtract. kg g 50 000 -32 200 17 800 He can carry 17kg 800g move weight. ###### . EXERCISE MG - 1\. Raju went to the market and bought some vegetables. If the shopkeeper used the weights as given below. Then how much vegetables did he bought in each case? Answer in one case has been given for you. ![](Sum up math-4_files/Sum20up20math-4-165.jpg) = 600 g. ![](Sum up math-4_files/Sum20up20math-4-166.jpg) kg g kg g. ![](Sum up math-4_files/Sum20up20math-4-167.jpg)![](Sum up math-4_files/Sum20up20math-4-168.jpg)Fill in the blanks. (One question has been solved for you): - (a) 600 g of rice can be weighed by using one 500 g and one 100 g weights. - (b) 1 kg of potato can be weighed by using 500 g and 200 g of weights. - (c) 3 kg of rice can be weighed by using 1kg, 500 g and 200 g of weights. - (d) 5 kg of vegetables can be weighed by using 1kg, 500 g and 100 g weights. - (e) 10 kg of wheats can be weighed by using 5 kg, 1kg, 500gof weights. How will you weight: - (a) 8 kgof potatoes by using a 10 kg and a 2 kg of weights. - (b) 7 kg of on ions by using a 10 kg and th ree 1 kgofweights. - (c) 3 kg of tomato by using a 5 kg and a 2 kgofweights. Convert into gram: (a) y kg (b) y kg (c) Tkg (d) y kg (e) To kg Add the following: (a) kg g (b) kg g (c) kg g 15 250 35 150 55 817 +17 520 +19 950 \+ 42 751 (d) kg g (e) kg g 22 555 73 857 \+ 37 675 \+ 55 235 - 6\. Add the following: - (a) 51 kg 830 g and 25 kg 754 g (c) 25 kg 280 g and 75 kg410 g - (e) 45 kg 15 gand 27 kg225 g - 7\. Subtractthe following: (b) 18 kg 980 gand 7 kg 570 g (d) 54 kg 750 g and 32 kg 175 g (a) kg 56 -44 g 735 240 (b) kg 57 -38 g 850 915 (c) kg 32 -16 g 510 750 (d) kg 74 -74 g 150 150 - 8\. Subtractthe following: (a) 12 kg495 gfrom 56 kg 735 g (b) (d) 18 kg 935 gfrom 57 kg 850 g 48 kg475 gfrom 74 kg 150 g (c) 15 kg 760gfrom 32 kg 510g - 9\. A packet can hold 60 kg of rice. This packet has only 1 7 kg 250 g of rice. How much more rice can be put into in it ? - 10\. Rani bought 15 kg 300 g of vegetable, 25 kg 750 g of rice and 30 kg 150 g of wheat. Find the total weights of all items she bought. - 11\. Mona purchased 12 kg 100 g mustered oil, 30 kg 915 g potatoes, 20 kg 300 g pumpkin and put them on a rickshaw to carry them. Find the total weights of goods on rickshaw. - 12\. Radha sold 15 kg 200 g of old books, 30 kg 562 g of old news paper, 22 kg 315 g of rusted iron to a kabariwala. What was the weight of total goods kabariwala purchased? - 13\. A shopkeeper had 200 kg 300 g of rice. Ramesh purchased 75 kg 750 g of rice from that shopkeeper. How much rice was left with shopkeeper ? - 14\. Sumi carried 15 kg 200 g of vegetables to home. 2 kg 520 g of vegetables were consumed. How much vegetables is left to her home ? - 15\. The weight of Gappu is 20 kg 150 g and the weight of Molu is 72 kg 340 g. How muc heavier is Golu than Gappu? ![](Sum up math-4_files/Sum20up20math-4-169.jpg) - 16\. Sumi lose 2 kg 920 g weight. What was the weight of Sumi earlier if she weighs 70 kg 200 g now? - 17\. Sonu purchased 1 75 kg 215 g of rice and 40 kg of vegetables. During carrying the goods home 22 kg 100 g rice and 13 kg 115 g of vegetable fell on the road. How much weight of rice and vegetables is left with him? Find the total good left with him also. MULTIPLICATION AND DIVISION OF WEIGHTS - Example 1: Multiply 1 7 kg 400 g by 4. Solution: 17kg400g= 17 x 1000g + 400g = 17400 g Now multiply it with 4 17400 x4 69600 Product = 69600 g = 69 kg 600 g - Example 2: The weight of a table is 32 kg 200 g. Find the weights of four such tables. Solution: Multiply 32 kg200 g with 4 32 kg200g = 32 x 1000g + 200g = 32200 g Now- 32200 x4 128800 Total weight = 128800 g = 128 kg 800 g - Example 3: The weight of 5 steel trunks is45kg 750g. Find the weight of one trunk. ![](Sum up math-4_files/Sum20up20math-4-170.jpg)Solution : Divide 45kg 750g by 5 45 kg 750 g = 45 x 1000 g + 750 g = 45750 g Now 9 15 0 5^)4 5 7 5 0 \- 4 5 7 5 2 5 - 2 5 0 .-. Weight of one steel trunk = 9150 g = 9 kg 150 g ![](Sum up math-4_files/Sum20up20math-4-171.jpg) ###### . EXERCISE 47 2\. Multiply: (a) 12 kg 150 g by 4 - (c) 55 kg 125 g by 3 Divide: - (a) 50 kg 500 g by 4 (c) 66 kg 888 g by 8 - (b) 41 kg 210 g by 10 - (d) 20 kg 325 g by 8 (b) 55 kg 600 g by 5 - (d) 125 kg 250 g by 2 - 3\. The weight of one person is 35 kg 250 g. Find the weight of similar 7 persons of same weight. - 4\. If a family needs 32 kg 200 g of rice in one month how much rice will it require in one year? - 5\. If 7 person eats 47 kg 250 g of vegetable in a month. How much vegetable will be enough for one person in a month ? - 6\. Radha has 100 kg of rice. She wants to put it into smaller containers. How many containers she needs if the capacity of container is: - (a) 50 kg (b) 20 kg (c) 10 kg ![](Sum up math-4_files/Sum20up20math-4-172.jpg)7\. If one kg of vegetable costs 17.45. Find the cost of: (a) 17kg200g (b) 22kg150g (c) 55kg20g - 8\. 250 kg of rice was equally distributed between Somu and Amit. Amit consumed 22 kg 250 g and Somu consumed 1 7 kg 125 g of rice. How much rice is left with each ofthem ? - 9\. A pack of goods weigh 27 kg 500 g. Another packet which is 8 times heavier is kept with firstone. What is the total weight of both packets ? - 10\. Rahul purchase 25 kg 250 g of apple. He ate — of the amount. How much apple is left with him? ' - 11\. A society distributed 1000 kg of food items among 125 people. How much food items did each people get? - 12\. During the flood relief officer calculated that 22 kg of ready food was sufficient for one family. If there are 127 family then how much ready food will be required ? - 13\. If a person eats 750 g of food in a day and there are 7 people in a family then how much food will be required for 20 families for 10 days ? ![](Sum up math-4_files/Sum20up20math-4-173.jpg)![](Sum up math-4_files/Sum20up20math-4-174.jpg) 13 (VcasuRcmcnt of Capacity ![](Sum up math-4_files/Sum20up20math-4-175.jpg) You have learnt in previous class that standard unit for measurement of liquid is "litre (I)". A litre is divided further in 1000 equal parts. Each small part is cal led one millilitre (ml). Therefore, 1 litre = 1000 millilitre (ml) You should know that large quantities are measured in litres and small quantities are measured in millilitre. Liquids like milk, petrol, kerosene oil, etc. are measured in litres. But medicines are measured in millilitres. You know that two types of containers are used for measuring milk, kerosene etc. ![](Sum up math-4_files/Sum20up20math-4-176.jpg)1 litre Container used to measuring milk. ![](Sum up math-4_files/Sum20up20math-4-177.png) Container used to measure petrol, kerosene etc. Usually container having capacity of one litre, 500ml, 200ml, 100ml are available. 1 litre = 2 x 500ml = 1000ml 1 litre = 5 x 200ml = 1000ml 1 litre = 10 x 100ml = 1000ml 500ml = — litre 2 200ml = litre 5 100ml = -^y litre - Example 1: 1 How many millilitre does — litre contain? ![](Sum up math-4_files/Sum20up20math-4-178.jpg)Solution : litre = ^- x 1000ml = 500ml 2 ADDITION AND SUBTRACTION OF CAPACITY MEASURES You have already learnt the addition and subtraction of kilograms and grams. You will do the same way of method in addition and subtraction of litresand millilitres. Always write millilitre in three digits while doing operation of addition or subtraction of litresand millilitres. - Example 2: Add 121200 ml and 51100 ml Solution: Write in the form of column and add. 1 ml 12 200 \+ 5 100 17 300 .•. Sum = 1 71300 ml. - Example 3: Add 181600 ml and 151 700 ml Solution: Write in column form and add - 1 ml 18 600 +15 700 34 300 /. Sum = 341300 ml. - Example 4: Add 81 160 ml and 121725 ml Solution: Write in column form and add 1 ml 81 060 ![](Sum up math-4_files/Sum20up20math-4-179.jpg) \+ 12 725 Sum = 93 1785 ml. 93 785 Example5: Subtract 121200ml from 21 1115ml Solution: Write in column form and subtract 1 ml 21 115 12 200 8 915 .-. Difference = 81915 ml. ###### {J. EXERCISE H8 ^ - 1\. Tickthe correct measure: ![](Sum up math-4_files/Sum20up20math-4-180.jpg) - (a) 200 ml 1001 ![](Sum up math-4_files/Sum20up20math-4-181.jpg) - (c) 51 - 5 ml - 2\. How much kerosene oil will be measured by using the containers of the following capacities: - (a) One 200 ml and one 500 ml (b) One 1000 ml and two 500 ml (d) Three 200 ml and four 500 ml (c) Five one litre and two 200 ml - 3\. Fill in the boxes. One is being solved foryou : How many times the container will be used to measure. 11 500 ml 200 ml 100 ml 50 ml - a. 200 ml of petrol - b. 500 ml of milk - c. 21750 ml of milk - d. 51300 ml kerosene - e. 71700 ml petrol 1 time ![](Sum up math-4_files/Sum20up20math-4-182.jpg)4\. Add the following: (a) i 52 ml 250 (b) i 65 ml 200 (c) 1 12 ml 800 \+ 35 150 \+ 75 915 \+ 27 425 J zz J (d) i ml 72 735 \+ 45 695 5\. Add the following: (a) 2 1650 ml and 151255 ml (b) 341 775 ml and 51 1552 ml (c) 43 1577 ml and 271335 ml (d) 741237mland 781935 ml 6\. Subtractthe following: (a) i ml (b) i ml (C) 1 ml 32 725 43 115 22 075 -16 910 -40 210 -09 210 J J zz - (d) 1 m| 37 675 -19 915 - 7\. Subtractthefollowing: - (a) 151815 ml from 321725 ml (b) 2 1905 ml from 43 1115 ml - (c) 12 1865 ml from 22 175 ml (b) 1 71 760 ml from 371675 m - 8\. A tanker has 150675 ml of milk. Find how much milk is present in litre and millilitre in the tanker ? - 9\. Rakesh bought 12 1 225 ml of milk on Monday, 13 1 110 ml on Tuesday and 20 1 125 ml on Wednesday. How much milk did he bought in these three days ? - 10\. Rakhi was carrying kerosene in a container having capacity of 50 1. The container was full. But because of leak 11 1225 ml of kerosene fell down. How much kerosene is left with her ? ![](Sum up math-4_files/Sum20up20math-4-183.jpg) - 11\. Ajeet got 25 litre of petrol in his car. He used 12 1 275 ml during his journey. How much petrol will be left in the tank of his car ? 2 2 MULTIPLICATION AND DIVISION OF CAPACITY MEASURES (BY CONVERSION) You have already learnt the method of Multiplication and Division of kilogram and gram in previous chapter. In this section same method will be applied in multiplication and divisions on capacity. - Example 1: A jar can hold 21250 ml of milk. How much milk will be needed to fill 5 such jars? Solution: We will multiply 2 1250 ml by 5 21250ml= 2 x 1000ml + 250ml = 2000 ml + 250 ml = 2250ml Now multiply this with 5 2250ml x 5 11250ml Therefore required milk = 11250 ml = 11 1250ml - Example 2: Ankit prepared 201 750 ml of sugar solution. He wants to fill it in 5 bottles. How much solution will each bottle hold ? Solution: We will divide 201 750 ml by 5 201750 ml = 20 x 1000 ml + 750 ml = 20000 + 750 ml = 20750 ml Now divide 20750 ml by 5 4 15 0 5^2 0 7 5 0 - \- 2 0 7 5 - 2 5 - 2 5 0 .•. Solution in each bottle4150 ml = 41150ml ###### J. EXERCISE 49 s - 1\. Multiply: 2. (a) 13 1225 ml by 6 (d) 32 1325 ml by 9 Divide: (b) (e) 1 71122 ml by 5 471215 ml by 3 (c) 241235 ml by 7 (a) 791350 ml by 6 (b) 851610 ml by 5 (c) 1691645 ml by 7 (d) 2901925 ml by 9 (e) 1481645 ml by 3 - 3\. 5 containers of milk, each holding 13 1 750 ml, are poured into a tank. Calculate how much milk now is in the tank Iftank was empty previously? - 4\. How much sauceswill be required to fill up 7 jars having the holding capacity of 121225 ml each ? - 5\. Nita like to put 30 1 750 ml of vegetable oil in 5 containers. Find the capacity of each container. - 6\. 121250 ml of milk is to be kept in 5 bottles. What will be the capacity of each bottle ? - 7\. Ramesh bought 70 1 750 ml petrol and filled it in his car. He went to a hill station. During his journey — of the petrol consumed. How much petrol will be left in his car ? - 8\. A petrol pump owner sold 225 1 750 ml of petrol on Monday and 4 times of that sold on Tuesday. How much petrol will be sold in these two days ? - 9\. Six bottles of coke each having 300 ml were shared by 12 friends in a school party. How much coke did each of them drink ? - 10\. 9 bottles of milk each having 2 1 were distributed among 30 children. How much milk did each child get ? - 11\. Ifthecostof 1 lofcoke is 250.50, find the cost of: - (a) 500 m I of coke (b) 100 m I of coke - (c) 250 ml of coke (d) 400 ml of coke ![](Sum up math-4_files/Sum20up20math-4-184.jpg) OTeusuRemeDt of Length ![](Sum up math-4_files/Sum20up20math-4-185.jpg) You read that unit of measurement is "metre". Metre is denoted by letter "m". Different types of metre scales are generally used which are given below: ![](Sum up math-4_files/Sum20up20math-4-186.jpg)Metre rod ![](Sum up math-4_files/Sum20up20math-4-187.jpg) When one metre is divided into 100 equal parts each parts is called centimetre and it is written as "cm". Therefore, 1 metre = 100 cm When one metre is divided into 10 equal part then each part is called decimetre and it is written in short as "dm". Therefore, 1 metre = 10 cm Students use generally scale having 15 cm of length. The figure is given here. ![](Sum up math-4_files/Sum20up20math-4-188.jpg) With the help of ruler you can observe that each centimetre is divided into 10 equal parts. Each part is called "millimetre" and it is written in short as "mm". Therefore, 1 cm = 10 mm We measure the length ofa pencil, pen, tooth-brush, booketc. in cm. We measure the length of table, room, playground etc. in metre. But we measure the distance between two cities in "kilometre". In short kilometre is written as "km". 1000 metre = 1 km or 1 km = 1000 metre ![](Sum up math-4_files/Sum20up20math-4-189.jpg) ![](Sum up math-4_files/Sum20up20math-4-190.jpg) Example 1: Which ofthefollowing length are supposed to betrue. The length of Rahul's pencil is 5 m. The length of Govind's tooth brush is 5 mm. The distance between Patna and New Delhi is 5 m. The length of Rahul's room is 3 metre. The length ofthe top of the table is 1.5 metre. (a) (b) (c) (d) (e) Solution : (a) False (d) True (b) (e) False True (c) False Measurement of Length lOmillimetre(mm) 10 centimetre 10 decimetre 1000 metre = 1 centimetre (cm) 1 decimetre (dm) 1 metre (m) 1 kilometre (km) Expressing bigger unit in terms of smaller units Example 2: Convert the following into centimetres: (a) 2 m (b) 5 m 40 cm (c) 3 m 20 cm (d) 1m 15cm Solution: (a) 2 m = 2 x 100 cm = 200cm (b) 5m40cm = 5 x 100cm + 40cm = 500 cm + 40 cm = 540 cm (c) 3m20cm = 3 x 100cm + 20cm = 300 cm + 20 cm = 320cm (d) 1m 15cm = 1 x 100 cm + 15 cm = 100 cm + 15 cm = 115 cm 1231 Example 3: Convert the following into centimetres: (a) 10 dm (d) 11 dm 2 cm Solution: (b) 3 dm 10 cm (c) 7 dm 22 cm (e) 27 dm 19 cm (a) 10dm = 10 x 10cm = 100 cm (b) 3 dm 10 cm = 3 x 10cm + 10cm = 30 cm + 10cm = 40 cm (c) 7 dm 22 cm = 7 x 10 cm + 22 cm = 70 cm + 22 cm = 92 cm (d) 11 dm 2 cm = 11 x 10cm + 2 cm = 110cm + 2 cm = 112 cm (e) 27 dm 19 cm = 27 x 10cm + 19cm = 270cm +19cm = 289 cm - Example 4: Convert into decimetres: (a) 5 m (d) 2 m 12 dm Solution: (b) 3 m 16dm (c) 16m 22dm (e) 21 m 21 dm (a) 5 m = 5 x 10dm = 50dm - (b) 3m 16dm = 3 x 10dm + 16dm = 30dm + 16dm = 46 dm - (c) 16m22dm = 16 x 10dm + 22dm = 160 dm + 22 dm 182 dm Get Set Go With Sum Up Mathematics-4 ![](Sum up math-4_files/Sum20up20math-4-191.jpg) - (d) 2m 12dm = 2 x 10dm + 12dm = 20dm + 12dm = 32 dm - (e) 21 m21 dm = 21 x 10dm + 21 dm = 210dm + 21 dm = 231 dm Example5: Convert the following into millimetres : - (a) 5 cm (b) 16 cm 20 mm - (d) 13 cm 27 mm (e) 19 cm 20 mm Solution: - (a) 5 cm = 5 x 10 mm = 50 mm - (b) 16 cm 20 mm = 16x10 mm + 20 mm = 160 mm + 20 mm = 180 mm - (c) 2 cm 12 mm = 2 x 10 mm + 12 mm = 20 mm + 12 mm = 32 mm - (d) 13cm27mm= 13x10mm + 27mm = 1 30 mm + 27 mm = 157mm - (e) 19 cm 20 mm = 19 x 10 mm + 20 mm = 190 mm + 20 mm = 210mm - Example 6: Convert into metres: - (a) 2 km (b) 5 km 20 m - (d) 3 km 1 7 m Solution: - (a) 2 km = 2 x 1000m = 2000 m (c) 2 cm 12 mm (c) 13 km 62 m - (b) 5 km 20 m = 5 x 1000 m + 20 m = 5000 m + 20 m = 5020 m - (c) 13km62 7m= 13 x 1000 m + 62 7 m = 13 000 m + 62 7 m = 13627m - (d) 3 km 17 m = 3 x 1000 m + 1 7 m = 3000 m + 1 7 m = 3017m ###### J. EXERCISE 50 ^------ 1\. What will be the better unit to measure the length of the following: (a) Book (b) Pen (c) Distance between two cities (d) Length of cloth (e) Length of cricket pitch (f) Length of playground (g) Length of a table (h) Length of a man (i) Height ofa building (j) Length of small key - 2\. Correct (if necessary) the following: - (a) The length of 5-rupee note is 2 m. - (b) The speed ofa car is 5 mm per hour. - (c) The heightofa building is 50 m. - (d) The distance of my school is 2 km from my house. - (e) The length ofa metre scale is 2 km. 3\. Convert into centimetres: (a) 5 m (b) 16 m 32 cm (c) 61 m 44 cm (d) 27 m 20 cm (e) 25 m 25 cm 4\. Convert into centimetres: (a) 2 dm (b) 13 dm 5 cm (c) 27dm 72 cm (d) 16 dm 25 cm (e) 52 dm 21 cm ![](Sum up math-4_files/Sum20up20math-4-192.jpg) - 5\. Convert into decimetres : 6\. (a) 9 m (b) 3 m12 dm (d) 27 m 13 dm (e) 31 m 12 dm Convert i nto m i 11 i metres: (a) 12 cm (b) 13 cm 7 mm (d) 21 cm 20 mm (e) 120cm25mm Convert into metres: (a) 25 km (b) 22 km 25 m (d) 125km210m (e) 27 km 615 m (c) 2 m 22 dm (c) 27 cm 20 mm (c) 210 km 410 m EXPRESSING SMALLER UNITS IN TERMS OF BIGGER UNIT Study the pattern of conversion- Conversion of millimetres to centimetres: - 10 mm = 1 cm 20 mm = 2 cm - 16 mm = 1 cm 6 mm 27 mm = 2 cm 7 m 65 mm = 6m 5 mm To convert millimetres into centimetres, divide cm by 10. Conversion of Centimetres to metres 200 cm = 2 m 105 cm = 1 m 5 cm 400 cm = 4 m 782 cm = 7 m 82 cm To convert centimetres to metre, divide cm by 100. Conversion of metres to kilometres. 4000 m = 4 km 2 720 m = 2 km 720 m 5500 m = 5 km 500 m 7000 m = 7 km To convert metres in to kilo metre divide metres by 1000. 127 ![](Sum up math-4_files/Sum20up20math-4-193.jpg) ###### ^. EXERCISE 51 ^ - 1\. Convert the fol lowing into centimetres : - (a) 30 mm (b) 332 mm (c) 55 mm (d) 272 mm (e) 2701 cm (e) 2755 m (e) 1905 mm 119cm 119355m - 2\. Convertthefollowing into metres : - (a) 600 cm (b) 672 cm (c) 1655 cm (d) - 3\. Convert the fol lowing into kilometres: - (a) 3000 m (b) 3520 m (c) 3010 m (d) ADDITION-METRES AND CENTIMETRES Example 1: Add 210 m 55 cm and 155 m 27cm. Solution: m cm 210 55 +155 27 365 82 .-. Sum = 365 m 82 cm. Add cm to cm and m to m - ^ Write cm in the form of two digits for example write 5 cm as 05 cm - Example 2: Add 12 m 87 cm and 125 m 35 cm. Solution: m cm 125 35 + 12 87 138 22 .•. Sum = 1 38 m 22 cm ADDITION-KILOMETRE AND METRE Kilometre and Metre will be added in similar way as we added the metres and centimetres. - Example 3: Add 12 km 125 m and 27 km 22 m. Solution: km m 12 125 Write 22 m in the form of 022 m and 5 m as 005 m. \+ 27 022 39 147 .-. Sum = 39 km 147 m. - Example 4: Add 21 km 72 5 m and 5 5 km 62 7 m. Solution: m cm 21 725 \+ 55 627 77 352 Required sum = 77 km 352 m. ###### Q. EXERCISE 52 । - 1\. Add the following: (a) 235 m 27cm and 121 m 92 cm (b) 352 m 72 cm and 211 m 29 cm (c) 12 m 52 cm and 622 m 95 cm - (e) 57 km 455 m and 26 km 927 m (g) 22 5 km 2 74 m and 216 km 3 5 r - (d) 127 m 26 cm and 226 m 59cm (f) 75 km 42 7 m and 162 km 73 5 m (h) 252 km 5 m and 126 km 522 m Playground in Rajan's school is 37 m 55 cm wide and 73 m 2 cm long. Calculate its total length. - 3\. The distance from Ketan's house to his school is 712 m 75 cm and distance of railway station from school is 625 m 57 cm. Calculate the distance of Railway Station from Ketan's house. - 4\. The distance of Patna from Varanasi is 400 km 235 m and from Varanasi to Delhi is 700 km 911 m. Calculate the total distance. - 5\. Rekha bought 5 m 27 cm cloth and Anju bought 3 m 82 cm cloth to make their suits. What will be the total length of cloth ? 129 ![](Sum up math-4_files/Sum20up20math-4-194.jpg)- 6\. Ankit has 75 m 12 cm long rope and Ashok has 12 m 91 cm long rope. They joined the rope together. Now find the length of total rope. - 7\. Ashok cover 30 km 20 m distance by cycle, 117 km 35 m by bus and 122 km 25 m by train. How much distance did he cover ? - 8\. A shopkeeper bought 210 m 25 cm of cloth. Again he bought 12 m 70 cm cloth. Calculate the total length of cloth he bought. - 9\. Rekha cover a distance of 12 km 125 m on Monday and 1 72 km 625 m on Tuesday. How much distance did she cover in these two days ? SUBTRACTION-METRES AND CENTIMETRE - Example 1: Subtract 93 m 55 cm from 122 m 21 cm Solution: m cm 122 21 \+ 93 55 28 66 - .-. Required difference = 28 m 66 cm SUBTRACTION-KILOMETRES AND METRES - Example 2: Subtract 82 km 500 m from 835 km 400 m. Solution: km m 835 400 \+ 82 500 752 900 Required difference = 752 km 900 m. ###### {J. EXERCISE 53 ![](Sum up math-4_files/Sum20up20math-4-195.jpg) - 1\. Subtractthe following : (a) 22 m 72 cm from 37 m 81 cm (c) 71m 55 cm from 92 m 6 cm m - (e) 235 km 627 m from 415 km 211 m (g) 71 Okm 22 m from 1012 km 210 m (b) 35 m 27cm from 70 m 12 cm - (d) 122 km 255 m from 410 km 22 (f) 312 km 210 m from 615 km 2 m (h) 127 m 77cm from 256 m 6cm - 2\. Arun purchased 12 m 12 cm suit length and gave 4 m 20 cm to Rahul. How much length of suit length is left with Arun ? - 3\. A shopkeeper had 50 metres of cloth. He sold 12 m 25 cm. How much cloth will be left with him ? A tailor had 340 m 22 cm of thread. He used 22 m 75 cm thread. How much long thread will be left with him ? Home of Ankit is 12 km 210 metre far from school. Rahul's house is 37 km 5 metre far from school. What is the distance between Rahul's and Ankit's house ? Kanpur is 400 km from New Delhi. Ashok covered a distance of 210 km 127 m from New Delhi. How much more distance did he have to cover now ? - 7\. A cloth merchant sold 521 m 20 cm cloth on 1st March. On the 3rd March he sold 622 m 12 cm of cloth. If he had sold a total of 2 700 m 22 cm in three days how much cloth did he sell on 2nd March ? - 8\. Ajit travel 22 km 2 m by cycle and 70 km 210 m by a car. Kolkata is 1 700 km from his hometown. How much more distance he have to cover to reach Kolkata ? MULTIPLICATION OF LENGTH MEASURES (BY CONVERSION) In this we will learn the multiplication of metres, centimetres and kilometres. You have already learnt the multiplication of kilograms and grams in previous chapter. In this section we will apply the same method of multiplication as we did during multiplying kilogramsand grams. It will be solved by the method of conversion. Let us see it. - Example 1: Multiply 12 m 25 m by 4. Solution: ![](Sum up math-4_files/Sum20up20math-4-196.jpg) First of all convert 12 m 25 cm intocmsthen multiply itwith given number4. Get Set Go With Sum Up Mathematics-4 ![](Sum up math-4_files/Sum20up20math-4-197.jpg)So, 12 m 25 cm = 12 x 100cm + 25 cm = 1200 cm + 25 cm = 1225 cm Now multiply by 4. 1225 x 4 4900 Required product = 49 m 00 cm. You may write it as 49 m only. - Example 2: Multiply 28 m 35 cm by 12 Solution : 28 m 85 cm = 28 x 100 cm + 85 cm = 2800 cm + 85 cm = 2885 cm Nowmultiply itby 12 2885 x 12 5770 28850 34620 Required product = 34620 cm = 346 m 20 cm - Example 3: Multiply 16 km 25 m by 1 7. Solution : 16km25m= 16x 1000 m + 25 m = 16000 m + 2 5 m = 1602 5 m Now multiply 16025 x 1 7 112175 160250 272425 So, required product = 2 7242 5 m = 272 km 425 m \[132 ###### {J. EXERCISE 5R f 1. Multiply: - (a) 12 m 57cm by 16 (d) 220 m 21 cm by 122 (g) 521 km 122 m by 19 (j) 17m32cmby215 - (b) 55 m 75 cm by 19 (e) 15 km 675 m by 210 (h) 215 km 221 m by 18 - (c) 112 m 54 cm by 18 (f) 125 km 215 m by 3 (i) 1125 m 55 cm by 21 2\. 3\. The length of a ribbon is 18 m 20 cm. How much will be the length of such 20 ribbon? The length of a playground is 70 m 25 cm. Rohan crossed it 9 times. How much distance did he cover ? Ramesh walks 2 km 50 m everyday. How much distance will he cover in one week? DIVISION OF LENGTH MEASURES (BY CONVERSION) Division of length measures will be done in same way as you learnt the division of measurement in previous chapters. - Example 1: Divide 66 m 42 cm by 3. Solution: 66 m 42 cm = 66 x 100 cm + 42 cm = 6600 cm + 42 cm = 6642 cm Nowdivide 2 2 14 - — 6 6 4 \_3\_\_ 1 2 1 2 0 Required quotient = 2214cm = 22 m 14cm. Q ![](Sum up math-4_files/Sum20up20math-4-198.jpg)Example 2: Divide 1 7 m 5 cm by 5. Solution: 17m 5cm = 1 7 x 100cm + 5cm = 1 700 cm + 5 cm = 1705 cm Nowdivide 3 4 1 5J 1 7 0 5 - \- 1 5 - 2 0 - 2 0 5 \_\_\_\_5 0 Required quotient = 341cm = 3 m 41 cm. Example 3: Divide 92 km 505 m by 7 Solution: 92 km 505 m = 92 x 1000 m + 505 m = 92000 m + 505 m = 92505 m Nowdivide ![](Sum up math-4_files/Sum20up20math-4-199.jpg) 13 2 15 7)9 2 5 0 5 - 7 2 2 2 1 1 5 1 4 1 0 7 3 5 3 5 0 So, required quotient = 13215 m = 13 km 215 m. Get Set Go With Sum Up Mathematics-4 ###### EXERCISE 55 J ![](Sum up math-4_files/Sum20up20math-4-200.jpg) Divide and find the quotient : (a) 408 m 64 cm by 4. (b) 51 m 12 cm by 6. (c) 410 m 83 cm by 7. (d) 2084 m 85 cm by 9. (e) 312 m 4 cm by 4. (f) 165 km 550 m by 5. (g) 1 77 km 184 m by 7. (h) 32 km 886 m by 9 (i) 37km210mby2. (j) 137 km 412 m by 3. Ashok reached a distance of 147 km 406 m in 7 days. Calculate the distance covered by him in oneday. - 3\. How much cloth will be required to make one shirt if to make 21 shirts 57 m 75 cm cloth is needed? ![](Sum up math-4_files/Sum20up20math-4-201.jpg)15 09e<J5UR€W€Dt of Time ![](Sum up math-4_files/Sum20up20math-4-202.jpg) You have learntthe measurement oftime in previous class. Let us recall that. Seethefigure ofawall clock as given here. The dial of a clock is divided into 12 equal parts and is labelled from 1 to 12. These numbers represents hours. When you will observe the clock minutely, you will see that two successive numbers are further divided into 5 small divisions. Thus a dial is divided into 5x12 = 60 divisions. Each of these small divisions representa minute. ![](Sum up math-4_files/Sum20up20math-4-203.jpg) There are two hands in a watch. One hand is longer and other is shorter. The shorter hand is called "hour hand" and longer hand is called "minute hand". It takes one hour to move from one number to next number by "hour hand". And longer hand that is "minute hand" goes once round the dial in one hour. Thus the "minute hand" has to cover 60 small divisions in one hour. Therefore 1 hour = 60 minutes. ![](Sum up math-4_files/Sum20up20math-4-204.jpg) READING TIME TO 5 MIN UTES CORRECTNESS See the figure. In this minute hand isat 6 and hour hand is between 1 and 2. The time is 30 minutes past. Or you can say it one-thirty. It is written as 1:30. It is called "half past one". Similarly, in the next figure you can see the minute hand is at 6 while hour hand is between 2 and 3. The time is 30 minutes past 2 or you can say it "half past two" or "two-thirty". It is written as 2:30. In next figure the "minute hand" is at 11 and hour hand is between 3 and 4. When you see minutely then you will see that "hour hand" is just before 4. The time is 55 minutes past 3 or three-fifty five. It is written as 3:55 It is generally said 5 to 4 or five minutes to four. READING TIME TOTHE NEAREST MINUTE In the given figure, the hour hand is between 1 and 2 and minute hand is between 6 and 7. \[136 ![](Sum up math-4_files/Sum20up20math-4-205.jpg) It shows thattime is between 1 O'clock between 2 O'clock. ![](Sum up math-4_files/Sum20up20math-4-206.jpg) When you will see minutely the minute hand, it is at 3 small division ahead of six. It shows that it has moved. 30 + 3 = 33 small division after 12. Thus the time is "33 minutes past 1" or "one thirty three". It is written as 1:33. It may be called "27minutesto2". Because 27 small divisions leftto reach the "minute hand" at12. ![](Sum up math-4_files/Sum20up20math-4-207.jpg) - Example 1: Read the time as given in figure. Solution: In the figure the time is "5 to 11" or ten-fifty five. It is written as 10:55. ###### JX EXERCISE SS J 1\. Read the figure of watches and complete the sentences : (a) The time is minutes past or the time is minutes to . It is written in symbol as . (b) The time is minutes past or the time is minutes to . It is written in symbol as . (c) The time is minutes past the time is minutes to . It is written in symbol as . (d) The time is minutes to minutes past . The time is . It is written in symbol as . (e) The time is minute to minutes past . The symbol is . The time is (f) The time is minutes to minutes past It is written symbol as . The time is ![](Sum up math-4_files/Sum20up20math-4-208.jpg) 2\. Draw the minute hand to show the time given below for each watch : ![](Sum up math-4_files/Sum20up20math-4-209.jpg)![](Sum up math-4_files/Sum20up20math-4-210.jpg)4:40 5:49 7:51 ![](Sum up math-4_files/Sum20up20math-4-211.jpg)3:12 4:22 1:52 - 3\. Match the time with watch given : - (a) 3:52 (b) 4:10 (c) 5:15 (d) 6:30 ![](Sum up math-4_files/Sum20up20math-4-212.jpg) USE OF A.M. AND P.M. You know that the time from one midnight to next midnight is called a day. The hour hand moves twice round the dial in a day. Hour hand takes 12 hours to complete one round therefore it completes two round in 24 hours that is in a day. Therefore, 1 day = 24 hours As "hour hand" moves twice round the dial so it is clear that hour hand shows the same time twice in a day. So, to show 5'clock in the morning a.m., is used and to show 5'clock in theevening, p.m. is used. Therefore, 5:00 a.m. is written to show 5 O'clock in the morning. 5:00 p.m. is written to show 5 O'clock in the evening. ![](Sum up math-4_files/Sum20up20math-4-213.jpg) ###### EXERCISE 57 f ![](Sum up math-4_files/Sum20up20math-4-214.jpg)5:00 in the morning ![](Sum up math-4_files/Sum20up20math-4-215.jpg)5:00 in the evening - 1\. Read the watches given below and write the time using a.m. or p.m.: ![](Sum up math-4_files/Sum20up20math-4-216.jpg)School opens ![](Sum up math-4_files/Sum20up20math-4-217.jpg) (c) ![](Sum up math-4_files/Sum20up20math-4-218.jpg)I go to play at ![](Sum up math-4_files/Sum20up20math-4-219.jpg) Papa goes to office at . ![](Sum up math-4_files/Sum20up20math-4-220.jpg)I go in bed to sleep at . ![](Sum up math-4_files/Sum20up20math-4-221.jpg) ![](Sum up math-4_files/Sum20up20math-4-222.jpg) - 2\. Fill inthe blanks with a. m.orp.m.: - (a) Rahul came to meet me in evening at 7:30 - (b) Papa returns from office in evening at 8:00 - (c) The sun rises in the east at 5:15 - (d) We take dinner at 9:30 . - (e) I return after playing at 6:30 - 3\. Writethetimeand usea.m. orp.m.: - (a) 15 minutes after 1:15 a.m. - (b) 1 hourafter 11:30 p.m. . - (c) 2 hour 30 minutes after 10:00 a.m. - (d) 2 hour 15 minutes after 6:00 p.m. - (e) 32 minutes after 11:30 a.m. 24-HOURCLOCKTIME Apart from saying or writing time in a.m. orp.m. There is another way to write the fore noon and afternoon time. This is known as 24-hour clock time. Using24-hourclocktime 1:00 p.m. is written as 1300 hours. Similarly 2:00 p.m. is written as 1400 hours. In this method 12 O'clock mid night is written as 0000 hours and 12 O'clock noon is written as 1200 hours. - Example 1: Express the time given before in 24-hour clock time. (a) 6:00 a.m. (b) 6:00 p.m. Solution: (a) 6:00a.m.—► 0600hours (c) 4:00 a.m.—>0400 hours (c) 4:00 a.m. (b) 4:00 p.m. (b) 6:00 p.m. —► 1800 hours (d) 4:00 p.m. —► 1600 hours ###### g. EXEHG1SB 58 %•--- - 1\. Writethetimegiven below using24-hourclocktime— (a) 12:00 noon (b) 12:00 o'clock midnight (c) 7:00 a.m. (f) 10:00 a.m. (d) 9:00 p.m. (e) 10:00 p.m. - 2\. Write the following using 12-hourclocktime: - (a) 1700 hours (b) 0100 hours (c) 1300 hours (d) 1900 hours (e) 0300 hours TIME DURATION OF AN ACTIVITY The difference between starting and finishing time shows the duration of activity. To calculate the time of activity do the following: - • Write the time in column form - • Subtract the starting time from finishing time. - Example 1: Train starts at 9:00 a.m. and reached the destination at 11:00 a.m. calculation the travelingtime of train. Solution: Writethetime in column form. hours minutes [1100](#bookmark599) [Finishingtime —> (-) 0900](#bookmark600) [Starti ng time —\* 200](#bookmark601) Therefore duration = 2:00 hours - Example 2: Science class starts at 11:30 a.m. and it finishes at 12:15 p.m. calculate the duration of time. Solution : 1 st method — ![](Sum up math-4_files/Sum20up20math-4-223.jpg) ![](Sum up math-4_files/Sum20up20math-4-224.jpg) ![](Sum up math-4_files/Sum20up20math-4-225.jpg) After 30 minutes After 15 minutes So, duration of class = 30 minutes + 15 minutes = 45 minutes Get Set Go With Sum Up Mathematics-4 ![](Sum up math-4_files/Sum20up20math-4-226.jpg) 2nd method - Time from 11:30 am to 12:00 noon - 30 minutes 12:00 noon to 12:15 p.m. - 15 minutes Total duration of time - Total time = 30 minutes + 1 5 minutes = 45 minutes - Example 3: Ramesh started from New Delhi at 10:30 a.m. and reached Kanpur at 4:00 p.m. calculate the total duration of time. Solution : Time taken from ![](Sum up math-4_files/Sum20up20math-4-227.jpg) 10:30a.m. to 11:00 a.m. = 30minutes 11:00 a.m. to 12:00 p.m. = 1 hours 12:00 p.m. to4:00 p.m. = 4 hours So total time of travelling = 4 hours + 1 hour + 30 minutes = 5 hours + 30 minutes = 5 hours 30 minutes FINISHING OF AN ACTIVITY If starting time and duration of activity is given, you can calculate the finishing time of an activity. - (a) Ramesh started his homework at 5:30 p.m. and he finished it in 1 hour. Then calculate the finishing time. Solution— The finishing time will be 1 hour after 5:30 p.m. that is 6 : 30 p.m. ![](Sum up math-4_files/Sum20up20math-4-228.jpg) ###### EXERCISE 59 %\*------- - 1\. Find the duration of time between : - (a) 8:00 a.m. to 11:00 am (b) 1:00 p.m. to 4:00 p.m. \_ (c) 6: 20 a.m. 7:15 a.m. (d) 8:15 a.m. to 9:30 a.m. ![](Sum up math-4_files/Sum20up20math-4-229.jpg) ![](Sum up math-4_files/Sum20up20math-4-230.jpg) - (e) 10:30p.m.to 12:30a.m. - (g) 1520 hours to 1840 hours How many minutes pass between : (a) 2 O'clock and half pastthree ? (c) Half past 9 and quarter past 10 ? Find the time. Usea.m. orp.m. - (a) 30 minute after 1:30 p.m. - (c) 15 minutes after 1:00 a.m. (f) 1400 hours to 1820 hours (h) 7:00a.m. to4:00 p.m. - (b) 2 O'clock and 15 to four ? - (d) 0100 hourand 0330 hours ? - (b) 45 minutes after 11:30 p.m. - (d) 1 hours 30 minutes after 11:00 p.m Rahul takes 50 minutes to reach school from his home. If he starts at 6:15 a.m. at what time does he reach school ? - 5\. Radha goes to play at 6:00 p.m. and she came back after 30 m i nutes. When does she come back? - 6\. Ankit goes to school at 0600 hours and he returns back at 1400 hours. After how many hour does he returns back ? - 7\. A trains leaves Delhi at 1200 hours and reaches Kanpur at 1710 hours. It starts again from Kanpur at 1750 hours and reaches again at Delhi at 2315 hours. Calculate the duration of time from : - (a) Delhi to Kanpur (b) Kanpurto Delhi - 8\. A flight leaves Kolkata at 0500 hours and reaches Shillong at 0730 hours. Again it starts from Shillong at 0915 hoursand reaches Kolkata at 1125 hours. Calculate: - (a) Duration offlightfrom Kolkata to Shillong. - (b) Duration offlightfrom Shillongto Kolkata. - (c) Duration of time starting from Kolkata and return at Kolkata. - 9\. Cricket match started at 9:00 a.m. and due to rain it stopped at 11:15 a.m., again it started at 2:15 p.m. and ended at 5:00 p.m. Calculate the duration of match played. - 10\. The "three idiot" movie started at 5:00 p.m. but because other four idiots in the cinema hall, manager had to stop it before the interval at 6:05 p.m. Calculate the duration of movie played. - 11\. A man starts fasting at 9:15 a.m. but because of some unknown reason he broke the fast after 3 hours 15 minutes only. At what time he broke his fast? ![](Sum up math-4_files/Sum20up20math-4-231.jpg)INTERPRETING A CALENDER You know that there are 7 days i n a week. The order of the days of the week is given below - - 1\. Monday 2. Tuesday 3. Wednesday - 4\. Thursday 5. Friday 6. Saturday - 7\. Sunday There are 12 months in a year. The names and order of month with number of days are given below: 1\. January — 31 days 2\. February — 28 days 3\. March — 31 days 4\. April — 30 days 5\. May — 31 days 6\. June — 30 days 7\. July — 31 days 8\. August — 31 days 9\. September — 30 days 10\. October — 31 days 11\. November — 30 days Span of 10 years is called a Decade and the 12\. December — 31 days Span of 100 years is called a Century. There are 365 days in ayear. But in a leap year there are 366 days. In a leap year the number of days become 29 in the month of February, while the numberofdays isonly 28 in February in a normal year. Theyearwhich isdivided exactly by4 isa leap year. - Example 1: 2004,2008,2012 etc. are leap years as these are divided exactly by 4. a complete year like 1200, 1500, 1300, 1100 will be a leap year if it is exactly divisible by 400, otherwise it will bea normal year. Look the calender of 2014 showing months of January and February. ![](Sum up math-4_files/Sum20up20math-4-232.jpg) May Year-2014 June 4 11 18 25 Sunday 1 8 15 22 29 5 12 19 26 Monday 2 9 16 23 30 6 13 20 27 Tuesday 3 10 17 24 7 14 21 28 Wednesday 4 11 18 25 1 8 15 22 29 Thursday 5 12 19 26 2 9 16 23 30 Friday 6 13 20 27 3 10 17 24 31 Saturday 7 14 21 28 You can see that the same day comes after seven days. Answer the following questions - - 1\. The month of May starts from which day of the week ? - 2\. On which day of the week? - 3\. The third Saturday falls on which date in the month ofjune ? - 4\. On whatday ofthe week last day ofjune falls ? - 5\. Is this a leap year ? - 6\. How many days these are in June 2014 ? - 7\. How many days are in the year of 2014 ? Solution: - 1\. Thursday 2. Saturday 3. 21st 4. Monday - 5\. No 6. 30 7. 365 CALCULATION OF TOTAL NUMBERS OF DAYS BETWEEN TWO DATES Observe the calender of year 2014 and answer the following question. Question: How many days are there in between 4th January and 15th January ? Solution: Subtract the day before starting date from latter date. - .•. Required number of days = 15-3 = 12 days Question : Rakesh went to his native place on 15th of March and returned back on 10th April. For how many days he was on tour ? Solution: Days in March = 31-14 = 17days Days in April = 9 days .•. Rakesh was on tour for 1 7 + 9 = 26 days FINDING THE DATE BEFORE OR AFTER SOME DAYS - Example 1: Ankittold Rakesh on 27th May that terminal exam would start after 1 7 days. Calculate the date of terminal exam. Solution: No of days left in May = 31-26 = 5 days Remaining days = 17-5 = 12 days - .•. Terminal exam will be started from 13th June. \-- DATE OF BIRTH-IN SHORT FORM - Example 2: If the date of birth of Rakesh is 15th October 1998. Write it short form. Solution: 15 10 1998 Day Month Year Short form of his birthdate - 15-10-1998. It is mandatory to mark the manufacturing and expiry dates on the medicine and packed food items. Take a bottle of medicine or strip of medicine, or a packet of biscuit or any other food item. Observe the manufacturing and expiry dates written on the packet. These are written in different format as Manufacturing date : 04/07 means April, 2007 Expiry date : 08/10 means August, 2010 Example: Write the fol lowing dates in short form : (a) 20th July 2011 (b) 17th June 2005 Solution: - (a) 20-07-2011 or 20.7.2011 (b) 17-06-2005 or 17.6.2005 ###### ^. EXERCISE 60 “3------------- - 1\. How many days are the from : - (a) 12 March to 28 March ? (b) 1 7 March to 12 July ? (c) 12 February 2012 to 1 7 April 2012 ? (d) 7th January to 28 February ? - 2\. Monu's school closed on 1 7th May for summer vacation and will reopen on 2nd July. How many days are summer vacation. - 3\. Rahul left Kolkata on 21 st August and came back on 1 7th September. For how many days was he in tour ? - 4\. Rani came to Ranju's house in summer vacation on 15th June and leave for her home on 1 stjuly. Find the duration of summer vacation ? - 5\. Amit joined a company on 2nd January and left the job on 1 7th February. For how many days did he worked ? - 6\. Ravindrafell sick on 12th March and recovered on 5th April. For how many days was he ill ? - 7\. Rahul returned a book to his friend on 17th September after 14 days. On which date he took the book ? - 8\. The birth date of Ajeet is 27th November 1985. Write this date in short form. - 9\. The expiry date of a medicine on its pack has been written as 07/12. What is the date of expiry ? - 10\. Write in short form : - (a) 25th September 2010 - 11\. Write the followingdate in longform : - (a) 16.1.1972 (b) 15th August 1947 (b) 14.7.2000 ![](Sum up math-4_files/Sum20up20math-4-233.jpg) ![](Sum up math-4_files/Sum20up20math-4-234.jpg) Let us recapitulate what you have learnt about lines and curves and about some plane figuresand solids, in earlier classes. LINE In the given figure, AB is a line. A line has no end points and it can be A B extended to any length on both sides. A line has no length. Some times a line is also shown by a small letter, ( 1 > like /. Line AB can be written as A B (b) Curved < line There are two types of line: - (a) Straight < line ![](Sum up math-4_files/Sum20up20math-4-235.png)Straight Line ![](Sum up math-4_files/Sum20up20math-4-236.jpg)Curved Line LINE SEGMENT A part of a line is called a line segment. In the given figure, AB is a line segment. There are two end points in a line segment. A line segment has a fixed length and so it can be measured. Line segment AB can be written as AB. A B CURVES Following figures show examples of curves: ![](Sum up math-4_files/Sum20up20math-4-237.png) ![](Sum up math-4_files/Sum20up20math-4-238.jpg) Closed Curves ![](Sum up math-4_files/Sum20up20math-4-239.jpg) A closed curve which does not cross itself is called a simple closed curve. ![](Sum up math-4_files/Sum20up20math-4-240.png)Simple Closed Curves ![](Sum up math-4_files/Sum20up20math-4-241.png) Complete Closed Curves ![](Sum up math-4_files/Sum20up20math-4-242.png) ![](Sum up math-4_files/Sum20up20math-4-243.png) ![](Sum up math-4_files/Sum20up20math-4-244.png) Closed curves made of line segments Closed curve not made of line segments POLYGON Polygon isasimplecurve which is made of line segment. Examples of polygon: ![](Sum up math-4_files/Sum20up20math-4-245.png) TYPE OF POLYGONS Triangle : The polygon which is made of 3 line segments is called triangle. ![](Sum up math-4_files/Sum20up20math-4-246.png) ![](Sum up math-4_files/Sum20up20math-4-247.png) ![](Sum up math-4_files/Sum20up20math-4-248.png) Line segments which make a triangle are called its sides. The meeting point of two sides is cal led a vertex. ![](Sum up math-4_files/Sum20up20math-4-249.jpg) Quadrilateral: A polygon which is made by 4 line segments is called quadrilateral. In this figure ABCD is a quadrilateral AB, BC, CD and AD are the A four sides of the quadrilateral. A, B, Cand D are the four vertices of the quadrilateral. AC is the diagonal of the quadrilateral. The line segment joining two opposite vertices of a quadri lateral is cal led its diagonal. Which istheotherdiagonal ofquadrilateral ABCD ? Square Rectangle Square and rectangle are special type ofquadrilateral. LAB ACTIVITY Draw a circle with a compass. IstStep : Fixapencil inthecompass. 2nd Step : Open the compass to a suitable length. 3rd Step : Make apointOon the paper. 4thStep : FixthemetallicpointedendofcompassatO. 5th Step : Touch the paper with pencil. 6th Step : Keep the metal I ic poi nt fixed at O and rotate the penci I to make a ci rcle. TERMS RELATED TO A CIRCLE Look at this figure. O is the centre of the circle. OA, OB and OC are the radius of the / / circle. The distance from the centre to the edge of the circle is called / / „ / radius. A B isthediametre of circle. D E is the chord of the circle. LAB ACTIVITY Finding the centre of a circle. IstStep : Draw a circle on a paperwith the help of a bangle. -^ 2nd Step : Cut out the circle. 3rd Step : Fold the circular sheet of paper into two halves. Press to form a crease. ![](Sum up math-4_files/Sum20up20math-4-250.jpg) 4th Step : Fold once again to get a shape as shown in the figure. Press to form a crease. 5thStep : Unfold the paper. You will get two creases. The point where the two creases cross each other is the centre of the circle. Relationship Between Radius and Diametre ![](Sum up math-4_files/Sum20up20math-4-251.jpg) In this figure; O C is the radius of the circle. OC = OA = OB Measure OC and A B you will find, A B = 2 OC Diameter = 2 x Radius It can be said that diameter is twice the radius. - Example 1: If the radius of a circle is 4 cm, find its diameter. Solution: Diameter = 2 x Radius = 2 x 4 cm = 8 cm ![](Sum up math-4_files/Sum20up20math-4-252.jpg) ###### EXERCISE 61 v - 1\. Which ofthese are simple closed curves ? ![](Sum up math-4_files/Sum20up20math-4-253.jpg) ![](Sum up math-4_files/Sum20up20math-4-254.jpg) ![](Sum up math-4_files/Sum20up20math-4-255.png) ![](Sum up math-4_files/Sum20up20math-4-256.jpg)(b) ![](Sum up math-4_files/Sum20up20math-4-257.jpg) ![](Sum up math-4_files/Sum20up20math-4-258.png) ![](Sum up math-4_files/Sum20up20math-4-259.jpg) In thefigure A B C D is a quadrilateral: AB = BC = CD = AD. What other name can be given to this quadrilateral. ![](Sum up math-4_files/Sum20up20math-4-260.png) ![](Sum up math-4_files/Sum20up20math-4-261.png)D In thefigure A B C D is a quadrilateral. Name the following: (a) (b) ![](Sum up math-4_files/Sum20up20math-4-262.jpg) Opposite sides Opposite vertices Diagonals ![](Sum up math-4_files/Sum20up20math-4-263.png) ![](Sum up math-4_files/Sum20up20math-4-264.jpg) ![](Sum up math-4_files/Sum20up20math-4-265.jpg) In the given figure name the following parts of the circle: (a) Centre (b) Radius ![](Sum up math-4_files/Sum20up20math-4-266.png) MEASURING A LINE SEGMENT Take the ruler from your instrument box. This ruler can measure a line segment up to 15 cm or upto 6 inch in length. In the given figure the ruler is placed so that O on the ruler is at the point A of line segment AB. ![](Sum up math-4_files/Sum20up20math-4-267.png) The point B coincides with 2 on the ruler. .-. Line segment AB is 2cm long. ![](Sum up math-4_files/Sum20up20math-4-268.jpg) ![](Sum up math-4_files/Sum20up20math-4-269.jpg)Look at this figure. Each centimeteron the ruler is divided into 10 equal parts. 10 mm llll|llll|llll|llll| cm 1 2 Each small part shows 1 millimetre. A B 11111111111111111111111111111111111111111111111111 1 2 3 4 5 Length of the line segment AB is more than 2cm but less than 3cm. Point B is 5 points ahead of 2cm. Soz it is 5 mm ahead of 2cm. .•. Length of AB is 2cm 5mm. DRAWING A LINE SEGMENT Draw a line segment of length 3cm. A B ![](Sum up math-4_files/Sum20up20math-4-270.png)12 3 4 1st Step : Mark a point A. 2nd Step : Place the rulerand ensure that its O coincides with A. 3rd Step : Markthe point B which coincides with 3 ofthe ruler. 4thStep : Drawa line joiningAand B. 5th Step : AB = 3cm Drawaline segment of length 5cm 11111111111111111111111111111111111111111111111111 1 2 3 4 5 1st Step : Mark a point A. 2nd Step : Place the ruler and ensure that its O coincides with A. 3rd Step : Markthe point B which coincides with 5 ofthe ruler. 4th Step : Drawa linejoiningAand B. 5th Step : AB = 5cm. Get Set Go With Sum Up Mathematics-4 ![](Sum up math-4_files/Sum20up20math-4-271.jpg) ###### {J. EXERCISE 62^------------- (b) 1\. Measure the following line segment: (a) A B 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 123456789 1 2 3 4 5 6 7 8 9 (C) A B 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 123456789 (d) A B 111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 123456789 ![](Sum up math-4_files/Sum20up20math-4-272.jpg) Draw line segments of following lengths : (a) 4 cm (b) 7 cm (c) 9 cm (d) 11 cm PERIMETEROF A FIGURE Length of all sides of a polygon is called perimeter. Perimeter is used in many cases. When a plot of land needs to be fenced we need to measure the perimeter of the field. - Example 1: In the given figure lengths of sides of the triangle ABC are given. Find the perimeter of the triangle. Solution: Perimeterof A ABC = AB + BC + AC = 5+7+6 = 18 cm. ![](Sum up math-4_files/Sum20up20math-4-273.png) A 60 cm ![](Sum up math-4_files/Sum20up20math-4-274.jpg)3 - Example 2: In the given figure lengths of sides of rectangle ABCD are given. Find the perimeter of the rectangle. Solution : AB = CD = 60cm BC = AD = 40cm Perimeter of rectangle ABCD = AB + BC + CD + AD = 60 + 40 + 60 + 40 = 200 cm ![](Sum up math-4_files/Sum20up20math-4-275.jpg) ###### EXERCISE 63 v 1\. Find the perimeters offollowingfigures : ![](Sum up math-4_files/Sum20up20math-4-276.jpg) - 2\. Find the perimeters of triangle whose sides are: (a) 15cm, 14cm, 13cm (b) 15cm, 12cm, 9cm - 3\. Find the perimeters of rectangles whose lengths and breadths are given below : - (a) Length = 8cm breadth = 1 7cm (b) Length = 55m breadth = 33m - 4\. Find the perimeters of squares whose sides are given below : (b) 18cm - 5\. Raju wants to fix cello tape around writing board. The length of writing board is 35cm and its breadth is 25cm. What is the length of cello tape needed by Raju ? - 6\. A garden is in rectangular shape. It is 30 feet long and 12 feet wide. How much barbed wire is needed forfencingthe garden ? - 7\. All sides of a carrom board are 60cm long. What is the length of the wooden beat which is fixed around the carrom board ? - 8\. A park is in rectangular shape. It is 120 cm wide and 300 m long. How much distance Priyanka has to cover if she makes one round of the park ? AREA Area gives the measurement of a region bounded by ashape. ^ ^ 2 3 4 B In the given figure the quadrilateral ABCD is covered by 4 1 tiles in a row and 4 tiles in a column. Which is divided into 4---- rows & 4 columns. Let us assume that all tiles are in the shape of a square. 3 Total number of square tiles = 4x4 = 16 4 It can be said that the area of quadrilateral ABCD is equal to 16 square tiles, or 16 square units. If one side of the square is 1 cm then the area of quad ri lateral ABCD is 16 square cm. Finding the Area using a Squared Paper. Squared paper can be used for finding the area of most of the figures. For this, following steps should be followed. 1st Step : Place the figure on a squared paper. Cover the maximum possible number of complete squares. 2nd Step : Count the number of complete squares. 3rdStep : .Count the number of half squares. Area of 2 half squares will givearea of - 1 complete square. 4th Step : Find the total area by adding areas ofcomplete squares and half squares. Example 1: Find the area of the shaded figures if the area of a square is 1 square cm. (a) ![](Sum up math-4_files/Sum20up20math-4-277.jpg) Solution (a): Solution (b): Number of complete squares = 13 Area = 13 square units = 13 square cm Number of complete squares = 7 Numberof half squares = 8 Area = \[7 +16 x 8\] square units = (7 + 4) square units = 11 square units ![](Sum up math-4_files/Sum20up20math-4-278.jpg) = 11 square cm ###### EXERCISE GM -------------- - 1\. Find the area of shaded figures. Assume that area of each square is 1 square centimetres. ![](Sum up math-4_files/Sum20up20math-4-279.jpg) (d) (e) ![](Sum up math-4_files/Sum20up20math-4-280.jpg) NETS OF SOLIDS Let us recall some key points about cubes and cuboids. Cube : A cube has six faces. Al I sides of a cube are equal. Al I faces of a cube are squares. Cuboid : Opposite facesofa cuboid are similar. When a hollow cube is opened by keeping all its faces intact, we get the net of the cube. LAB ACTIVITY Make the net of a given cube. (a) 1st Step : Take a hollow cubical box of card hoard ![](Sum up math-4_files/Sum20up20math-4-281.jpg) ![](Sum up math-4_files/Sum20up20math-4-282.jpg) 2nd Step: Open its top by a scissor. ![](Sum up math-4_files/Sum20up20math-4-283.jpg) ![](Sum up math-4_files/Sum20up20math-4-284.jpg) / //(c) Get Set Go With Sum Up Mathematics-4 (b) 3rd Step : Open its front face. ![](Sum up math-4_files/Sum20up20math-4-285.jpg) ![](Sum up math-4_files/Sum20up20math-4-286.jpg) ![](Sum up math-4_files/Sum20up20math-4-287.jpg) 4th Step : After opening all the faces you will get a shape as shown in this figure. This is the net of the cube. ![](Sum up math-4_files/Sum20up20math-4-288.jpg) Fold the shape as shown in this figure. You will get a cube without cover. Fold the shape as shown in this figure. You will get a cube with no top and no bottom. ![](Sum up math-4_files/Sum20up20math-4-289.jpg) DRAWING OF SOLIDS Let us use Isometric Dot paper to draw a cube and a cuboid. All dots are equidistant in isometric dot paper. ![](Sum up math-4_files/Sum20up20math-4-290.jpg) A cuboid is drawn in this figure. Draw a cube by same method. ![](Sum up math-4_files/Sum20up20math-4-291.jpg) ###### Q. EXERCISE 65 v - 1\. Trace these nets on a cardboard. Cut along the boundary lines. Fold along the dotted Iines to make cubes and cuboids. (c) - 2\. Complete the following figures to make a cube or a cuboid : ![](Sum up math-4_files/Sum20up20math-4-292.jpg) VIEWS OF AN OBJECT If an object is viewed from the top, it is cal led plan of the object. If an object is viewed from the front, it is cal led elevation of the object. If an object is viewed from the side, it is cal led side view of the object. ![](Sum up math-4_files/Sum20up20math-4-293.jpg) ![](Sum up math-4_files/Sum20up20math-4-294.jpg) ![](Sum up math-4_files/Sum20up20math-4-295.jpg) ![](Sum up math-4_files/Sum20up20math-4-296.jpg) ![](Sum up math-4_files/Sum20up20math-4-297.jpg) ###### J. EXERCISE 66 । - 1\. Draw the elevation of a book. - 2\. Draw the side new of a cone. - 3\. Match the object with its elevation. ![](Sum up math-4_files/Sum20up20math-4-298.jpg) ![](Sum up math-4_files/Sum20up20math-4-299.jpg) ![](Sum up math-4_files/Sum20up20math-4-300.jpg) ![](Sum up math-4_files/Sum20up20math-4-301.jpg) TILING A FLOOR In most of the modern homes you will see tiles. Tiles make floors and walls beautiful. You will notice that certain types of polygons are used for tiling. Not all closed curves can be used for tiling. For example, a circular file or a star-shaped tile can't be used for tiling a floor. Why is it so? Ask your teacher for answer. Examples of tiles: ![](Sum up math-4_files/Sum20up20math-4-302.jpg)Single type of tiles ![](Sum up math-4_files/Sum20up20math-4-303.jpg)Two types of tiles ###### {£. EXERCISE 67 J Selectthe tiles which can be used for tiling the floor: ![](Sum up math-4_files/Sum20up20math-4-304.jpg) ![](Sum up math-4_files/Sum20up20math-4-305.jpg) SYMMETRY When a figure can be folded into two equal halves along a line, it is called a symmetrical figure. Lookatfollowingexamples. ![](Sum up math-4_files/Sum20up20math-4-306.jpg) ![](Sum up math-4_files/Sum20up20math-4-307.jpg) You can trace these figures on a paper and fold to see their symmetry. The line which divides a figure in two equal halves is called the line ofsymmetry or mirror line. LAB ACTIVITY ![](Sum up math-4_files/Sum20up20math-4-308.jpg) ![](Sum up math-4_files/Sum20up20math-4-309.jpg) ![](Sum up math-4_files/Sum20up20math-4-310.jpg) 1st Step : Take a sheet of paper. 2nd Step: Fold itfrom the middle. 3rd Step : Draw a shape as shown. 4thStep : Cutalongthe lineoftheshape. 5th Step : Unfold the shape to get a figure. Trace these figures on a sheet of paper to find if they are symmetrical or not: ![](Sum up math-4_files/Sum20up20math-4-311.jpg) ![](Sum up math-4_files/Sum20up20math-4-312.jpg) ![](Sum up math-4_files/Sum20up20math-4-313.jpg) ![](Sum up math-4_files/Sum20up20math-4-314.jpg)Find their mirror lines also. Some figures can have more than one line of symmetry. Look at fol lowing examples. ![](Sum up math-4_files/Sum20up20math-4-315.jpg) ![](Sum up math-4_files/Sum20up20math-4-316.png) ###### £g. EXERCISE 68 s ![](Sum up math-4_files/Sum20up20math-4-317.jpg) ![](Sum up math-4_files/Sum20up20math-4-318.jpg)## 3 WRV72 3\. Find the lines of symmetry in these figures: ![](Sum up math-4_files/Sum20up20math-4-319.jpg)![](Sum up math-4_files/Sum20up20math-4-320.jpg) ![](Sum up math-4_files/Sum20up20math-4-321.jpg) GEOMETRICAL PATTERNS You can see many geometrical patterns in daily life. Geometrical patterns are used in making beautiful designs. Following are some examples of geometrical patterns. ![](Sum up math-4_files/Sum20up20math-4-322.jpg) ![](Sum up math-4_files/Sum20up20math-4-323.jpg) ![](Sum up math-4_files/Sum20up20math-4-324.jpg) LAB ACTIVITY Let us make some geometrical patterns. Take chart papers of two colours. A. 1st Step : Cut similar sized squares from both chart papers. 2nd Step : Paste these squares on another chart paper. 3rd Step : You can make many designs. Some examples are given below: B. ![](Sum up math-4_files/Sum20up20math-4-325.jpg) 1st Step : Cut bigger squares from a chart paper of one colour. 2nd Step : Cut smaller squares from a chart paper of another colour. 3rd Step : Make some interesting designs usingthese squares. ![](Sum up math-4_files/Sum20up20math-4-326.jpg) ![](Sum up math-4_files/Sum20up20math-4-327.jpg) ![](Sum up math-4_files/Sum20up20math-4-328.jpg) NUMBER PATTERNS In earlier classes you have read about simple number patterns. Let us try to understand patterns and learn some mathematical concepts through these patterns. PATTERNS IN ADDITION AND SUBTRACTION - Example 1: Let us see the pattern of sum of 3 consecutive numbers. Complete the series after that. 1+2+3 = 6 2+3+4 = 9 3+4 + 5 = 12 5+6+7 = 7+5+9 = 9 + 10 + 11 = 10+11+12 = Solution: 1+2 + 3 = 6 (3 X 2 = 6) 2+3+4 = 9 (3 X 3 = 9) 3+4+5 = 12 (3 X 4 = 12) 5+6+7 = 18 (3 X 6 = 18) 7+8+9 = 24 (3 X 8 = 24) 9 + 10 + 11 = 30 (3 X 10 = 30) 10 + 11+12 = 33 (3 X 11 = 33) Example 2: Let us see the pattern of sum of the first counting numbers. Complete the series after that. 1+2 = 3 - 1 + 2 + 3 = 6 1+2 + 3+ 4 = 10 1+2 + 3+ 4 + 5 = 15 ![](Sum up math-4_files/Sum20up20math-4-329.jpg) 1+2 + 3+ 4 + 5 + 6 = 21 Get Set Go With Sum Up Mathematics-4 1+2 + 3+ 4 + 5 + 6+ 7 = 28 1+2+3+4+5+6+7+8= 1+2+3+4+5+6+7+8+9= 1 + 2 + 3+ 4 + 5 + 6 + 7 + 8 + 9+10 = 1+2+3+4+5+6+7+8+9+10+11= Solution: 1 + 2 = 3 = 3 x 1 1+2+3=6=3x2 1+2 + 3+ 4 = 10 = 5x2 1+2 + 3+ 4 + 5 = 15 = 5x3 1+2 + 3+ 4 + 5 + 6 = 21=7x3 1+2+3+4+5+6+7=28=7x4 Observation: In case of even number ofterms the sum is equal to the product of following: (numbers of terms +1) x 1/2 number ofterms. In case of odd number ofterms the sum is equal to the productoffollowing: Last term x Middle term. .•. 1+2 + 3+ 4 + 5 + 6+ 7 + 8 (even number ofterms) = (8+1)x4 = 9x4 = 36 1 + 2 + 3+ 4 + 5 + 6+ 7 + 8 + 9 (odd number ofterms) = 9 x 5 = 45 1 + 2 + 3+ 4 + 5 + 6 + 7 + 8 + 9+10 = (10 + 1) x 5 = 11 x 5 = 55 1 + 2 + 3+ 4 + 5 + 6+ 7 + 8 + 9 + 10 + 11 = 11 x 6 = 66 - Example 3: Let us seethe pattern ofsum of odd numbers. Complete the series afterthat. 1+3=4 1 + 3 + 5 = 9 1+3 + 5 + 7=16 1+3+5+7+9= ![](Sum up math-4_files/Sum20up20math-4-330.jpg)Solution: 1+3=4=2x2 1+3 + 5 = 9 = 3x3 1+3 + 5 + 7=16 = 4x4 Observation: Numberofterms x Numberofterms = Sum 1+3 + 5 + 7 + 9 = 5x5 = 25 1+3 + 5 + 7 + 9 + 11 =6x6 = 36 1+3 + 5 + 7 + 9 + 11+13 = 7x7 = 49 - Example 4: Look at these patternsand fill the missing terms: - (a) 45 30 20 5 (b) Zfn Solution (a): The numbers in the second row are obtained by taking difference of two consecutive numbers in the previous row: 45-30 = 15 45 30 20 5 30-20 = 10 15 10 15 20-5 = 15 5 5 Solution (b) : The difference of opposite number is 7 Hence; 10-7 = 3 5 + 7 =12 Example: Study the arrangement in this number pyramid. After that add two more rows : ![](Sum up math-4_files/Sum20up20math-4-331.jpg) Solution : ![](Sum up math-4_files/Sum20up20math-4-332.jpg) ![](Sum up math-4_files/Sum20up20math-4-333.jpg) Numbers in next row can be written as follows : 1 4 6 4 1 \\ \\ \\ \\ Z 1 5 10 10 5 1 \\ Z \\ Z \\ Z \\ / \\ Z 1 1 6 15 20 15 6 - j. EXERCISE 69 “/------------- - 1\. Observe the pattern and fill in the blanks : - [(a) 3 6 9 12 • • ••](#bookmark706) - <b> « 4» 14 » 3 0 0 - [(c) 10 30 50 □□□□](#bookmark707) - (d) m^w^vw - [2. 3+4+5+6+7= 25](#bookmark708) [4+5+6+7+8= 30](#bookmark709) - [(a) 5 + 6 + 7 + 8 + 9=](#bookmark710) - (b) 7 + 8 + 9+10 + 11 = - (c) 9+10 + 11+12 + 13 = - [3. 2 + 4 + 6=12](#bookmark711) [4 + 6 + 8=18](#bookmark712) [6 + 8 + 10=24](#bookmark713) - (a) 12 + 14 + 16 = - (b) 20 + 22 + 24 = - [4. 2 + 4 + 6 + 8 + 10=30](#bookmark714) [4 + 6 + 8+10+12=40](#bookmark715) ![](Sum up math-4_files/Sum20up20math-4-334.jpg) - (a) 12 + 14 + 16 + 18 + 20 = - (b) 14 + 16 + 18 + 20 + 22 = - [5. 1 + 3 + 5 + 7 =16](#bookmark716) 1+3+5+7+9 = 25 - [(a) 1+3 + 5 + 7 + 9 + 11+13 + 15=](#bookmark717) - (b) 1+3 + 5 + 7 + 9 + 11+13 + 15 + 17+19 = - [6. 1+2 + 3+ 4 + 5 + 6=21](#bookmark718) [1+2 + 3+ 4 + 5 + 6+ 7 + 8=36](#bookmark719) - [(a) 1+2 + 3+ 4 + 5 + 6+ 7 + 8 + 9 + 10=](#bookmark720) - [(b) 1+2 + 3+ 4 + 5 + 6 + 7 + 8 + 9+10 + 11 +12 =](#bookmark721) - 7\. Study the patternsand fill the missingterm. One is solved for example: ![](Sum up math-4_files/Sum20up20math-4-335.jpg) - 8\. Study the fol lowi ng pattern and write next three terms: - [(a) 9,16,25 ,,](#bookmark722) - [(b) 11,121,1331,14441, ,,](#bookmark723) - [(c) 3,5,7,11,13, ,,](#bookmark724) PATTERNS IN MULTIPLICATION AND DIVISION Have you careful ly observed the table of 9? 1\[\] \[18\]^7|^\[45\]^4l\[63l^2l\[8^\[90 ![](Sum up math-4_files/Sum20up20math-4-336.jpg) In all numbers the sum of digits is 9. Get Set Go With Sum Up Mathematics-4 ![](Sum up math-4_files/Sum20up20math-4-337.jpg) Casting out 9 Let us take the number 4352 Digital sum = 4 + 3 + 5 + 2 = 14 Further sum of digits = 1 +4 = 5 We can also see that 14 - 9 = 5 So casting out 9 from the digit sum of a number gives the digit sum ofthe digit sum. Let us take another number 5067 Digitsum = 5 + 0 + 6 + 7 = 18 And 1+8 = 9 By casting out 9, the digit sum = 9. You can check multiplication by casting out 9. Look atthe following example. Digit sums 6 8 3 -----> 8 , \---->8 x 7 = 56----> 2 digit sum x 2 5----> 7 3 4 15 13 6 6 1 7 0 7 5 -----> 2-----> digit sum Here, digitsum of 8x 7 = digitsumofl 7075 Hence the multiplication is done correctly. - Example 1: Study the pattern and write next three terms. - (a) 2,4,8,16,32, - (b) 2,6,18,54 - (c) 4,9,16, , Solution: ![](Sum up math-4_files/Sum20up20math-4-338.jpg) (a) (b) Each term is multiplied by 2 to get the next term. So the series can be written as follows: - 2, 4, 8, 16, 32, 64, 128, 256 Each term is multiplied by 3 to get the next term. So the series can be written as follows: - 2, 6, 18, 54, 162, 486, 1458 ![](Sum up math-4_files/Sum20up20math-4-339.jpg)2 3 4 (c) First term = 2 2nd term = 3 3rd term = 4 So the series can be written as fol lows: 4, 9, 16, 25, 36, 49 Example 2: Study the pattern and fill in the blanks: (a) 37 x 3 x 1 = 111 (b) (2 x 2) \- (1 x 1) =3 37 x 3 x 2 = 222 (3 x 3) \- (2 x 2) =5 37 x 3 x 3 = 333 (4 x 4) \- (3 x 3) =7 37 x 3 x 7 = (15x15) \- (14 x 14) = 37 x 3 x 9 = (25 x 25) \- (24 x 24) = Solution: - (a) 37 x 3 multiplied by 1 gives 111 37 x 3 multiplied by 2 gives 222 37x3 multiplied by 7 gives 777 37 x 3 multiplied by 9 gives 999 - [(b) (2 x 2)-(1 x 1) = (2 + 1) x 1 =3](#bookmark731) [(3 x 3)-(2 x 2) = (3 + 2) x 1 =5](#bookmark732) [(4 x 4)-(3 x 3) = (4 + 3) x 1 =7](#bookmark733) (15 x 15)-(14 x 14) = (15 + 14) x 1=29 [/. (2 5 x 2 5)-(24 x 24) = (2 5 + 24) x 1 =49](#bookmark734) Example 3: Study the pattern and fill in the blanks: - (a) 25 = 5 = 5 250 = 5 = 50 2500 = 5 = 500 2500000 - 5 = ? - (b) 90 = 3 = 30 900 = 3 = 300 9000 = 3 = 3 000 900000 = 3 = ? Solution: Number ofzeroes is same in the quotient and division : - (a) 2500000 = 5 = 500000 - (b) 900000 = 3 = 30000 ![](Sum up math-4_files/Sum20up20math-4-340.jpg) ###### J. EXERCISE 70 ^--- - 1\. Find the digit sum of these numbers after casting out 9 : (a) 3267 (b) 4879 (c) 34723 - 2\. Check the answer after casti ng out 9 : - (a) 3 5 8 7 (b) 3 5 0 8 (c) 9 4 8 X9046 x 4 6 9 2 x57 3\. Study the pattern and the complete the blank figures: ![](Sum up math-4_files/Sum20up20math-4-341.jpg) Observe the pattern and fill in the blanks: (a) 1x1=1 (b) 1x9 + 2 =11 11x11 = 121 12x9 + 3 =111 111 x 111 = 12321 123 x 9 + 4 =1111 1111 x 1111 = 1234321 12345 x 9 + 6 = 111111x111111 = 123456 x 9 + 7 = (c) 22 x 5 = 110 (d) 222 x 5 = 1110 3x5=15 33 x 5 = 165 2222 x 5 = 11110 333 x 5 = 1665 222222 x 5 = 333333 x 5 = ![](Sum up math-4_files/Sum20up20math-4-342.jpg) - (e) 4 x 5 = 20 (f) 1x9 + 1 = 44 x 5 = 220 10 x 9 + 10 = 444 x 5 = 2220 100 x 9 + 100 = 44444 x 5 = 1000 x 9 + 1000 = 10000 x 9 + 10000 = - (g) 5x4 = 55 x 4 = 555 x 4 = 5555 x 4 = 55555 x 4 = - 5\. Look at patterns and write the next two terms: - [(a) 1,2,3,5,8 ,.](#bookmark737) - [(b) 12345654321,123454321,1234321, ,.](#bookmark738) - [(c) 5,25,125, ,.](#bookmark739) - [(d) 3,9,27,81, ,.](#bookmark740) - 6\. Using the grid make your own pattern of numbers. Give the rule for your pattern. One example has been encircled foryour reference: 1,7,13,19,25 1+6=7 - 7 + 6 = 13 - 13 + 6 = 19 19 + 6 = 25 [1 2 3 45](#bookmark741) [6 7 8 910](#bookmark742) [11 12 13 1415](#bookmark743) [16 17 18 1920](#bookmark744) [21 22 23 2425](#bookmark745) ![](Sum up math-4_files/Sum20up20math-4-343.jpg)In the previous class you learnt about tally marks and pictograph. In this class let us learn using a bar graphs. Let us recapitulate pictographs. - Example 1: Gattu bought different types of candies and chocolates for his birthday party. Candies Chocolates Toffee Chewing gum [20 15 6035](#bookmark746) Represent this data by pictograph. Solution: [Candies](#bookmark747) [Chocolates](#bookmark748) Toffee ★★★★★★★★★★★★ Chewing gum ★★★★★★★ Here 1 ★ represents 5 items. Example2: Lola bought fol lowing items for her guests. Samosa Pastries Lollipop Cookies 20 24 32 40 Solution: Here all the numbers are divisible by 4; so let us divide them by 4. ![](Sum up math-4_files/Sum20up20math-4-344.jpg)Ssmosa ★ ★★★★ Pastries ★★★★★★ Lollipop ★★★★★★★★ Cookies ★★★★★★★★★★ Here 1 ★ represents 4 items. BARGRAPH In bar graph; the given data is represented by bars. - • Titlesand otherdetails are shown in bar graph. - • Barscan be vertical or horizontal. - • Width of bars in uniform. - • Gap between two bars is uniform. - • Length of the bar shows the value of data. - Example 3: The following bar graph shows the attendance of students in class 5, fora week. ![](Sum up math-4_files/Sum20up20math-4-345.jpg)Attendance in class for a week Readingthe bar graph. - • The bar graph shows attendance of students in class 5 for Monday, Tuesday, Wednesday, Thursday, Friday and Saturday. Get Set Go With Sum Up Mathematics-4 ![](Sum up math-4_files/Sum20up20math-4-346.jpg) - • The maximum attendance is on Wednesday. - • The minimum attendance is on Saturday. - Example 4: Read the following graph and try to answer following questions. ![](Sum up math-4_files/Sum20up20math-4-347.jpg) - 1\. Which toy is in the highest number ? - 2\. Which toy is in the least number? - 3\. Howmanycarsdoes Atul have ? - 4\. What is the total number of toys ? Solution: - 1\. Kites 2. Bat ###### J. EXERCISE 71 ![](Sum up math-4_files/Sum20up20math-4-348.jpg) 1\. Arjun's grand father has given him some rare coins which are no longer in use : ![](Sum up math-4_files/Sum20up20math-4-349.jpg) ![](Sum up math-4_files/Sum20up20math-4-350.jpg)Here 1 coin represents4 coins. Answer these questions. - (a) How many 5 p coins does Arjun have? - (b) Which coin is in the maximum number ? - (c) Which coin is in the least number ? - (d) What is the total number of coins ? - (e) How many 10 p coins are there? - 2\. This bar graph shows the number of items sold in a day. Answer the following questions : - (a) What is the total number of items sold in a day ? - (b) Which item was sold the maximum ? - (c) Which item was sold the least? - 3\. This bar graph shows the number of legs of different animals. Answer the following questions: - (a) Which animals has that least number of legs? - (b) Which animals has the most number of legs ? - (c) If the number of each animal is 1; then what is the total number of legs? This graph shows the marks obtained by 4 students in mathematics. Answer these questions: - (a) Who is the topper ? - (b) How many students have scored more than Satyam ? - (c) How many students have scored less than Satyam ? 30 Items sold in a day ![](Sum up math-4_files/Sum20up20math-4-351.jpg) ![](Sum up math-4_files/Sum20up20math-4-352.jpg) ![](Sum up math-4_files/Sum20up20math-4-353.jpg) - 5\. This graph shows the popularity of TV channels among students of class 5. Answer these questions : ![](Sum up math-4_files/Sum20up20math-4-354.jpg) - (a) Which isthe most popular channel ? - (b) Which isthe least popular channel ? - (c) How many students I ike the Discovery ? - 6\. This bar graph shows different kinds of breakfast brought by students. Answer the following questions : ![](Sum up math-4_files/Sum20up20math-4-355.jpg) - (a) Which isthe least popular breakfast? (b) Which isthe most popular breakfast ? (c) What is the total number of students ? ![](Sum up math-4_files/Sum20up20math-4-356.jpg)0 cWamination Time ![](Sum up math-4_files/Sum20up20math-4-357.jpg) ###### . EXERCISE 72 ![](Sum up math-4_files/Sum20up20math-4-358.jpg) - 1\. Write the number names : (a) 56712 (b) 78504 (c) 80010 (d) 94001 - (e) 50313 (f) 80005 - 2\. Write the following numbers in figures : - (a) Twenty thousand three hundred eight. - (b) Fifty fourthousand nine hundred seventeen. - (c) Ninety thousand five hundred. - (d) Three thousand three hundred three. - (e) Eighty thousand eighty. - (f) Thirty eight thousand nine. - (g) Eleven thousand one hundred eleven. - 3\. Write the smallest number of 5 digits in figures and words. - 4\. Write the greatest number of 6 digits in figures and words. - 5\. Choose 4 cards to write: 9 6 10 - (a) The greatest number (b) The least number. - (c) An even number. (d) An odd number. - 6\. Write the place value of 7 in each of the numbers: - (a) 78201 (b) 7085 (c) 58702 (d) 96107 - 7\. Add the following: - (a) 8 0 735 (b) 8 0 797 50728 53241 8732 7203 181 ![](Sum up math-4_files/Sum20up20math-4-359.jpg) - 8\. Subtractthefollowing: - (a) 5 4 3 0 8 (b) 52 5 70 39190 32565 - 9\. Inthe following sum, replace \* by correct digit: - (a) 6 \* 5 \* 9 (b) 7 \* 5 \* 9 [\*3\*5\*\*2\*8\*](#bookmark755) 110845 111158 - 10\. In the following subtraction sum replace \* by correct digit: - (a) 1 \* 2 \* 8 (b) 7 \* 8 \* 9 [\*9\*1\*\*421\*](#bookmark756) [380542646](#bookmark757) - 11\. Multiply the fol lowing and write the number sentence: - (a) 5206x23 (b) 218x901 - 12\. Inthe followingsum ofmultiplication, replace \* by correct digit: - [(a) 4 \* 6 (b)\* 1 2](#bookmark758) [\*g \*-|\*](#bookmark759) [1\*0830\*2](#bookmark760) [3\*883\*2](#bookmark761) [\*6\*8\*1\*\*6](#bookmark762) 1 \* 1 \* 9 \* - 13\. Divide and find the quotient and remainder: - (a) 90837-72 (b) 30702-84 - 14\. Write a story for each of these : - (a) 3653 + 9240 = ? (b) 2142x12 = ? (c) 625-5 = ? - 15\. Simplify: 123x51 +914 - 16\. One banana costs Rs. 176. What is the price for one dozen bananas ? - 17\. A table costs Rs. 3575. How many tables can be bought for Rs. 14300 ? ![](Sum up math-4_files/Sum20up20math-4-360.jpg) 18\. Chana dal costs Rs. 58 per kg. What is the cost of 7 packets of chana dal if each packet contains 4 kg of dal ? 19\. A jar of candies can be filled with 144 candies. A shopkeeper needs to fill 35 jars of candies. He has 5000 candies in a gunny sack. Does he need more candies to fill all the jars ? 20\. Find the greatest common divisor ofthe following: (a) 35 and 42 (b) 54 and 42 21\. Find the least common multiple ofthe following: (a) 5 and 6 (b) 15 and 20 22\. Fill in the blanks by choosing correct symbols from >,< or = : (a) A A (b) A A (c) A A (d) 11 12 5 5 7 7 4 8 13 13 2 3 4 - 23\. Write the nextthree similar fraction : —, —, — 11 ' 11 ' 11 - 24\. What is the difference of of Rs. 2400 and of Rs. 2000? 4 5 25\. The cost of 5 kg of butter is Rs. 500. What is the cost of 250 g of butter ? 26\. Arrange these fractions in ascending order : (a) 2 8 7 j 3 \_8\_ 7 ^ 6 U 13'13'13 d 13 12'12 12 9 10 13 11'11'11 27\. Arrange thefollowingfractions in descending order : , . J\_\_8\_\_LIP. 4a A JL A JL a 17' 17 ' 17 ' 17 7' 7' 7' 7 ,.498 6 (c) ----- ----- ----- ----- 12'12'12'12 28\. Add: 29\. ,.321 . 7 2 8 ,.111213 (a) 6 + 6 + 6 (b) 3 + 3 + 3 (C) 13+ 13 1 13 Subtract ,.85 ,,.97 ,.84 a 13 13 11 11 C 17 17 - 30\. Fill in the blanks: [z A 4 7 5 9 z x 64](#bookmark763) - [a 19 + “19 11 + “11 C 13““13](#bookmark764) - 31\. Fill in the blanks: [z \\ 2 zi x 3 6](#bookmark765) - (a) T"T <b) I”- (c) b" 26 [3 46](#bookmark766) - [32. A ribbon is cut into three pieces measuring cm, -^remand -r-cm. What was the length of the ribbon ?“](#bookmark767) [3 54](#bookmark768) - 33\. Heights of three toys are ^ feet, Tjy feet and feet respectively. What is the total height of these toys ? - 34\. Rahul bought 3 apples for Rs. 42. Nitin buys 5 apples at the same rate. How much many does Nitin pays. - 35\. There are four baskets of guava. They weight 5 kg 700 g, 12 kg 200 g and 4 kg 500 g. What is the total weight of the four baskets ? - 36\. Priyanka gets 1200 as pocket money. She spends Rs. 392.50 on stationeries, and Rs. 484.75 in giving treats. How much Priyanka saves from her pocket money ? - 37\. A bag of sugar has 48 kg 750 g sugar. Golu takes out 13 kg 250 g sugar and Molu take 14 kg 500 g sugar from it. How much sugar is left in the bag ? - 38\. The capacity of a tanker is 800 litre 500 mililitre. There is 475 litre 1 75 ml water in it. How much more water can be filled in thistanker ? - 39\. Mr. Khanna's office is 27 km 500 m from his house. Her travels 11 km 250 m by bus and 12 km 750 m by autorickshaw. He walks rest of the distance. How much distance Mr. Khanna walks. - 40\. Mahtab bought 392 eggs. He found y of them are rotten. How many eggs are in good condition ? - 41\. A tincture of homeopathic medicine comes in a 5 litre container. A doctor packs it in small bottleof50 ml capacity. How many such bottlescan be filled by the tincture ? - 42\. Convert: - (a) 14 m 11 dm into dm (b) 7 cm 5 mm into mm (d) 7 I 257 ml into ml - (c) 15 kg 75 gm into g ![](Sum up math-4_files/Sum20up20math-4-361.jpg) (a) 724 m 42 cm and 113 m 1 7cm (b) 624 km 615 m and 7 km 300 m - 44\. A fruit seller has 12 dozen and 14 bananas. He sold 7 dozen and 7 bananas. How many bananas are left with him ? - 45\. A 15 m 30 cm long dosa is divided equally among 9 boys. What is the length of each piece of dosa ? - 46\. Draw a line segment AB = 7 cm - 47\. Separate the simple closed curves from the following: 48\. 49. 50\. 51. (a) ![](Sum up math-4_files/Sum20up20math-4-362.png) (e) ![](Sum up math-4_files/Sum20up20math-4-363.png) (b) (f) ![](Sum up math-4_files/Sum20up20math-4-364.jpg) Draw a circle with centre O and radius 3 Name the partsand fill in the blanks: (a) (b) (c) (d) AB is O is OC is AC is of circle. of circle. of circle. of circle. Fill in the blanks: - (a) A triangle has - (b) A quadrilateral has - (c) A square has ![](Sum up math-4_files/Sum20up20math-4-365.png) ![](Sum up math-4_files/Sum20up20math-4-366.jpg) ![](Sum up math-4_files/Sum20up20math-4-367.jpg) sides. vertiles, diagonals. Look at the following figures answer the questions which follow : (b) (d) (c) ![](Sum up math-4_files/Sum20up20math-4-368.jpg) ![](Sum up math-4_files/Sum20up20math-4-369.jpg) ![](Sum up math-4_files/Sum20up20math-4-370.jpg) ![](Sum up math-4_files/Sum20up20math-4-371.jpg) ![](Sum up math-4_files/Sum20up20math-4-372.jpg) Which of the given figure are : (a) Quadrilaterals (b) Triangles (c) Polygons (d) Closed curves (e) Simple closed curve 52\. Calculate the perimeteroffollowingfigures : ![](Sum up math-4_files/Sum20up20math-4-373.jpg)53\. The sides ofatriangle are 13 cm, 12 cm and 5 cm. Find the perimeter of triangle. - 54\. Sides of a rectangle are 10 cm and 8 cm. What is the perimeter of rectangle ? - 55\. A mouse makes a complete round of a room which is 120 inches long and 96 inches wide. What is the distance covered by the mouse ? - 56\. Agarden is 56 m longand 26 m wide. What is the cost of fencing at the rate of Rs. 120 per metre ? 57\. Findtheareaoftheshadedfigure. Area of one square is 1 square cm. ![](Sum up math-4_files/Sum20up20math-4-374.jpg) ![](Sum up math-4_files/Sum20up20math-4-375.jpg) - 58\. Make a net similar to the given figure and fold to make a cute: 3 cm ◄-----► - 59\. Tick (/) the correct choice : - (i) Theelevationofacuboid will be - (a) square (b) circle (c) triangle (d) rectangle - (ii) The elevation of a cone will be - (a) square (b) circle (c) triangle (d) rectangle - 60\. What time ¡twill be 2 hours45 minutes after 2:20 pm ? - 61\. Neha Halekar is a social activist. She sat on dharnafrom 7:30 am on Monday to 12:30 pm on Tuesday. For how many hours did she sit on the dharna ? - 62\. A movie is shown from 8:20 PM to 12:30 AM on a popular movie channel. How long one needs to sit to watch the movie ? - 63\. Look at the calendar of th is year and find on which day the fol lowing fall: - (a) Children's Day (b) Gandhi Jayanti - (c) Christmas (d) New Year's Day - 64\. The one day cricket match starts at 9:30 a.m. and ends at 5:30 pm. What is the total duration of the match ? - 65\. Write Roman Numeralsforthefollowing: - (a) 37 (b) 23 (c) 18 (d) 32 - 66\. Write Arabic numerals forthe following: - (a) XIX (b) XXIX (c) XVII (d) XXIV - 67\. Write in short form : 26th January 1950 and 2nd October 1851. - 68\. Where will the minute hand pointat6:45 pm ? - 69\. Measurethefollowinglinesegments: ![](Sum up math-4_files/Sum20up20math-4-376.png)Get Set Go With Sum Up Mathematics-4 ![](Sum up math-4_files/Sum20up20math-4-377.jpg) - 70\. Fill intthe blanks : (a) 108 110 114 120 (b) 8 16 32 - 71\. Read the bar graph and answer these Number of flowers questions : - (a) Which flower is maximum in number ? - (b) Which flower is least in number ? - (c) What is the total number of flowers ? - (d) How many roses are there ? Rose Juhi Sunflower Marigold - 72\. Observe the pattern and complete the series: 18^9 = 180^9 = 1800^9 = 18000^9 = 18000000^9 = - 73\. Draw mirror lines for these figures: ![](Sum up math-4_files/Sum20up20math-4-378.png) ![](Sum up math-4_files/Sum20up20math-4-379.png)(b) ![](Sum up math-4_files/Sum20up20math-4-380.png)(d) - 74\. Rahul bought chocolates for Rs. 13.75, soap for Rs. 28.35 and pencil box for Rs. 44.25. He gave a hundred rupee note to the shopkeeper. How much money is returned by the shopkeeper ? - 75\. Use isometric dot paper and complete the cube: ![](Sum up math-4_files/Sum20up20math-4-381.jpg) ![](Sum up math-4_files/Sum20up20math-4-382.jpg) FORMATIVE ASSESSMENT-1 (Chapter 1 to 6) Time: 1 hr.F.M. 20 - 1\. Countingby2's write the numbers from : - (a) 15364 to 15378 (b) 20686 to 20698 - 2\. The difference of two numbers is 8675. If the greater number is 15325, find the smallernumber. - 3\. How much is the product of 5412 by 12 less than 70000 ? - 4\. The cost of 33 books is Rs. 4719. Find the price of one book ? - 5\. Writetheplacevaluesof3's in 36931 and find their difference. - 6\. Add 142317,52705, 99238. - 7\. Subtract: 20534form 89273. - 8\. Rohit bought 2 kg potato for Rs. 22.50, 1 kg cabbage for Rs. 12.75 and half kg mushroom for Rs. 13.50. He gave a 100-rupees note to the shopkeeper. How much money is returned by the shopkeeper ? - 9\. Write the numbers by observing the patterns carefully: - (a) 28576, 30576, 32576 , . - (b) 753203, 755203, 757203 , . - 10\. The difference of two numbers is 24596. If the smaller number is 5629, find the greater number. ![](Sum up math-4_files/Sum20up20math-4-383.jpg) ![](Sum up math-4_files/Sum20up20math-4-384.jpg) ![](Sum up math-4_files/Sum20up20math-4-385.jpg) FORMATIVE ASSESSMENT-2 (Chapter 7 to 10) Time: 1 hr. F.M. 20 - 1\. Find the least common multiple of 25 and 30. - 2\. Fill in the blanks: [3 212](#bookmark779) - (a) V (b) 4 = — [2 163](#bookmark780) - 3\. Simplify: - (a) -12. + -2- (b) -12 + -12 [17 17 1919](#bookmark781) - 4\. By which numbershould 81 bemultipliedtoget2187 ? - 5\. In Ramlila Maidan 5767 people came on Saturday, 6896 people came on Sunday and 3215 people came on Monday. How many people came in three days ? - 6\. Find the greatest common factor of 16 and 24. - 7\. Find all possible factors of 24. - 8\. Simplify: 603058 + 25301 x 2 - 9\. Write 22 as a sum of two prime numbers. How many such pairs of prime number are possible? - 10\. Write the smallest number that should be subtracted from an odd number to make it even. ![](Sum up math-4_files/Sum20up20math-4-386.jpg) ![](Sum up math-4_files/Sum20up20math-4-387.jpg)FORMATIVE ASSESSMENT-? (Chapter 11 to 14) Time: 1 hr.F.M. 20 - 1\. Subtract 15 m 650 cm from 30 m. - 2\. Sides of a triangular sandwich are 1 5 cm, 12 cm 9 cm. Find the perimeter of the triangle. - 3\. A cow gives 5 litre 750 ml milk. The milkman sells 4 litre 250 ml milk and rest of the milk is used in his home. How much milk is used in his home ? - 4\. A jar contains 7 kg 250 g of pulses. How much pulse is there in 3 such jars ? - 5\. Convert: - (a) 12 1375 ml into ml (b) 18 cm 27 mm into mm (c) 5km52mintom - 6\. Rs. 6000 is to be divided among 30 people equally. Find the amount which each person gets. - 7\. 5 empty bottles can be filled by taking 13 / 500 ml vinegar. What is the capacity of each bottle ? - 8\. The painting class starts at 11:05 am and lasts for 55 minutes. When does the painting class ends ? - 9\. How many 10-rupee notes exchange of a 50-rupee note ? - 10\. Ramu bought 8 packets of biscuits. If 1 packet of biscuit costs 12.10, how much did Ramu pay to the shopkeeper? ![](Sum up math-4_files/Sum20up20math-4-388.jpg) ![](Sum up math-4_files/Sum20up20math-4-389.jpg) ![](Sum up math-4_files/Sum20up20math-4-390.jpg) FORMATIVE ASSESSMENT-4 (Chapter 15 to 18) Time: 1 hr. F.M. 20 - 1\. A square has how many mirror lines? - 2\. Bobby went to play in the park at 5:15 pm and came back at 7:45 pm. Find the time for which Bobby played ? 3\. This bar graph shows price of vegetables. Answer the following questions: ![](Sum up math-4_files/Sum20up20math-4-391.jpg) 5\. Draw plan and elevation of followingfigures: 6\. Which of these are simple closed curves ? ![](Sum up math-4_files/Sum20up20math-4-392.jpg) (a) Which vegetable is the costliest ? (b) Which is the cheapest vegetable ? (c) What is the cost of 2 kg of ladyfinger ? Find the perimeter of these figures: ![](Sum up math-4_files/Sum20up20math-4-393.jpg) ![](Sum up math-4_files/Sum20up20math-4-394.png) ![](Sum up math-4_files/Sum20up20math-4-395.jpg) Exercise-1\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 7\. (a) 1 5939,1 5438,1 5437,1 5436,1 5435. - 8\. (a) 1 361 5,1 3620,13625,1 3630,1 3635. - 9\. (a) 28310, 28320, 28330, 28340. - 10\. (a) 68110, 68210, 68230, 68240, 68250. - 11\. (a) 84221,85221,86221,87221. - 12\. 10000. 13. 100000. - (b) 99235, 99234, 99233, 99232, 99231 - (b) 27441,27446, 27451,27456, 27961 (b) 87516, 87526, 87536, 87546. (b) 37371,37471,37571,37671,37771 (b) 65999, 66999, 67997, 68999. 14\. 100 Exercise-2--------------------------------------------------------- 1\. (a) T-Th Th H T O 2\. (a) 3, (b) 8, 5, (c) 4, 7,6, (d) 9, 7,4, 3, (e) 8,4, 5, 6, 7. a 5 3 0 5 4 3\. (a) Forty five thousand three hundred sixty two. b 3 6 2 5 0 - (b) Ninety fourthousand eight hundred sixty five. - (c) Twenty fourthousand three hundred fifty nine. c 7 5 3 4 3 to; seventy seven tnousana Tour nunarea ninety nine. (e) Twenty thousand fifty nine. (f) Forty thousand four. (g) Thirty seven thousand. (h) Eighty eight thousand ninety. 4\. (a) 50725, (b) 50439, (c) 85085, (d) 90090, (e) 30700, (f) 67503, (g) 70000, (h) 22048. Exercise-3\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) Thousand, (b) Ten thousand, (c) Hundred, (d) Thousand, (e) One thousand, (f) Thousand and ten, (g) Ten thousand and hundred, (h) Thousand and ten. 2. five thousand and five ten - 11\. thousand and hundred; yes - 12\. (a) 30030, (b) 5505, (c) 40404, (d) 70707. - 13\. (a) 27085 — 25087, (b) 1 7621 - 1 1627, (c) 95047-97045, (d) 55800-50805. - 14\. (a) 8571 5 — 1 5785, (b) 38618 - 18638, (c) 42416 - 12446, (d) 85905 - 5985. Exercise-H\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 4000 + 800 + 40 + 8, (b) 70000 + 7000 + 300 + 40 + 5, (c) 80000 + 8000 + 800 + 80, (d) 60000 + 3000 + 40 + 7, (e) 80000 + 500 + 5, (f) 30000 + 700 + 40 + 8. - 2\. (a) 64345, (b) 97065, (c) 78560, (d) 20939, (e) 82030, (f) 50502, (g) 40087, (h) 58372, (i) 860507. - 3\. (b). 4. (d). 5. 5862768697 Exercise-5--------------------------------------------------------- - 1\. (a) >,(b) <,(c) >,(d) >,(e) <,(f) <,(g) =,(h) =,(i) =. - 2\. (a) 24220,22204, (b) 88800,80088, (c) 25800,25000, (d) 511 776, 51667. 3\. - (a) 844 < 3048 < 6072 < 20600 < 26200. (b) 360 < 985 < 4400 < 6602 < 40044. (c) 244 7001 < 18036 < 44232 < 45602. (d) 80008 < 80088 < 80808 < 88000 < 88008 < ![](Sum up math-4_files/Sum20up20math-4-396.jpg)4\. (a)27612 > 24612 > 17612 > 8887 > 4041. (b) 27414 > 22002 > 14212 > 1 780 > 880. - (c) 602303 > 44072 > 38244 > 1 761 6 > 1 5412. (d) 88808 > 88088 > 88008 > 80888 > 8808. - 5\. (a) Ascending, (b) Ascending, (c) Neither, (d) Weither. - 6\. (a) 8432 and 2348, (b) 7542 and 2457, (c) 9851 and 1589, (d) 8631 and 1368. - 7\. (a) 85421 and 12458, (b) 98532 and 23589, (c) 86420 and 20468, (d) 75320 and 20357. - 8\. (a) 6653 and 3356, (b) 4410 and 1004, (c) 5522 and 2255. - 9\. (a) 77652 and 22567, (b) 55430 and 30045, (c) 55520 and 20005. - 10\. (a) 12567, (b) 34467, (c) 20456, (d) 20046. 11. (a) 64312, (b) 84443, (c) 85430, (d) 64200. - 12\. (a) 99999, (b) 98765, (c) 98376. - 13\. (a) 12345, (b) 10000, (c) 32222, (d) 11160, (e) 14110. - 14\. 369 > 396 > 639 > 693 > 936 > 963. 15. 304 > 340 > 403 > 430. - 16\. (a) 43968 one rupee coins, (b) 86752 one rupee notes. Exercise-6\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 7, (b) 12, (c) 27, (d) 36, (e) 25, (f) 31, (g) 18, (h) 23. 2. (a) <,(b) <,(c) >,(d) =,(e) >,(f) >. - 3\. (a) —4,(b)-3,(c)-2,(d)-d. 4. (a) II, (b) XI, (c) XIII, (d) XXVI, (e) XXXII, (f) XXXIV, (g) XXXIX, (h) XXXVII. 5. (a) No, (b) No, (c) Yes, (d) Yess, (e) No, (f) No, (g) No. - 6\. (a) - D, (b) — A, (c) — B, (d) — c. 7. Do it yourself. 8. Do it yourself. Exercise-7\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (i) 47989, (ii) 79789, (iii) 65779, (iv) 93890, (v) 78999, (vi) 38898, (vii) 71 62, (viii) 761 3, (ix) 9251, (x) 8220, (x) 8220, (xi) 7062, (xii) 8619, (xiii) 8662, (xiv) 5120, (xv) 1 7875, (xvi) 14513, (xvii) 11217, (xviii) 12350, (xix) 9079, (xx) 9834, (xxi) 10314, (xxii) 75604, 2. (a) 53624, (b) 111551, (c) 81725, (c) 101595, (xxvii) 87861, (xxviii) 822089266, (xxix) 52160, (xxx) 70909, (xxxi) 101869, (xxxii) 99243, (xxxiii) 5712, (xxxiv) 7504, (xxxv) 4313, (xxxvi) 42396, (xxxvii) 52387, (xxxviii) 68662, (xxxxix) 7645, (xxxxx) 72 712 Exercise-8--------------------------------------------------------- 1\. 6325 2\. 9282 3\. 7419 4\. 10277 5\. 7583 6\. Vimal's vote = 5134, Total = 8959 7\. 41144 8\. 47357 9\. 33594 10\. 9325 11\. 24342 12\. 50971 13\. 65855 14\. 77614 15\. 58293 m 16\. 86543 17\. 99125 Exercise-9--------------------------------------------------------- 1\. (a) 8000, (b) 13000. 2. (a) 20,000, (b) 80000. - 3\. (a) Actual = 8211, Estimate = 8000. (b) Actual = 42,421, Estimate = 42,000. - 4\. (a) Actual = 91,805, Estimate = 90000. (b) Actual = 98081, Estimate = 80,000. - 5\. 4000. 6. 94000. Exercise-10 ![](Sum up math-4_files/Sum20up20math-4-397.jpg)Do it yourself. 1\. (a) 23546, (b) 22053, (c) 23324, (d) 11122, (e) 22321, (f) 55014, (g) 30252, (h) 74134, (i) 01222. 2\. (a) 11421, (b) 12281, (c) 43704, (d) 44534, (e) 44044, (f) 53325. 3\. (a) 30022, (b) 43413. 4\. £0 7 6 5 3 4(b) 5 8 6 5 \- 2 4 1 3 0 \- 2 0 5 2 3 6 3 5 2 3 2 5 3 4 2 ![](Sum up math-4_files/Sum20up20math-4-398.jpg) Exercise-11---------------------------------------------------------- Exercise-12\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 8 thousands, (b) 1 tens, (c) 9 thousands 7 hundreds, (d) 15 hundreds 4 tens, (e) 7 thousands 5 hundreds. - 2\. (a) 7444, (b) 4452, (c) 1461, (d) 1276, (e) 4007, (f) 1181, (g) 3484, (h) 6994, (i) 5551, (j) 58336, (k) 1 7732, (I) 16944, (m) 49689, (n) 49689, (o) 77605. 3\. (a) 541 7, (b) 3370, (c) 7766, (d) 54760, (e) 15090, (f) 25158. 4\. (a) 5385, (b) 54634, (c) 6 5 2 3 (d) 8 5 5 0 (e) 9 4 9 3 2 \- 1 3 5 8 5 8 3 4 \- 2 8 5 6 6 5 1 6 5 5 7 1 6 6 6 3 6 6 Exercise-13\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1\. 4310\. 2\. 4661\. 3\. 1592. 4\. 1316\. 5\. 9948\. 6\. 6255\. 7\. 7017\. 8\. 15806. 9\. 11440\. 10\. (a) 2895, (b) 7386. 11\. 1489. 12\. 8579. 13\. 27827\. 14\. 64460\. Exercise-W\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) Actual = 2524, Estimate = 3000, (b) Actual = 13211, Estimate = 13000. - 2\. (a) Actual = 16588, Estimate = 1 7000, (b) Actual = 44222, Estimate = 44000. - 3\. 6000. 4. 2000. 5. (a) 6668, (b) 1025. Exercise-15\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 39123, (b) 68428, (c) 41664, (d) 55055, (e) 33096, (f) 60393. - 2\. (a) 24086, (b) 44808, (c) 63066. Exercise-16\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1\. 1456. 2\. 4446. 3\. 5105\. 4. 5628\. 5\. 7966\. 6\. 9576. 7\. 8980. 8\. 9688\. 9. 9656\. 10\. 11808\. 11\. 7992. 12\. 9312. 13\. 26105\. 14. 34153\. 15\. 28944\. 16\. 49888. 17\. 58060. 18\. 49364. 19\. 66825. 20\. 93753. Exercise-17 1\. (a) 8, (b) 80, (c) 8. 2. (a) 50, (b) 50, (c) 5000. 4\. (a) 112, (b) 1120, (c) 11200. 5. (a) 108, (b) 1080, (c) 10800. 7\. 9500. 8. 55800. 9. 6760. 10. 6750. 3\. (a) 52, (b) 520, (c) 5200. 6\. (a) 75, (b) 750, (c) 7500. 11\. 8500. 12\. 16250. Exercise-18\_ 1\. 3825. 2\. 4\. 12954\. 5\. 18404\. 4485\. 3\. 4484\. 6\. 31046. 7\. 22825\. 8\. 21918\. 9\. 21195\. 10\. 17262\. 11\. 17925. 12\. 24970\. 13\. 81347\. 14\. 90048\. 15\. 71691\. 16\. 97740. 17\. 7872\. 18\. 65263\. 19\. 116337\. 20\. 38944\. Exercise-19\_ — 1\. 4550. 2\. 14147\. 3\. 27857\. 4\. 4342\. 5\. 88000\. 6\. 92365. 7\. 49545\. 8\. 54226\. 9\. 77682\. 10\. 73008\. 11\. 65709. 12\. 70122\. 13\. 87604\. 14\. 36987\. 15\. 76635\. 16\. 58500. 21\. 65000. 17\. 90571\. 18\. 82761\. 19\. 35500\. 20\. 8900\. Exercise-20\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 2\. 9675\. 3\. 33475\. 4\. 109545 litre. 5\. 317725\. 6\. 1500\. 7\. 58410\. 8\. 75795\. 9\. 69525\. 10\. 51940\. 11\. 12495 kg. 12\. (a) 8 7 5 (b) 9 6 3 X X x X x x x x 7 \[Z x x UES 0 x x 7 Œ Œ 7 6 6^5 x 4 Exercise-21-------------------------------------------------------- - 1\. (a)Actual = 16184, Estimate = 16800, (b)Actual = 85547, Estimate = 89600. - 2\. (a) Actual = 7425, Estimate = 8500. 3. Do ityourself. 4. Do ityourself. Exercise-22\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a)42 = 6 = 7,42 = 7 = 6, (b) 68 = 34 = 2, 68 = 2 = 34, (c) 297 - 3 = 99,297 = 99 = 3, (d) 16 - 4 = 4,(e)49 - 7 = 7,(f) 144 - 12 = 12. 2. (a) 5 - 7, (b) 11 x 5, (c) 9 x 8. Exercise-23-------------------------------------------------------- - 1\. (a) Q = 897, R = 5, (b) Q = 1622, R = 4, (c) Q = 1187, R = 4, (d) Q = 5581, R = 3, (e) Q = 3673, R = 2, (f) Q = 28439, R = 0, (g) Q = 8978, R = 1, (h) Q = 1 321 6, R = 6, (i) Q = 7629, R = 6, - (j) Q = 5328, R = 3, (k) Q = 12252, R = 2, (I) Q = 1556, R = 1. - 2\. (a)Q = 4762,R = 3,(b)Q = 1946, R = 4, (c)Q = 6891, R = 1. Exercise-^\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1\. Q = 70, R = 8. 2. 5\. Q = 481,R = 7. 9\. Q = 8555, R = 5. 10. ![](Sum up math-4_files/Sum20up20math-4-399.jpg)Q = 37, R = 0. 14. 17\. Q = 340, R = 4. Q = 60,R=11. 3. Q = 70, R = 1 7. 4. Q = 280, R = 1 7. - 6\. Q = 701,R=1. 7. Q = 1752, R = 7. 8. Q = 1808,R = 7. Q = 7zR = 0. 11. Q = 9, R = 9. 12. Q = 7, R =17. Q = 51,R=1. 15. Q = 86,R = 56. 16. Q = 216, R = 1 7. G=— Exercise-25\_\_\_ - 1\. Q = 56, R=10. - 5\. Q = 152,R=1. - 9\. Q = 982,R=14. - 13\. Q = 246, R = 35. - 17\. Q = 1436, R = 15 - 2\. Q = 53,R = 6. - 6\. Q = 476, R = 2. - 10\. Q = 117, R = 3. - 14\. Q = 337, R = 22. - 18\. Q = 790, R = 20. - 3\. Q = 54,R=1. - 7\. Q = 432,R = 4. - 11\. Q = 111, R = 12. 15\. Q = 694, R = 5. - 4\. Q = 126,R=1. - 8\. Q = 222, R=12. - 12\. Q = 216, R = 15. 16\. Q = 595, R = 0. Exercise-26\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1\. 237. 2\. 48\. 3\. 56\. 4\. 5845\. 5\. 5616. 6\. 214. 7\. 9\. 8\. 122,26. 9\. 108\. 10\. 472. 11\. 145. 12\. 72\. 13\. Q = 35714R = 7\. 14\. 1815. 15\. 84. 16\. 14\. 17\. 718\. Exercise-27-------------------------------------------------------- - 1\. (a) 4, (b) 2, (c) 4, (d) 2, (e) 6, (f) 9, (g) 8, (h) 13, (i) 23, (j) 20, (k) 20, (I) 6, (m) 82, (n) 64, (o) 114. - 2\. Do it yourself. Exercise-28\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. 2910. 2. 25976. 3. 21045. 4. 636. 5. 6945. - 6\. 507. 7. 1070. 8. 28230. 9. 14242. 10. 772. - 11\. 534. Exercise-29\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. Yes. 2. Yes. 3. Yes. 4. Yes. 5. 1,2,3,4,6,9,12,18,36 - 6\. 1,2,3,4,6,8,12,16,24,48 7. 1,2,4,31,62,12 5. - 8\. 1,2,4,5,10,14,28,33,70,140. 9. 1. 10.48. - 11\. (a) True, (b) True, (c) False, (d) False, (e) False, (f) True, (g) False. 12. 1,2,3,6,7,14,21,42 - 13\. 1,2,4,7,14,28 14. 1,2,3,4,5,6,10,12,15,20,30,60. Exercise-30-------------------------------------------------------- - 1\. 1,3, 5, 7,11,13,17,19,23.2. 61,67, 71,73, 79, 83,89, 91,93, 97. 3. 12,14,16,18. - 4\. Prime — 109,113,127,133. Composite — 102,104,105,112,122,128,132. - 5\. 11,19. 6. 3,5,7,11,13 7. 5.7.11.13 8. 17 + 5,19 + 3 - 9\. 5,13,19,47,53,67,89,97 10. 5,1 3,1 9,47, 53, 67, 89, 97 - 11\. Even numbers —24,48,02,182,294,498,90926. 12. Odd numbers —31,43, 67, 374,1043. - 13\. 1. 13. (a) Even, (b) Odd, (c) Even, (d) Odd. Exercise-31\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1\. 1,2,4,4. 2. 1,2,4,4. 3. 1,2,4,8,8. 4\. 1,1. 5\. 1,3,3. 6\. 1,5,5. 7. 1,2,2. 8. 1,3,3 ![](Sum up math-4_files/Sum20up20math-4-400.jpg) ![](Sum up math-4_files/Sum20up20math-4-401.jpg)Exercise-32\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1\. 4,8,12. 2. 5,10,15,20. 3. 8,16,24,32,90. 4. 150. 5. 114. 6\. Yes. 7. No. 8. (a) False, (b) True, (c) False. 9\. 30,35 Exercise-33-------------------------------------------------------- - [1. 1 (0 3 (J) 5 (0 7 (0X®](#bookmark784) [11 @ 13 @ X ® 17 @ 19(20)](#bookmark785) [M @ 23 (24) 25 (26) X ® 29@)](#bookmark786) - 2\. 9,18,27,36,45 3. 18,24,30,36 - 4\. (a) 6,12,18, 24, (b) 12, 24, 36,48, (c) 20.40. 60. 80, (d) 12, 24, 36,48. - 5\. (a) 12,24, 36, LC-36, (b) 36, 54, 72, LC-36, (c) 36, 72,108, LC-36. Exercise-SH-------------------------------------------------------- - 1\. (a) -|, (b) 4k ^ ^ (e) (f) 4' (g) 4' (h) 4k ^ 4k o y io i □ iz / o y - 2\. (a)N = 1,D = 5,(b)N=4,D = 9,(c)N = 11,D = 6. 3. (a) -^(b)-^(c) -^(d) -^ Exercise-35-------------------------------------------------------- - 4\. (a) 8, (b) 15 kg, (c) 6, (d) 6, (e) 9 I, (f) 9. - 5\. 21, 6. 7, 7. 15, 8. 7, 9. 54, 10. (a) 0.5, (b) 0.25, (c) 0.75 (d) 0.5 Exercise-36-------------------------------------------------------- - 1\. (a) Yes, (b) No, (c) Yes, (d) Yes. 2. (a) and (b) —and (c) and 4k - 3\. Do it yourself. Exercise-37-------------------------------------------------------- !. (a) W, (bl| , (c^ . 2. (a) |, \_L, (b) ^, |, (c)^, (d)^,^. - 3\. (a)y2 ' (b) 25, (c) 75 • 4- ‘60 ' (b) 64 ' (b) TT‘ Exercise-38\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1 . (a) Like fraction, (b) Like fraction, (f) Like fraction. - 2 n 3 4 5 3 4 5 n 4 5\_\_7\_ , ± J\_\_L W 6 ' 6 ' 6 M ; 11 ' 11 ' 11 12 ' 12 ' 12 ’ 4 '7 '36 ' Exercise-39\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) <,(b) <,(c) <,(d) >. ![](Sum up math-4_files/Sum20up20math-4-402.jpg) G=-- Exercise-40\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1 J\_ + JL = 4 + 3 =J\_ ± , ± = 5 + 4 = \_9\_ , . 6 5 \_ 11 12 12 12 12 15 6 15 15' 21 21 21' 15 a m 7 10 M ?? ,.J5 M 17 ?? , > 4 (d) yy + yy = yy . 2. (a) yy, (b) yy, (c) yy , (d) yy , ^ JT' W FT' (g) “¡T ' (h) 1'(i) 4' ^ 4(k) 4'(l) 4- Exercise-Hl\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) -|-, (b) -^, (c) -¡y, (d) -^, (e) -¡y, (f) -|, (g) ^p (h)^-, (i) y^-, (j) -^, (k) ^-, (I) ^-. Exercise-43\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. 7. 2. 2. 3. 5. 4. 11andp50. 5. 130. - 6\. 465. 7. 20 notes. 8. (a) 12640 p, (b) 2305 p. - 9\. (a) 14.09, (b) 84.65,(c) 156.07. 10. (a) 515 and 40 p, (b) 470. Exercise-MH-------------------------------------------------------- - 1\. (a) 550.1 7, (b) 445.08, (c) 774.65,(d) 666.09, (e) 518.8, (f) 1016.55. - 2\. (a) 1022.00, (b) 799.50, (c) 1069.99.3. (a) 46.34, (b) 107.35, (c) 227.45, (d) 223.5. - 4\. 99.15. 5. 258.25. 6. 133.80 7. 33.90. 8. 247.70,403.70 Exercise-45 1\. (a) 430.00, (b) 4456.50, (c) 1538.16, (d) 6317.88. 2\. (a) 101.99, (b) 196.24, (c) 77.20, (d) 63.15. 3\. 424.15. 4. 96.80. 5. 14.62. 6. 28.10. 7. 197.40. 8\. 131.40. 9. 80.10. 10. 94.50. 11. 153.10. 12. 167.35. 13\. 41.15. 14. 102.00. 15. 3150.30. 16. 612.50. Exercise-MG-------------------------------------------------------- - 1\. (a) 100 g, (b) 100 g, (c) 1 kg 100 g, (d) 3 kg 850 g, (e) 7 kg 150 g. - 2\. Do It Yourself. 3. Do It Yourself - 4\. (a) 500 g, (b) 200 g, (c) 100 g, (d) 700 g, (e) 500 g. - 5\. (a) 32 kg 770 g, (b) 55 kg 100 g, (c) 98 kg 568 g, (d) 60 kg 230 g, (e) 129 kg 092 g. - 6\. (a) 77 kg 584 g, (b) 26 kg 550 g, (c) 100 kg 690 g, (d) 86 kg 925 g, (e) 72 kg 240 g. - 7\. (a) 12 kg405 g, (b) 18 kg 035 g, (c) 15 kg 760 g, (d) 48 kg475 g. - 8\. (a) 44 kg 240 g, (b) 38 kg 915 g, (c) 16 kg 750 g, (d) 25 kg 675 g. 9. 42 kg 750 g. - 10\. 71kg200g. 11. 63kg315g. 12. 68kg77g. 13. 124 kg 550 g. - 14\. 12 kg 680 g. 15. 52kg190g. 16. 67kg280g. - 17\. 153 kg 115 g rice; 26 kg 885 g vegetables, Total weight is 180 kg. ![](Sum up math-4_files/Sum20up20math-4-403.jpg) Exercise-^ - 1\. (a) 48 kg 600 g, (b) 412 kg 100 g, (c) 165 kg 3 75 g, (d) 162 kg 600 g. - 1\. (a)12kg625g,(b)11 kg 120 g, (c) 8 kg 361 g, (d) 62 kg625 g. 3. 246 kg 750 g. - 4\. 386 kg400 g 5. 1kg 575 g. 6. (a) 2, (b) 5, (c) 10. - 7\. (a) 300.14, (b) 386.517, (c) 630.099.7. Amit—102 kg 750g. Somu — 107kg875 g. - 9\. 247kg500g. 10. 20kg200g. 11.8kg. 12.2794kg. 13.1050kg. Exercise-48-------------------------------------------------------- - 1\. (a) 200 ml, (b) 5 ml, (c) 5 I, (d) 40 ml. 2. (a) 700 ml, (b) 1 I 500 ml, (c) 5 1400 ml, (d) 2 1400 ml. - 3\. (a) 500 ml onetime, (c) 1 I towtimes, 500 ml 1 time, 200 ml onetimeand 50 ml onetime, - (d) 1 litre 5 times, 200 ml onetime, 100 ml onetime, (e) 1 I 7times, 500 ml onetime, 00 ml onetime. - 4\. (a) 471400 ml, (b) 141 1115 ml, (c) 40 I 225 I, (d) 118 1430 ml. - 5\. (a) 1 71 905 ml, (b) 86 I 327 ml, (c) 70 I 912 I, (d) 153 11 72 ml. - 6\. (a) 15 I 815 ml, (b) 02 I 905 ml, (c) 12 I 865 I, (d) 1 7 I 760 ml. - 7\. (a) 16 I 910 ml, (b) 40 I 210 ml, (c) 9 I 210 I, (d) 19 I 915 ml. - 8\. 1501675ml. 9. 451460ml. 10. 381775ml. 11. 121725ml 12. 121985ml 13.101625ml. 14. 184 I 800 ml. 15. (a) 10, (b) 15, (c) 20, (d) 7 Exercise-49\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 79 I 350 ml, (b) 85 I 610 ml, (c) 169 I 645 I, (d) 290 I 925 ml, (e) 148 I 645 ml. - 2\. (a) 13 I 225 ml, (b) 1 71122 ml, (c) 24 I 235 I, (d) 32 I 325 ml, (e) 471 215 ml. - 3\. 681750ml. 4. 851575 ml. 5. 61150ml. 6. 2 1450ml 7. 28 I 300ml - 8\. 11281750ml. 9. 150ml. 10.600ml. - 11\. (a) 125.50, (b) 25.05, (c) 62.625, (d) 100.20. Exercise-50-------------------------------------------------------- - 1\. (a) cm, (b) cm, (c) km, (d) m, (e) m, (f) m, (g) m, (h) m or cm, (i) m, (j) mm. - 3\. (a) 500 cm, (b) 16 m 32 cm, (c) 61 m 44 cm, (d) 27 m 20 cm, (e) 25 m 25 cm. - 4\. (a) 20 cm, (b) 13 dm 5 cm, (c) 27dm 72 cm, (d) 16 dm 25 cm, (e) 52 dm 21 cm. - 5\. (a) 90 dm, (b) 3 m 12 dm, (c) 2 m 22 dm, (d) 283 dm, (e) 322 dm. - 6\. (a) 120 mm, (b) 137 mm, (c) 290 mm, (d) 230 mm, (e) 1225 mm. - 7\. (a) 25000 m, (b) 22025 m, (c) 210410 m, (d) 125210 m, (e) 27615 m. Exercise-51-------------------------------------------------------- - 1\. (a) 3 cm, (b) 33 cm 2 mm, (c) 5 cm 5 mm, (d) 27 cm 2 mm, (e) 190 cm 5 m. - 2\. (a) 6 m, (b) 6 m 72 cm, (c) 16 m 55 cm, (d) 27 m 1 cm, (e) 1 m 19 cm. - 3\. (a) 3 km, (b) 3 km 520 m, (c) 3 km 10 m, (d) 2 km 755 m, (e) 119 km 355 m. Exercise-52-------------------------------------------------------- ![](Sum up math-4_files/Sum20up20math-4-404.jpg) - (a) 357 m 19 cm, (b) 564 m 01 cm, (c) 635 m 47 cm, (d) 353 m 85 cm, (e) 84 km 382 m, (f) 238 km 162 m, (g) 441 km 309 m, (h) 378 km 527 m. \* Get Set Go With Sum Up Mathematics-4 ![](Sum up math-4_files/Sum20up20math-4-405.jpg) 2\. 110m57cm. 3. 1338m32cm. 6\. 88 m3 cm. 7. 269 km 80 m 4\. 1101km146m. 5. 9m9cm. 8\. 222 m 95 m. 9. 184 km 750 m. Exercise-53\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 60 m 53 cm, (b) 36 m 09 cm, (c) 164 m 15 cm, (d) 532 km 475 m, (e) 650 km 838 m, (f) 927 km 41 m, (g) 1 720 km 43 m, (h) 384 m 37cm. - 2\. 7 m 92 cm. 3. 37 m 75 cm. 4. 31 7 m 47cm. 5. 24 km 795 m. - 6\. 189 km 873 m. 7. 1556 m 90 cm. 8. 1607 km 788 m. Exercise-S^\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 201 m 12 cm, (b) 1059 m 25 cm, (c) 2025 m 72 cm, (d) 26865 m 62 cm, (e) 3291 km 750 m, (f) 375 km 645 m, (g) 9901 km 318 m, (h) 3873 km 978 cm, (i) 23636 m 55 cm, (j) 3723 m 80 cm. - 2\. 365 m. 3. 632 m 25 cm. 4. 14 km 350 m. Exercise-55\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1\. (a) 102 m 16 cm, (b) 8 m 52 cm, (c) 58 m 69 cm, (d) 231 m 65 cm, (e) 78 m 1 cm, (f) 33 km 110 m, (g) 25 km 312 m, (h) 3 km 654 cm, (i) 18 km 605 cm, (j) 45 km 804 m. - 2\. 21 km 58 m - 3\. 2 m 75 cm Exercise-56\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ (a) 45,6, 15,8, 4:45, (b)55,6, 5,7, 6:55, (c)40,8, 5,7, 8:40, (d)42,2, 18,3, 2:42, (e)44,10 16,11, 10:44, (f)48,2, 12,3, 2:48. ![](Sum up math-4_files/Sum20up20math-4-406.jpg) ![](Sum up math-4_files/Sum20up20math-4-407.jpg) ![](Sum up math-4_files/Sum20up20math-4-408.jpg) ![](Sum up math-4_files/Sum20up20math-4-409.jpg) ![](Sum up math-4_files/Sum20up20math-4-410.jpg) ![](Sum up math-4_files/Sum20up20math-4-411.jpg) ![](Sum up math-4_files/Sum20up20math-4-412.jpg) - 3\. (a) III, (b) I, (c) IV, (d) II. Exercise-57\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 7:30 a.m., (b) 9:00 a.m., (c) 5:15 p.m., (d) 2:30 p.m., (e) 10:00 p.m., (f) 5:30 a.m. - 2\. (a) p.m., (b) p.m., (c) a.m., (d) p.m., (e) p.m. - 3\. (a) 1:30 a.m., (b) 12:30 a.m., (c) 12:30 p.m., (d) 8:15 p.m., (e) 12:02 p.m. Exercise-58--------------------------------------------------------- - 1\. (a) 1200 hours, (b) 0000 hours, (c) 0700 hours, (d) 2100 hours, (e) 2200 hours, (f) 1000 hours. - 2\. (a) 5:00 p.m., (b) 1:00 a.m., (c) 1:00 p.m., (d) 7:00 p.m., (e) 3:00 a.m. ![](Sum up math-4_files/Sum20up20math-4-413.jpg) G=-- Exercise-59\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 3 hours, (b) 3 hours, (c) 55 minutes, (d) 1 hours 15 minutes, (e) 2 hours, (f) 4 hours 20 minutes, (g) 3 hours 20 minutes, (h) 9 hours. - 2\. (a) 90 minutes, (b) 105 minutes, (c)45 minutes, (d) 150 minutes. - 3\. (a)2:00p.m., (b) 12:15a.m., (c) 1:15a.m., (d) 12:30a.m. 4. 7:05a.m. - 5\. 6:30 p.m. 6. 8 hours. 7. (a) 5 hours 10 minutes, (b) 5 hours 25 minutes. - 8\. (a) 2 hours 30 minutes, (b) 2 hours 10 minutes, (c) 6 hours 25 minutes. 9. 5 hours. - 10\. 1 hours5 minutes. 11. 12:30p.m. Exercise-60-------------------------------------------------------- 1\. (a) 1 7days, (b) 118days, (c) 66days, (d) 53 days. 2. 46days. 3. 27days - 4\. 16 days 5. 46 days 6. 24 days 7. on 1 st October. - 8\. 27-11-1985. 9. July2012. 10. (a) 25.9.2010, (b) 15.8.1947. - 11\. (a) 16th January 1972, (b) 14thjuly 2000. Exercise-61\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1\. (a), (c), (d). 2. (c), (d). 3. (a), (c). 4. (a), (d). 5. Square. - 6\. (a) AB and CD, BC and AD, (b) A and C; B and D. (c) AC and BD. - 7\. (a)O, (b)OC, AOandOB. (c) DE. (d) AB. 8. (a) 10 cm, (b) 24. (c) 14 cm. (d) 18 cm. - 9\. (a) 6 cm, (b) 9 cm. (c) 13 cm. (d) 22 cm. 10. (a) T, (b) T. (c) F. (d) T. (e) T. (f) F. - 11\. (a) vertex, (b) 3. (c) all. (d) closed, (e) twice. Exercise-62\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 2 cm, (b) 6 cm, (c) 9 cm, (d) 3 cm. 2. Do it yourself. Exercise-63\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 148 m, (b) 121 m. (c) 63 m. (d) 32 cm, (e) 32 m, (f) 29 m. (g) 36 cm. (h) 40 m. - 2\. (a) 42 cm, (b) 36 cm. 3. (a) 50 cm, (b) 1 76 m. 4. (a) 50 cm, (b) 72 cm. - 5\. 120. 6. 84 feet. 7. 240 cm. 8. 840 cm. Exercise-64-------------------------------------------------------- 1\. (a) 14 square cm, (b) 9 square cm. (c) 18 square cm. (d) 8 square cm, (e) 10 square cm. Exercise-69\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 15,18, 21,24, (b) 25, 201 5, (c) 70, 90,110,1 30, (d) 11,1 3,15. 2. 35,45,55. - 3\. 80,66. 4. 80,90. 5. 64,100. 6. 55,78. - 7\. Doityourself. 8. (a) 36,49, 64, (b) 1555551,1666661,1777777. Exercise-70\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1\. (a) 0, (b) 1, (c) 1. 2. (a) 32,448,002, (b) 16,459, 536, (c) 54,036. 3. Doityourself. ![](Sum up math-4_files/Sum20up20math-4-414.jpg) (a) 12345654321, (b) 111111,1111111, (c) 1111110, (d) 1666665, (e) 222220, ![](Sum up math-4_files/Sum20up20math-4-415.jpg)(f) 10,100,1000,10000,100000, (g) 20, 220, 2220, 22220, 222220. 5\. (a) 1 3, 21, (b) 12321,121, (c) 625, 3125. Exercise-71\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1\. (a) 8, (b) 25 p, (c) 5 p, (d) 112, (e) 12. 2. (a) 75, (b) jeans, (c) shoes. - 3\. (a) bird, (b) Dragon, (c) 30. 4. (a) Mahindra, (b) 1, (c) 2. - 5\. (a) Cartoon, (b) Star news, (c) 4. 6. (a) Sandwich, (b) Idli, (c) 75. Exercise-72\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) Fifty six thousand seven hundred twelve, (b) Seventy eight thousand five hundred four, - (c) Eighty thousand ten, (d) Ninety four thousand one, (e) Fifty thousand three hundred thirteen, (f) Eighty thousand five. - 2\. (a) 20,308, (b) 54,907, (c) 90,500, (d) 3,303, (e) 80,080, (f) 38,009, (g) 11,111. - 3\. 10,000, Ten thousand. 4. 999999, Nine lakh ninety nine thousand nine hundred ninety nine. - 5\. (a) 9610, (b) 1069, (c) 1096, (d) 6091.6. (a) Ten thousand, (b) Thousand, (c) Hundred, (d) ones. - 7\. (a) 140395, (b) 141240. 8. (a) 21 743, (b) 13 3 80. - 9\. (a) 67589 + 43256 = 110845, (b) 78569 + 32589 = 111158. - 10\. (a) 13218-9413 = 110845, (b) 76859-34213 = 42646 - 11\. (a) One lakh nineteen thousand seven hundred thirty eight, (b) One lakh ninety six thousand four hundred eighteen. - 12\. (a) 4 3 6 (b) 512 13. (a) W = 2737, R = 9, (b) Q = 365, R = 42 [------x 3 16](#bookmark787) [1 3 0 8 3 0 72](#bookmark788) [3 4 8 0 5 1 20](#bookmark789) 3 6 1 8 8 \_\_\_1 5 3 6 0 \-------- 16 17 9 2 - 14\. (a) Ramesh has 3653 and Mahesh has 9240. How much money can be pooled by then? - (b) A pen costs 12. Priyanka bought 2142 pens. What is the total cost of pens? - (c) Ravi paid 625 fora box of eggs. If each egg costs 5, then how many egg are there in the box? - 15\. 7187. 16. 2112. 17. 4chairs. 18.1624. - 19\. Yes, 144 x 35 = 5040 so he needs 40 more candies. - 22\. (a)<,(b)>,(c)=,(d)<. 23.^,-^,- ' 1 ' 13' 13' 13' 1 3 '12' 12' 12'(° 11 ' \_9\_ 8 6 5 M 9 8\_\_6\_ \_6\_ - 29\. (a)^,(b)^,(c)^. 30. (a) ^(b) -^(c) - 32\. 1 cm. 33. 1 feet. 34. Get Set Go With Sum Up Mathematics-4 20\. (a) 7, (b) 6. 21. (a) 30, (b) 60. . 24. 200. 25. 25. 10 13 27 (10 8\_\_L ± 11'11’ 17 ' 17' 17 ' 17 28\. (a)1,(b) -^ (c) ^| -y 31. (a)1,(b)8,(c)4. 70\. 35. 25 kg 500 g. ZX ![](Sum up math-4_files/Sum20up20math-4-416.jpg) ![](Sum up math-4_files/Sum20up20math-4-417.jpg) 36\. 369.75. 37. 21 kg. 40\. 280. 41. 100. 43\. (a) 83 7 m 59 cm, (b) 631 km 915 m. 46\. Do it yourself. 47. (a), (f), (g). - 38\. 324 litre 325 millilitre. 39. 3 km 500 m. - 42\. (a) 151 dm, (b) 75 mm, (c) 15075 g, (d) 7257 ml. - 44\. 5 dozen 7 bananas. 45. 1m 70 cm. - 48\. Do it yourself. - 49\. (a) Diameter, (b) Centre, (c) Radius, (d) Chord. 50\. (a)3,(b)4,(c)2. - 51\. (a) a,b,l, (b) d, i, j, (c) a, b, c, d, g, j, k, I, (d) all, (e) a, b, c, d, e, g, i, k, I. - 52\. (a) 25 cm, (b) 42 cm, (c) 16 cm, (d) 33 cm. 53. 30 cm. 54. 36 cm. 55. 432 inches. - 56\. 19,680. 57. (a) 22 sq cm, (b) 13 sq cm. 59. (a) d, (b) c. 60. 5:05 pm. 61\. 29 hours. 62\. 4 hours 10 minutes. 64\. 8 hours. - 65\. (a) XXXVII, (b) XXIII, (c) XVIII, (d) XXXII. - 67\. 36/01/1950 and 02/10/1859. - 71\. (a) Marigold, (b) Sunflower, (c) 70, (d) 15. - 73\. Do ityourself. 74. 13.65. 66\. (a) 19, (b) 17, (c) ???, (d)24. 68\. 9. 69. Do ityourself. 72\. 2, 20, 200, 2000, 2000000. 75\. Do ityourself. ![](Sum up math-4_files/Sum20up20math-4-418.jpg) Get Set Go With Sum Up Mathematics-4