--- title: "Sum Up Math 3" book: "xxxxx" category: "MA" publisher: "Ratan Prakashan Mandir Pvt. Ltd." type: "Educational Material" ---  ![](Sum Up Math-3_files/Sum20Up20Math-3-1.jpg)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) ISBN: 978-93-7899-962-8 MRP: ' 325 BRANCHES ![](Sum Up Math-3_files/Sum20Up20Math-3-2.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-3.jpg) Agra Ahmedabad Bengaluru Gorakhpur Indore Jaipur Kanpur Kolkata Lucknow Meerut Mumbai Nagpur Noida Patna : 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. 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Ph.: 0120-4541101,02, Mob.: 9891179480 : Chunni Lal Market, BM Dass Road, Patna. Ph.: 0612-6456562, Mob. : 9931568925 ![](Sum Up Math-3_files/Sum20Up20Math-3-4.jpg) © 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 Typeset & Illustrated at : Typeface ![](Sum Up Math-3_files/Sum20Up20Math-3-5.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-6.jpg) # Preface 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 ## (\\ ![](Sum Up Math-3_files/Sum20Up20Math-3-7.jpg) 1\. Number & Number Name 5 2\. Addition 23 3\. Subtraction 36 4\. Multiplication 48 5\. Division 63 6\. Fractions 77 7\. Money 86 8\. Measurement Length 98 9\. Measurement Mass 108 10\. Measurement Capacity 113 11\. Time 119 12\. Geometry 132 13\. Patterns 141 14\. Data Handling 144 Formative Assessment -1 to 4 150 Answers 155 ![](Sum Up Math-3_files/Sum20Up20Math-3-8.jpg) ##### Kumbex and Kumb^x Nume ![](Sum Up Math-3_files/Sum20Up20Math-3-9.jpg) In this lesson you will learn about 4 digit numbers. You already know about - 3 digit numbers. Answer the following questions and test your knowledge. - [1. Which is the smallest 2 digit number ? \[\]](#bookmark8) - [2. Which is the greatest 2 digit number ? \[|](#bookmark9) - [3. Which is the smallest number of 3 digit ? \[\]](#bookmark10) - [4. Which is the greatest number of 3 digit ? \[\]](#bookmark11) [When we added 1 to 999 it becomes 1000. \[\]](#bookmark12) 999 + 1 = 1000 We also write it in this form. 999 + 1 = 9 hundreds + 9 tens + 9 ones + 1 ones = 9 hundreds + 9 tens + 10 ones = 9 hundreds + 9 tens + 1 tens = 9 hundreds + 10 tens = 9 hundreds + 1 hundreds = 10 hundreds = 1 thousands = 1000 ( The smallest number of 4 digits is 1000 ) 1000 is the smallest number of four digits. 1000-This number is read as "Onethousand". 1001 - It is read as "One thousand one" and written in this form also. - 1 thousands, 0 hundreds, 0 tens and 1 ones. - 1010 - It is read as "One thousand ten" and written as 1 thousands, 0 hundreds, 1 tens and 0 ones. 2000 - It is read as "two thousand" and written in 2 thousands, 0 hundreds, 0 tens and 0 ones. Similarly, 3000 is read as "three thousand". So on upto 9000. 9999 is read as "nine thousand nine hundred ninety nine." 9999 isthe greatest number of fourdigits. ![](Sum Up Math-3_files/Sum20Up20Math-3-10.jpg) ###### Use of Spike Abacus Number are shown on spike abacus as follows: and is written as 1. 1 ones is shown as Where - Th Stands for "Thousand" ![](Sum Up Math-3_files/Sum20Up20Math-3-11.jpg)H Stands for "Hundred" T Stands for "Ten" O Stands for "One" 10 ones or 1 tens is shown as ![](Sum Up Math-3_files/Sum20Up20Math-3-12.jpg)and is written as 10 Th H T O 10 tens or 1 hundreds is shown as ![](Sum Up Math-3_files/Sum20Up20Math-3-13.jpg) and is written as 100 10 hundreds or 1 thousands is shown as and is written as 1000 Example 1: Read the spike abacus and write the number: ![](Sum Up Math-3_files/Sum20Up20Math-3-14.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-15.jpg) (c) 2442 ##### . EXERCISE 1 - 1\. Read the spike abacus and write the number in the box. ![](Sum Up Math-3_files/Sum20Up20Math-3-16.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-17.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-18.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-19.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-20.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-21.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-22.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-23.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-24.jpg) - 2\. Write all numbers between : - (a) 1001 and 1006 — \[ | \[ I | I - (b) 2321 and 2326 — \[ ) \[ I \[ \] - (c) 5477 and 5482 — - 3\. Write the number next to each of the following number : (a) 4320 —; - (b) 6437 — \[ - (c) 7549 — ( Write the number before each of the following numbers : (a) 4578 —; - (b) 7771 — \[ - (c) 8695 — ( - 5\. Write the next three numbers for each of: - (a) 8472 - (b) 6589 — | - (c) 7855 I I - 6\. Counting by two, write number starting from : - [(a) 7748 - \[ \] O \[\]](#bookmark17) - [(b) 6405-](#bookmark18) 7\. Counting by 7, write number starting from : - (a) 2606 — - (b) 5719 — I I I I - 8\. Counting by tens, write numbers starting from : - (a) 6520 - |\_\_\_\_\_\_\_\_| (\_\_\_\_\_\_\_| |\_\_\_\_\_\_\_\_\_ - (b) 8777 - - 9\. Counting by hundreds, write numbers starting from - (a) 4026 - |\_\_\_\_\_\_\_\_| |\_\_\_\_\_\_\_\_| |\_\_\_\_\_\_\_\_| - (b) 3235 - |\_\_\_\_\_\_\_\_| |\_\_\_\_\_\_\_\_| |\_\_\_\_\_\_\_\_| - 10\. Counting by thousands, write numbers starting from - (a) 5318 - |\_\_\_\_\_\_\_\_| (\_\_\_\_\_\_\_\_| |\_\_\_\_\_\_\_\_| - (b) 6520 - - 11\. Look at the pattern and write next three numbers : - [(a) 3208,3212,3216—](#bookmark19) - [(b) 4919,4819,4719—](#bookmark20) - [(c) 7820, 6820, 5820—](#bookmark21) - 12\. Write the greatest number of : - (a) 2 digits \[ \] (b) 3 digit | | (c) 4 digits - 13\. Write the smallest number of: - (a) 2 digits | \] (b) 3 digit | | (c) 4 digits ###### Number in words (Number Names) Consider the following numbers. - (a) 2148 (b) 3472 (c) 5445 We can see that: - (a) 2148 has 2 thousands, 1 hundreds, 4 tens and 8 ones. We name it as "two thousand one hundred forty eight". - (b) 3472 has 3 thousands, 4 hundreds, 7 tens and 2 ones. We name it as "three thousand four hundred seventy two". - (c) 5445 has 5 thousands, 4 hundreds 4 tens and 5 ones. We name it as "five thousand four hundred forty five". Number in Figures: Think the fol lowing number names: - (a) Three thousand six hundred fifty one. - (b) Five thousand two hundred seventy seven. - (c) Six thousand forty three. We can write the above number as: (a) 3651 (b) 5277 (c) 6043 ![](Sum Up Math-3_files/Sum20Up20Math-3-25.jpg) ##### . EXERCISE 2 1\. Write the number names of the following numbers : ![](Sum Up Math-3_files/Sum20Up20Math-3-26.jpg) Thousands Hundreds Tens Ones 3 6 5 1 5 2 7 7 6 0 4 3 Therefore, the numbers in figures are - 2\. Write the following numbers in figures : - (a) Two thousand three hundreds twenty two. - (b) Three thousand fifty six. - (c) Four thousand six hundreds nine. - (d) Seven thousand two hundreds thirty. - (e) One thousand six hundred ninty two. - (f) Nine thousand nine. - 3\. Rewrite the following numbers interchanging the digits at the thousands and tens place: Example: 6 742 —> 4 762 - (a) 5671 \[ ) (b) 3964 I \] (c) 6532 - 4\. Rewrite the following number using the digits in the reversed order: Example: 3541 —» 1453 - (a) 7632 \[ I (b) 6549 I \] (c) 8573 ###### Expanded Forms Example 1 : Write the expanded form : - (a) 2653 (b) 6325 Solution: - (a) 2653 has 2 thousands, 6 hundreds, 5 tens and 3 ones. /. 2653 = 2000 + 600 + 50 + 3 - (b) 6325 has 6 thousands, 3 hundreds, 2 tens and 5 ones. /. 6325 = 6000 + 300 + 20 + 5 (/. Stands for therefore) - Example 2 : Write the following numbers in short form : - (a) 5000 + 600 + 40 + 3 (b) 7000 + 400 + 20 +1 (c) 3000 + 60 + 2 Solution : (a) ![](Sum Up Math-3_files/Sum20Up20Math-3-27.jpg) 5000 + 600 + 40 + 3 stands for 5 thousand, 6 hundreds 4 tens and 3 ones, that is, 5643 /. 5000 + 600 + 40 + 3 = 5643 - (b) 7000 + 400 + 20 + 1 stands for 7 thousand, 4 hundreds, 2 tens and 1 ones, that is, 7421 7000 + 400 + 20 + 1 = 7421. - (c) 3000 + 60 + 2 stands for 3 thousand, 0 hundreds, 6 tens and 2 ones, that is 3062 /. 3000 + 60 + 2 = 3062. - 1\. Fill in the blanks : (a) 2719 = thousands hundreds tens ones (b) 3526 = thousands hundreds tens ones (c) 5072 = thousands hundreds tens ones (d) 7403 = thousands hundreds tens ones (e) 9620 = thousands hundreds tens ones 2\. Write the following numbers in the expanded form : (a) 3739 = + + + (b) 7306 = + + + (c) 5072 = + + + (d) 4960 = + + + (e) 6321 = + + + (f) 8076 = + + + 3\. Write the following numbers in the short form : (a) (b) (c) 5000 + 600 + 70 + 2 3000 + 900 + 6 8000 + 80 + 2 (d) 7000 + 6 = I \] (e) 2000 + 600 + 1 = ###### Place Value - Face value Let us take the number 54 54 = 5 tens + 4 ones ![](Sum Up Math-3_files/Sum20Up20Math-3-28.jpg) = 50 + 4 Get Set Go With Sum Up Mathematics-3 ![](Sum Up Math-3_files/Sum20Up20Math-3-29.jpg) In 54, 5 is at the tens place. The place value of 5 is 50 The digit 4 is at the ones place. The place value of 4 is 4 The face value of 5 is The face value of 4 is 5 4 Now let us take a three digit number 645 645 = 6 hundreds + 4 tens + 5 ones = 600 + 40 + 5 In 645, the digit 6 is at the hundreds place. The place value of 6 is 600 The digit 4 is at the tens place. The place value of 4 is 40 The digit 5 is at the ones place. The place value of 5 is 5 The face value of 6 is The face value of 4 is The face value of 5 is 6 4 5 Take a four digit number: 4321 = 4 thousands + 3 hundreds + 2 tens + 1 ones = 4000 + 300 + 20 +1 In 4321,4 is at the thousands place. The place value is 4 is 4000 The digit 3 is the hundreds place. The place value of 3 is 300 The digit 2 is at the tens place. The place value of 2 is 20 The digit 1 is at ones place. The place value of 1 is 1 The face value of 4 is The face value of 3 is The face value of 2 is The face value of 1 is 4 3 2 1 From the above example, we have learnt that: The place of a digit changes according to the place it occupies in the number, but the face value remains unchanged and is the value of the digit itself. ![](Sum Up Math-3_files/Sum20Up20Math-3-30.jpg) Example 1 : Find the place value of each digit in 541 7. Solution: 5 4 17 7 ones \------------► 1 tens 4 hundreds 5 thousands Note - • Place value of 0 is always Zero. - Example 2 : Find the place value of two sixes. Solution: 3 6 6 1 xL 6 0 0 Place Value 7 10 400 5000 3 6 6 1 6 0 Place value of 6 = 60 Place value of 6 = 600 - Example 3 : Write the face value of 6 in the following number: 631, 2564 and 6354. Solution : In 631, the face value of 6 is 6. In 2564, the face value of 6 is 6. In 6354, the face value of 6 is 6. ##### Q. EXERCISER %■--- - 1\. Arrange the numerals in the place value table : Thousands Hundreds Tens Ones 3816 7634 609 8058 2\. Write the place value in the box of each red coloured digit in the following numbers: 3 4 2 7 6 4 7 9 2 4 6 9 2 8 9 7 6 4 5 5 6 3 2 3 9 12 6 7 8 2 3\. Write the place value of the digit 7 in the box : 72 679 8637 5788 4070 2700 4\. Write the place values of 6's in 6564. ![](Sum Up Math-3_files/Sum20Up20Math-3-31.jpg) - 5\. Find the difference of the place value of two fours in 7464. - 6\. Tick Anmol'sjeep number. It has 3 hundreds, 2 ones, 1 tens and 4 thousands. [3214 1432 43124123](#bookmark33) - 7\. Encircle Shreya's house number. It has 6 tens and 4 thousands. [4006 6004 60404060](#bookmark34) - 8\. Which of the following statements are correct ? - (a) The place value of 5 in 4568 is 568 - [(b) The place value of 6 in 5468is 68](#bookmark35) - [(c) The place value of 8 in 2387is 80](#bookmark36) - 9\. Solve the number puzzle by writing numbers. ###### Across : - 1\. 3 hundreds 8 tens 9 ones - 3\. 3 hundreds 6 tens 5 ones - 5\. 4 thousand 5 hundred 8 tens - 7\. Two thousand three hundred twenty two - 8\. Eight thousand nine hundred forty four - 9\. 5 hundred + thirty five - 11\. Seven hundreds seven tens seven ones - 13\. 9 thousand 5 hundreds eighty ![](Sum Up Math-3_files/Sum20Up20Math-3-32.jpg) - 15\. Six thousand two hundred sixteen - 16\. 20 more than 160 - 17\. 1 thousand 4 hundreds 6 tens ![](Sum Up Math-3_files/Sum20Up20Math-3-33.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-34.jpg) ###### Down : - 1\. 3 thousand 8 hundred 88 - 2\. Nine thousands four hundreds twenty four - 3\. 3 thousands 1 hundred + twenty five - 4\. Five thousands 6 hundreds six tens five ones - 6\. 5 thousands 3 hundreds + 49 - 10\. Three thousands six hundred + eighty eight - 11\. 7 hundreds six tens 5 ones - 12\. 30 more than 681 - 14\. 200 less than 710 ![](Sum Up Math-3_files/Sum20Up20Math-3-35.jpg) ###### Order Relation Now you will learn about the method of finding the greater of the two given 4-digit numbers. You already know about the method of finding the greater of the two given numbers having less than 4 digit. You know that "6 is greater than 3" and it is written as 6> 3. You also know that "5 is less than 8" and it is written as 5 < 8. Also, 6 is greater than 2 is the same as 2 is less than 6. .-. In symbols, 6 > 2 is the same as 2 < 6. ![](Sum Up Math-3_files/Sum20Up20Math-3-36.jpg) Q We have al ready learnt that: - (a) A number having more digits is greater than the number having less digits. For example, 1 75 > 25; 14 > 7; 207 > 77. - (b) If the two given numbers have the same number of digits, then we compare the digits on the extreme left and decide. - (c) If the digits on the extreme left are equal, we keep on comparing the next digits on the right. Forexample, 76 > 65; 256 > 242; 378 > 372. Now, by using these rules, we can solve some examples. - Example 1: Which is greater: (a) 571 or 1021 (b) 2879or4572? Solution: - (a) 571 has three digits 1021 has four digits Four digit number is greater than three digit number. /. 1021 >571 - (b) Each number has 4 digits. We compare the digits on the extreme left. The digit on the extreme Ieftof2879 is2 The digit on the extreme left of 4572 is 4 VVe know that 4 > 2 /. 4572 > 2879 - Example 2: Which issmaller452 7or4931 ? Solution: Each number has 4 digits. We compare the digit on the extreme left. Both are equal. Now we will compare next digit atthe hundreds's place. 4527 has 5 hundreds. 4931 has 9 hundreds. - 5 hundreds is smaller than 9 hundreds. .-. 452 7 is smallerthan 4931. or 452 7 < 4931 - ###### Example 3: Which is greater: 7432 or 7451 ? Solutions: 7432 has 7 thousands and 4 hundreds. 7451 has 7 thousands and 4 hundreds. Because both, the numbers have same digit at the place of thousand and hundreds, therefore, we compare the digits at the ten's places. 7432 has 3 tens and 7451 has 5 tens. - 5 tens is greaterthan 3 tens. /. 7451 > 7432 or 7451 is greaterthan 7432 ##### U- EXERCISE 5 ^------------ Put >, < or = in each box to make sentence true: (a) 455 £ ) 455 (b) 654 ( 3 745 (c) 7295 £ ) 7682 (d) 2451 3 995 (e) 2701 Q ) 7120 (f) 3529 ( 3 2593 (g) 4532 C ) 4798 (h) 6345 ( 3 6354 (i) 2345 C ) 2348 (j) 500 + 25 3 525 (k) 3400 O Three thousand and 4 hundred. (I) 2254 O Two thousand two hundred and forty five. (m) 4506 O Fourthousand six hundred five. (n) 5025 O 5000 + 20 + 5. - (o) The number of houses in two block A and B is 4364 and 4634 respectively. Which block has less houses ? - (p) A block has 1421 girls and 1498 boys. Which are more in number, girls or boys ? ###### Ascending-Descending Order Ascending means "from smaller to greater". Descending means "from greater to smaller". ![](Sum Up Math-3_files/Sum20Up20Math-3-37.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-38.jpg) - ###### Example 1: Write the following numbers in ascending (increasing) order. 3652,835,5210,56. Solution: - 56 is the smallest number in given four numbers. Otherthree numbers greaterthan 56 in order are 835, 3652 and 5210. .’. The given numbers when written ascending order are: 56,835, 3652, 5210. - Example 2: Write the following numbers in descending (decreasing) order. 585,895,1531,3245,5643. Solution: 5643 is the greatest number in given four numbers. The other four numbers smallerthan 5643 in decreasing order are 3245,1531,895 and 585 .-. The given numbers when written descending order are: 5643,3245,1531,895,585. ###### Successor-Predecessor The number that comes just after a individual number is called it successor. For example: Number Successor 46 242 3453 45 241 3452 The successor of a number is 1 more than the given number. The number that comes just before a individual number is called its predecessor. For example: ###### Number Predecessor 25 566 4788 26 567 4789 ![](Sum Up Math-3_files/Sum20Up20Math-3-39.jpg) The predecessor of a number is 1 less than the given number. Accordingly, for a given number, we can find its successor and predecessor. ###### Note - ###### • The predecessor of 'Zero' will be taught in higher classes. ###### Formation of Smallest and Greatest Numbers Suppose you have three integers (whole number) 2, 5 and 8. You want to form these in smallest number, using all the given integers without repetition. First you select the smallest integer and write it in the hundreds place. Then you write the next greater integer in the ten's place and in last the greatest interger in the one's place. The smallest number is 258 ###### H T O 2 5 8 If you want to form these integers in greatest number without repetition integers. First you select the greatest integers and write it in hundred's place. Then you write the next smaller integer in the ten's place and lastly, the smallest integer in the one's place. The greatest number in 852 ###### H T O 8 5 2 Now, take four integers 2, 8, 0, 6 and form smallest and the greatest numbers of four digits without repetition. According to the above explanation the smallest number is ###### Th H T O 0 2 6 8 You know the smallest# digit numbers is 1000 not 0001. In first method, 0 on the extreme left place has no meaning. Therefore the correct# digit smallest number will be 2 0 6 8 ###### Note - • 0 is not written on the extreme left place of a number. - • 0268 is a 3 digit number 268. According to the above explanation for the greatest number of 3 digit, the greatest numberof 4 digits number will be 8620. - ###### Example 3: Write the greater and smaller numbers of 2 digits using# and 2 only once ? ###### Solution: ![](Sum Up Math-3_files/Sum20Up20Math-3-40.jpg) Write# in tens column and 2 inones column which makes greater number Get Set Go With Sum Up Mathematics-3 Greater number = 42 4 2 Similarly, smaller number 2 4 Smaller number = 24 - ###### Example 4 : Write the smallest and the greatest numbers using 6, 1, 8 (without repeating a digit). - (a) 2 digits (b) 3 digits Solution : - (a) 2 digitsmallest number is 16 (b) 3 digit smallest number is 168 2 digit greatest number is 86 3 digit greatest number is 861 Examples: Write the smallest and the greatest number of given 4 digit numbers by changing position of the digits. (a) 2798 Solution: - (a) Smallest number = 2789 Greatest number = 9872 (b) 4619 - (b) Smallest number = 1469 Greatest number = 9641 ##### (J. EXERCISE 6 %•-------------- - 1\. In each of the following, tick (/) the greatest numbers: - (a) 43 7,521,625,211 (b) 102,365,615,318 (c) 9782,5945,2612,3515. - 2\. In each of the following, tick (/) the smallest numbers: - (a) 251,402,196,719 - (b) 936,596,742,2855 - (c) 7896,6987,5945,3412. ![](Sum Up Math-3_files/Sum20Up20Math-3-41.jpg) - 3\. Rewrite the following numbers in increasing order in the box provided : - (a) 1561,965,95,565,1865 - (b) 681,795,1645,805 - (c) 3289,1206,981,1565,2100 - 4\. Rewrite the following numbers in decreasing order in the box provided : - (a) 15 7,13 62,42 7,92 6 - (b) 1751,981,351,1201 - (c) 1234,4321,3789,5525 - 5\. Write the ascending ordescending order in the box for the following number: - (a) 87,301,528,829,1230 - (b) 225,345,641,928,1350 - (c) 509, 795,1245,1501,1697 - (d) 4055,3081,2995,2100,1595 ![](Sum Up Math-3_files/Sum20Up20Math-3-42.jpg) 8\. Write the successor of each ofthe following numbers in the boxes: (a) 565 - | | (b) 2451 - | | (c) 1956 Write the predecessor of each ofthe following numbers in the boxes: (a) 748 - | | (b) 3242 - | | (c) 4546 Write the smaller and the greater numbers of 2 digits using 6 and 5 (without repeating a digit): Smaller- Greater- - 9\. Write the smaller and the greater numbers of 3 digits (without repeating a digit) (a) 5,3,2 (b) 6,1,7 - 10\. Write the smaller and greater numbers of 4 digits (without repeating a digit): Smaller number Greater number - (a) 2,4,8, 3 11\. Write the smallest and the greatest 2 digit numbers (without repeating a digit) from the following digits: Smaller number Greater number ![](Sum Up Math-3_files/Sum20Up20Math-3-43.jpg) - (a) 3,0,9 - (b) 5,4,7 Get Set Go With Sum Up Mathematics-3 - 12\. Write the smaller and the greater 3 digit numbers by changing the position of thedigits. Smaller number Greater number - (a) 254 - (b) 734 - 13\. Write the smallest and the greatest 4 digit numbers by changing the position of thedigits. Smaller number Greater number - (a) 3416 - (b) 6287 ###### Mental Drills - 1\. Circle the correct answer: - (a) The number consisting of 3 tens, 4 thousands, 2 hundred and 5 ones is : 3425 or 4235 - (b) The smallest 3 digit number consisting of 0, 3, 7 is : 307 or 037 - (c) The smallest 3 digit number is : 100 or 101 - (d) The successor of 5636 is : 5637 or 5635 - (e) 1 less than 4392 is its : Predecessor or successor - (f) The number consisting of 7 ones and 4 thousand is : 4267 or 4709 - (g) Arranging the numbers from smallest to greatest is called : descending order or ascending order 2\. Write 'Yes' or 'No' in the box provided for answer: (a) (b) (c) (d) ![](Sum Up Math-3_files/Sum20Up20Math-3-44.jpg) Is the smal lest 2-digit number, the predecessor ofthegreatest 1 -digitnumber ? Is the greatest 2-digit number, the predecessor ofthesmallest3-digitnumber? Is the greatest 3-digit number, the predecessor ofthe smal lest 4-digit number? Is the predecessor of 1000, the greatest number of 3-digit ? Is the smallest 3-digit number the successor ofthe greatest 3-digit number ? ##### Addition ![](Sum Up Math-3_files/Sum20Up20Math-3-45.jpg) You have already learnt in your 2nd standard, the addition of 2-digit numbers without and with regrouping. You also learnt the addition of 3-digit numbers without regrouping. In this class, we will first repeatthem and then learn the addition of 3-digit and 4-digit numbers with regrouping. After the addition which you get as result is called the sum. Addition without Regrouping - Example 1: Add : 431 and 546. Solution: Putthe numbers in the column form: ###### H T O H T O 4 3 1 \+ 5 4 6 7 Adding ones : 1+6 = 7 4 3 1 \+ 5 4 6 7 7 Adding tens : 3+4 = 7 4 3 1 5 4 6 9 7 7 Adding hundreds: /. 431 + 546 = 977 Same rules apply to add 4-digit numbers. - Example 2: Add: 4351 and 2301. Solution: Put the numbers in the column form: Th H T O Th H T O ###### Th H T O ###### Th H T O 4 3 5 1 \+ 2 3 0 1 2 Adding ones 1+1=2 /. Sum of 4351 4 3 5 1 \+ 2 3 0 1 5 2 Adding tens 5 + 0 = 5 2301 is 6652 4 3 5 1 \+ 2 3 0 1 6 5 2 Adding hundreds 3 + 3 = 6 [4 3 51](#bookmark87) [+ 2 3 01](#bookmark88) [6 6 52](#bookmark89) Adding thousands 4 + 2 = 6 ![](Sum Up Math-3_files/Sum20Up20Math-3-46.jpg) ##### g. EXERCISE 7 - 1\. Add : H O 2 5 3 \+ 434 ###### H T O (c) H T O 4 1 3 3 2 5 \+ 542 \+ 373 (d) + Th H O 3 2 2 5 5 3 4 1 (e) 3 0 5 2 6 10 2 (f) Th H T O 8 6 2 3 13 5 4 Th H T o 5 3 6 8 \+ 16 11 (h) Th H T O 5 14 3 3 2 10 4 4 3 0 5 3 6 7 Th H o 4 5 16 2 3 6 3 ###### Th H T O Th H O 6 4 0 1 3 4 5 8 7 4 12 10 5 3 (m) + Th H o 2 3 0 1 4 3 15 (n) 4 3 0 7 (q) (P) Th H T O 8 6 2 3 \+ 10 4 5 ![](Sum Up Math-3_files/Sum20Up20Math-3-47.jpg) 2 0 2 7 (o) + (r) + Th H T O 6 4 0 6 2 3 8 0 Th H O 4 5 12 0 4 8 5 Th H T O Th H O ![](Sum Up Math-3_files/Sum20Up20Math-3-48.jpg)(u) Th H T O 4 3 2 1 5 4 5 6 \+ 0212 4 3 2 2 2 14 \+ 5 3 3 2 [6 5 32](#bookmark96) [3 45](#bookmark97) [+ 2 0 21](#bookmark98) - 2\. Write in columns and add. Write the sum in words : - (a) 3046 + 2421 + 3520 - (b) 4130 + 2324 + 443 - (c) 413 + 2304 + 6252 - (d) 312 + 7243 + 343 ###### Regrouping ![](Sum Up Math-3_files/Sum20Up20Math-3-49.jpg)and ![](Sum Up Math-3_files/Sum20Up20Math-3-50.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-51.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-52.jpg) 13 tens = 130 - 8 tens + 5 tens = 13 tens 13 tens = 1 hundred and 3 tens Similarly, - (a) 8 hundreds + 42 tens = 12 hundreds and 2 tens - (b) 2 hundreds + 21 tens + 12 ones = 4 hundreds 2 tens 2 ones - (c) 6 hundreds + 8 hundreds = 14 hundreds or 1 thousand 4 hundreds. - ##### B. EXERCISE 8 %\*-------------- 1\. Fill in the boxes : (a) (b) 6 tens + 8 tens 9 hundreds 35 tens = tens or hundreds and hundreds tens tens (c) 14 hundreds 28 tens = hundreds tens or (d) (e) 9 hundreds + 7 hundreds 5 hundreds 15 tens 27 ones thousand hundreds or thousand and hundreds hundreds tens hundreds tens ones or (f) 16 hundreds 24 tens 35 ones hundreds hundreds tens ones tens ones or (g) 12 hundreds + 13 hundreds hundreds tens ones or thousand hundreds tens ones hundreds or thousandsand \_\_ hundreds Addition with regrouping (3-digit numbers) - Example 1 : Add: 574 and 246. Solution. ###### H T O H T O 1 1 5 7 4 2 4 6 ###### H T O 1 5 7 4 2 4 6 0 2 0 1 1 5 7 4 2 4 6 8 2 0 Add ones 4 + 6 = 10 ![](Sum Up Math-3_files/Sum20Up20Math-3-53.jpg)10 ones = 1 tens + 0 ones Add tens 1+7 + 4 = 12 12 tens = 1 hundred + 2 tens Add hundreds 1 + 5 + 2 = 8 :. 5 74 + 246 = 820 Sum = Eight hundred twenty - Example 2 : Add : 624 and 798. ###### Solution : Th H T O 6 2 4 7 9 8 ###### Add ones ![](Sum Up Math-3_files/Sum20Up20Math-3-54.jpg) 4 + 8 =12 12 ones = 1 tens + 2 ones 2 ![](Sum Up Math-3_files/Sum20Up20Math-3-55.jpg) ###### Add tens 1+2 + 9 = 12 12 tens = 1 hundred + 2 tens ###### Add hundreds 1+6 + 7=14 14 hundreds = 1 thousand 4 hundreds. .-. 624 + 798 = 1422 Sum = One thousand four hundred twenty two. ##### J. EXERCISE 9 ^------------ 1\. Add : Th H O (b) ![](Sum Up Math-3_files/Sum20Up20Math-3-56.jpg)(c) ###### Th H T O (d) ###### Th H T O [8 7 13 7 7](#bookmark121) [+ 549+ 396](#bookmark122) [6 7 87 8 6](#bookmark123) [+ 569+639](#bookmark124) ![](Sum Up Math-3_files/Sum20Up20Math-3-57.jpg) - 25\. Add and Write the sum in words : (a) 422 + 578 (b) 748 + 656 (c) 856 + 866 ![](Sum Up Math-3_files/Sum20Up20Math-3-58.jpg)###### Addition of three numbers (3-digit) Example 1 : Add : 328, 13 7 and 242. ###### Solution : ###### H T O 1 1 3 2 8 - 1 3 7 \+ 2 4 2 7 0 7 ##### ^. EXERCISE 10 , - 1\. Add : - ###### (a) H T O - ###### (b) H T O - ###### (c) Th H T O (d) ###### H T O [1 7 84 3 7](#bookmark142) [+ 2 4 5 + 1 43](#bookmark143) [+ 3 0 1 + 2 65](#bookmark144) [6 6 43 4 6](#bookmark145) \+ 1 7 4 + 4 6 5 [+ 19 3+15 4](#bookmark146) - 2\. Find the sum : - (a) 315 + 279 + 250 - (b) 513 + 297 + 211 - (c) 356 + 190 + 265 - (d) 623 + 236 + 57 - 3\. More addition sums : - [(a)(b)](#bookmark147) [1 8 44 4 5](#bookmark148) [+ 371+118](#bookmark149) [+ 12 4 +6 9](#bookmark150) [(c)(d)](#bookmark151) [2 0 73 1 2](#bookmark152) [+ 12 5+215](#bookmark153) [+ 380+249](#bookmark154) ![](Sum Up Math-3_files/Sum20Up20Math-3-59.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-60.jpg) [4 3 12 8 5](#bookmark155) [+ 13 9+218](#bookmark156) [+ 7 3+417](#bookmark157) [(g)(h)](#bookmark158) [1 8 53 6 5](#bookmark159) [+ 278+264](#bookmark160) [+ 342+223](#bookmark161) [(i)(j)](#bookmark162) [15 318 1](#bookmark163) \+ 2 2 6 + 3 1 2 \+ 4 4 + 3 3 7 [(k)(I)](#bookmark164) [2 8 61 7 0](#bookmark165) [+ 307+335](#bookmark166) [+ 237+246](#bookmark167) [(m)(n)](#bookmark168) [1 8 64 7 9](#bookmark169) 3 2 7 \+ 14 3 \+ 271 [+ 313+132](#bookmark170) \+ 2 2 1 + 2 8 3 ###### Word Problem We use the concept of addition so many times in ourdaily routine. Look at the following examples. - Example 1: Shalu has 446 chocolates. Her mother gave her 287 chocolates more. How many chocolates does she has ? Solution : Add all chocolates [11](#bookmark173) [Number of chocolates shalu has -----►446](#bookmark174) Number of chocolates her mother gave her ----► +287 [Total chocolate shalu has ------►7 3 3](#bookmark175) - ###### Example 2: In a colony, there are 3257 houses in A block and 2413 houses in B block. How many houses are there in colony ? ![](Sum Up Math-3_files/Sum20Up20Math-3-61.jpg) Solution: [Add Total houses](#bookmark178) [Houses in A block -----► 3 2 57](#bookmark179) Houses in B clock ---► +2413 [Total Houses -----► 5 6 70](#bookmark180) Example3: A florist solds 356 roses, 48 lotuses and 568 marigolds. How many flowers did he sell ? Solution: [Add total flowers](#bookmark181) [Roses -----►3 5 6](#bookmark182) [Lotus -----► +4 8](#bookmark183) [Marigold ---►+568](#bookmark184) [Total flowers gold ------►](#bookmark185) {J. EXERCISE 11 %•-------------- - 1\. Anmol packed 274 mangoes, 68 pomegranates and 135 apples in the box for gift. How many fruits did he packed? - 2\. Sneha wear 182 beads of necklace and her mother 245 beads of necklace. How many total beads they have? - 3\. In a house, left side's wall is build of 2595 bricks and right side's wall is build of 2782 bricks. How many bricks are there in the house? - 4\. Rahul has two boxes of marbles. In one box there are 286 marbles and in another box 347 marbles. How many marbles he has? - 5\. There are 4592 males in a village and 3 745 females. How many people are there in the village? - 6\. At a petrol pump, there is 3527 litres of petrol in a tank and 5678 litres of diesel in anothertank. What is the quantity of total oil atthat petrol pump? - 7\. A shopkeeper sold 382 video game cassettes and 575 C.D. games in a week. How many total things he sell? ![](Sum Up Math-3_files/Sum20Up20Math-3-62.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-63.jpg) - 8\. There are 645 seeds in one water melon and 592 in second water melon. How many total seeds are there? - 9\. A cow gives 356 litre of milk, a buffaloes gives 489 litre and a goat gives 56 litres in a month. How much milkall of them gave in a month? - 10\. A shopkeeper sold 179 copies, 287 pencils and 190 pens in two days. How many total items did he sell? - 11\. In a garden Suhani picked 187 flowers, Nancy picked 295 leaves and Rohan picked 78 stones. How many total items did they pick? - 12\. Anmol collected 369 coins of ? 2 and 194 coins of ? 5. How many coins did he collect? ###### Properties of Addition See the following additions : 1 8 + 27 Is the sum in both cases the same? 2 6 + 37 Is the sum in both cases the same? 3 8 + 49 Is the sum in both cases the same? ![](Sum Up Math-3_files/Sum20Up20Math-3-64.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-65.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-66.jpg) 5 5 + 46 ![](Sum Up Math-3_files/Sum20Up20Math-3-67.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-68.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-69.jpg) Is the sum in both cases the same? ![](Sum Up Math-3_files/Sum20Up20Math-3-70.jpg) Is the sum in both cases the same? [3 6 95 1 9](#bookmark188) [+ 519+369](#bookmark189) Is the sum in both cases the same? [2 3 73 8 4](#bookmark190) [+ 384+237](#bookmark191) Is the sum in both cases the same? ![](Sum Up Math-3_files/Sum20Up20Math-3-71.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-72.jpg) Is the sum in both cases the same? Here, we noticed that the sum of two numbers is the same when we change the order of the numbers. ###### See few more examples: (32 + 47) + 83 ###### =79+83 = 162 Is the sum in both the cases the same? 32 + (47 + 83) = 32 + 130 = 162 Yes ![](Sum Up Math-3_files/Sum20Up20Math-3-73.jpg) (634 + 596) + 213 634 + (596 + 213) = 1230 + 213 = 634 + 809 = 1443 = 1443 Is the sum in both the cases the same? Yes 483 + (993 + 656) (483 + 993) + 656 = 483 + 1649 = 1476 + 656 = 2132 = 2132 Is the sum in both the cases the same? Yes Note BiiillfeililBiiilsBH^^ - • The sum of three number is the same when we change the grouping of the numbers. - • When zero is added to a number or a number is added to zero, the sum is the number itself. We see those in following example. Add: ![](Sum Up Math-3_files/Sum20Up20Math-3-74.jpg) Add and fill in the blanks: (a) 721 + 0 = ............... (b) 0 + 183 =.............. ##### £a EXERCISE 12^------------ - 1\. Fill in the blank without adding: (a) (b) ![](Sum Up Math-3_files/Sum20Up20Math-3-75.jpg) 265 + 391 = 391 + 387 + 695 = + 695 738 + 873 = + 873 595 + 0 = 0 + 295 + 575 + 446 = + 575 + 446 (f) 747 + 995 + = 314 + 995 + 747 (g) 989 + 0 = — (h) 625 + 424 + = 578 + \+ 424 (i) 707 + 300 + 555 = 555 + 300 + (j) 818 + + 377 = 377 + + 413 ![](Sum Up Math-3_files/Sum20Up20Math-3-76.jpg) ###### Mental Drills 1\. Fill in the blanks : 69 + 23 = 72 + (a) (b) (c) 231 + 87 = 238 + 145 + 98 = 175 + 2\. Write true or false for following statements (T/F) - (a) 5 tens = 50. - (b) 1 hundreds = 10 tens. - (c) The greatest number of 3 digits are (999 + 1). - (d) 2 hundreds 18 tens and 16 ones = 2 hundreds 1 7 tens and 1 7 ones. - (e) 64 is the sum of 34 and 32. - (f) The sum of greatest 3-digit number and the smallest 4-digit number is 1999. (g) 177 + 365 = 365 + 177. ![](Sum Up Math-3_files/Sum20Up20Math-3-77.jpg) In your 2nd standard, you learnt the subtraction of 2-digit numbers with and without decomposing. You also learnt the subtraction of 3-digits number without decomposing. In this class we will first repeat them and then learn the subtraction of 3-digit and 4-digit numbers. After the subtraction which you get as result is cal led the difference. Subtraction without Decomposing - Example 1: Subtract 253 from 597. Solution: Put the numbers in the column and subtract: ###### H T O ###### H T O ###### H T O 5 9 7 - 2 5 3 4 Subtract ones 7-3 = 4 ones 5 9 7 - 2 5 3 4 4 Subtract tens 9-5 = 4 tens 5 9 7 \- 2 5 3 3 4 4 Subtract hundreds 5-2 = 3 hundreds /. 597-253 = 344 Same rule apply to subtract 4-digit numbers. - Example 2: Subtract 3245 from 7568. Solution: Put the numbers in the column and subtract: ![](Sum Up Math-3_files/Sum20Up20Math-3-78.jpg) |Th H T Oil I |Th H T O| T |Th H T O|T |Th H T O|l 7 5 6 8 7 5 6 8 7 5 6 8 7 5 6 8 3 2 4 5 \- 3 2 4 5 \- 3 2 4 5 \- 3 2 4 5 3 2 3 3 2 3 4 3 2 3 Subtract ones Subtract tens Subtract hundreds Subtract thousand 8-5 = 3 ones 6-4 = 2 tens 5-2 = 3 hundreds 7-3 = 4 thousand 7568-3245 = 4323 ![](Sum Up Math-3_files/Sum20Up20Math-3-79.jpg) ##### EXERCISE 13 s Subtract: ###### H T O (b) 4 5 6 -234 ![](Sum Up Math-3_files/Sum20Up20Math-3-80.jpg) (c) ###### H T O 8 5 7 -423 ![](Sum Up Math-3_files/Sum20Up20Math-3-81.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-82.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-83.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-84.jpg)Find the difference : - (a) 8479-2316 = (c) 5284 - 3032 = (e) 9687-6423 = - (b) 7895 - 3462 = (d) 8352 -4241 = - 3\. Fill in the boxes: (a) ###### Th H T O (b) ###### Th H T O [48 9](#bookmark216) [- 2 34](#bookmark217) 3 3 [9 73](#bookmark218) [-](#bookmark219) 3 5 1 ###### Borrowing (Decomposing) 1 ten = 10 ones 1 hundred = 10 tens Similarly, - (a) 3 tens 5 ones = 2 tens 15 ones - (b) 5 tens 0 ones = 4 tens 10 ones - (c) 6 hundreds 3 tens 7 ones = 5 hundreds 13 tens 7 ones - (d) 5 hundreds Otens 8 ones = 4 hundreds 10tens 8 ones = 4 hundreds 9 tens 18 ones ##### ^. EXERCISE M ^----------- - ###### 1. Decompose and fill in the blanks : - (a) 3 hundreds 4 tens 7 ones = 2 hundreds!\_\_\_I tens 7 ones. (b) (c) (d) (e) (f) (g) 4 tens 5 ones = 5 hundreds 2 tens 3 3 hundreds 5 tens 6 4 hundreds 4 tens 8 tens 15 ones. ones tens 3 ones. ones = 3 hundred ones tens 16 ones. hundred 14 tens 8 ones. 5 hundreds 5 ones = 4 hundreds 6 hundreds4 ones = 5 hundreds tens 5 ones. tens 4 ones. = 5 hundreds 9 tens ones. ###### Subtraction (with decomposing) Example 1: Fill in the blanks: 4 hundreds 3 tens 4 ones - 1 hundred 4 tens 6 ones = 4 hundreds 2 tens ones-1 hundred 4 tens 6 ones ![](Sum Up Math-3_files/Sum20Up20Math-3-85.jpg) = 3 hundreds = 2 hundreds tens 14 ones - 1 hundred 4 tens 6 ones tens 8 ones ![](Sum Up Math-3_files/Sum20Up20Math-3-86.jpg) ###### Solution : 4 hundreds 3 tens 4 ones - 1 hundred 4 tens 6 ones = 4 hundreds 2 tens 14 ones - 1 hundred 4 tens 6 ones = 3 hundreds 12 tens 14 ones - 1 hundred 4 tens 6 ones = 2 hundreds 8 tens 8 ones Example 2 : Subtract 569 from 887. Solution : ![](Sum Up Math-3_files/Sum20Up20Math-3-87.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-88.jpg) Subtract the ones We cannot subtract 9 ones from 7 ones. So we will borrow to tens for ones. - 8 tens 7 ones = 7 tens 1 7 ones Now we can subtract 1 7 ones - 9 ones = 8 ones Subtract the tens - 7 tens - 6 tens = 1 tens Subtract the hundreds - 8 hundreds - 5 hundreds = 3 hundreds /. 887- 569 = 318 Example 3 : ![](Sum Up Math-3_files/Sum20Up20Math-3-89.jpg) Subtract the ones We cannot subtract 7 ones from 4 ones. So, we will borrow to tens for ones. 6 tens 4 ones = 5 tens 14 ones. Now we can subtract 14 ones - 7 ones = 7 ones ![](Sum Up Math-3_files/Sum20Up20Math-3-90.jpg) Subtract the tens H T O 15 14 5 6 4 \- 2 8 7 7 7 We cannot subtract 8 tens from 5 tens. So, we will borrow to hundreds for tens. 5 hundreds 5 tens = 4 hundreds 15 tens. Now we can subtract 15 tens - 8 tens = 7 tens. ![](Sum Up Math-3_files/Sum20Up20Math-3-91.jpg) Subtract the hundreds - 4 hundreds - 2 hundreds = 2 hundreds 564-287 = 277 Example 4 : Subtract 478 from 700. Solution : ![](Sum Up Math-3_files/Sum20Up20Math-3-92.jpg) We cannot subtract 8 ones from 0 ones, so we borrow 1 tens. But here is no tens, so first We borrow 1 hundred or 10 tens leaving behind 6 hundreds. From 10 tens, we borrow 1 tens or 10 ones, leaving behind tens. Now 10 ones - 8 ones = 2 ones 9 tens - 7 tens = 2 tens 6 hundreds - 4 hundreds = 2 hundreds. 700-4 78 = 222. ##### EXERCISE 15 - 1\. Fill in the blank boxes : - (a) 3 hundreds 7 tens 4 ones - 4 tens 9 ones = 3 hundreds 6 tens ones - 4 tens 9 ones = 3 hundreds tens ones. ![](Sum Up Math-3_files/Sum20Up20Math-3-93.jpg) (b) 7 hundreds 3 tens 9 ones - 4 hundreds 8 tens 6 ones ![](Sum Up Math-3_files/Sum20Up20Math-3-94.jpg) (a) (e) (m) (q) = 6 hundreds = 2 hundreds 4 2 3 2 0 5 6 3 4 3 2 9 7 8 3 5 4 7 9 4 5 6 9 1 5 4 6 ![](Sum Up Math-3_files/Sum20Up20Math-3-95.jpg) tens 9 ones - 4 hundreds 8 tens 6 ones tens 3 ones. (b) (f) (n) ![](Sum Up Math-3_files/Sum20Up20Math-3-96.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-97.jpg) 3 5 8 8 7 4 5 3 6 ###### H 1 ##### 9E1 8 3 4 5 7 3 7 3 7 3 8 5 6 2 5 4 5 0 (b) (c) 5 5 3£ 6 4 7 ![](Sum Up Math-3_files/Sum20Up20Math-3-98.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-99.jpg)- 4\. More Subtraction: (a) (e) (m) (q) ![](Sum Up Math-3_files/Sum20Up20Math-3-100.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-101.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-102.jpg) 3 3 4 2 8 7 9 1 1 5 2 5 3 0 5 1 4 5 6 2 5 3 5 0 6 0 7 3 8 2 ###### Word Problem Like addition, the concept of subtraction is used in daily life problems. It is clear from the following example: - Example 1 : Sonu have a 985 pages of a story book. He read 549 pages of his story book. How many pages are still to be read ? Solution : Number of pages in the book ![](Sum Up Math-3_files/Sum20Up20Math-3-103.jpg)Number of pages read Remaining pages 7 15 9 8 5 5 4 9 ##### □HB ###### Example 2: A poultry farm has 3689 eggs. If it sold 2435 eggs in the day, how manyeggs are remaining ? Solution: Number of total eggs 3 6 8 9 2 4 3 5 IBHQ Eggs sold Remaining eggs ##### g. EXERCISE 16 ^------------ - 1\. There are 425 students in a school. The number of boys are 257. How many girls are there ? - 2\. A shopkeeper has 247 packets of chips. He sold 129 packets of chips in a week. How many packets ofchips are left with him? - 3\. Suhani had ? 178 with her. He bought a copy and some toys for ? 129. How much amount is left with her? - 4\. There are 389 books in a school library. 199 books were taken out by some students. Now how many books are left in the library? - 5\. Out of 416 chairs in a block of stadium, 389 chairs are full in a match. How many chairs are vacant in that match? - 6\. Anmol has a 726 pages story book. He read 459 pages of the book. How many pages are sti 11 to be read? - 7\. In an acqurium, there are 231 fishes. 69 Fishes died. How many fishes are alive now? - 8\. There are 258 mangoes in a basket. 79 mangoes are rotten. How many mangoes are left? - 9\. Shanu and Monu collected 31 7 coins. Monu alone collected 139 coins. How many coinsdid Shanu collect? - 10\. A factory produces 536 bulbs on Monday and 269 bulbs on Tuesday. How many more bulbs were produced on Monday when compared to Tuesday? - 11\. Shivam isfond of collecting post office stamps. Hecollected 853 stampsand his brother collected 394 stamps. How many more stamps were collected by Shivam when compared to his brother? ![](Sum Up Math-3_files/Sum20Up20Math-3-104.jpg) - 12\. A poultry farm had 2367 eggs. It sold 1010 eggs in a day. How many eggs are left? - 13\. There are 816 houses in two block of a colony. 398 houses are in one block. How many houses are in another block? - 14\. A shopkeeper has 357 bottles of milk. He sells 169 bottles of milk in a day. How many bottles are left with him? - 15\. By how much is 189 less than 333? ##### {J. EXERCISE 17 %®--- - 1\. 36-29 = 2. 83-63 3\. 42-36 5\. 56-48 7\. 78-26 9\. 92-45 4\. 71-59 6\. 55-48 8\. 36-17 10\. 60-25 ###### Writing a number in different ways Any number can be written in different ways by using the signs of' +' and '-' between two numbers. ###### For example: 56 = 46 + 10 = 36 + 20 = 26 + 30 = 16 + 40 = 43 + 13 = 60-4 = 70-14 = 80-24 = 5 9-3etc. ###### Addition and Subtraction together Example 1: Solve: 155-87 + 376. ###### Solution : ![](Sum Up Math-3_files/Sum20Up20Math-3-105.jpg) First subtract 87 from 155 15 5-8 7 + 3 76 = 444 1 5 5 -87 ##### HEI then add the difference to 376 6 8 \+ 376 ##### HEID ###### Example 2 : Solve: 3 75 + 249-447. ###### Solution : First add 375 to 249 3 7 5 2 4 9 ##### BHD ![](Sum Up Math-3_files/Sum20Up20Math-3-106.jpg) then subtract 447 from 624 6 2 4 4 4 7 ##### DHH 3 75 + 249-447 = 177 ###### Example 3 : Solve: 475 - 316 + 520-2 76. ###### Solution : First method : First subtract 316 from 475 4 7 5 3 1 6 ##### DHH Now add 159 to 520 1 5 9 5 2 0 DHH Then subtract 276 from 679 Second method: Here some numbers have 1 +' sign, some are '-' sign and some havn't any sign (in first number) before them. Let us add the two types of numbers seperately. ###### Note • If there is no sign before the first number, its sign is always considered as plus. First add numbers 475 to 520 (with ' +' sign or no sign before them). then add 316 to 276 (with '-' sign before them, since'-' and '-' arealways ' +') ![](Sum Up Math-3_files/Sum20Up20Math-3-107.jpg) 4 7 5 5 2 0 ##### E1E1H 3 1 6 2 7 6 ##### HE1H Now subtract the second sum from first sum : /. 475-316 + 520-2 76 = 403 9 9 5 5 9 2 ##### DHH ![](Sum Up Math-3_files/Sum20Up20Math-3-108.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-109.jpg) ###### Example 4 : Solve : 348 - 79 + 136 - 274 + 269 Solution : 3 4 8 7 9 \+ 274 HEKI First add number with plus signs \+ 13 6 Second add number \+ 2 6 9 with minus signs ### mo 7 5 3 3 5 3 □□□ Now subtract the second sum from first sum : 348 - 79 + 136 - 274 + 269 = 400 ##### (J. EXERCISE 18 ^------------- - 1\. Write in four different ways using plus sign only : - (a) 49 (b) 82 (c) 96 Write in four different ways using minus sign only : (a) 56 (b) 47 (c) 78 Solve the following : - (a) 425 - 137 + 122 = - (b) 456 + 379 -256 = - (c) 786- 581 + 311 = - (d) 283 + 619 - 378 = - (e) 786 - 284 + 355 - 265 = - (f) 644 + 171 - 13 5 -2 34 = - (g) 460- 177 + 352 -201 = - (h) 841 + 193 - 595 - 156 = 396 - 2 hundreds + 3 hundreds - 5 tens = 6 hundreds + 8 ones - 3 hundreds and 2 tens = ###### Mental Drills - 1\. Fill in the boxes : - [(a) 55 - 23=](#bookmark291) - [(c) 78 - 56=](#bookmark292) - [(e) 65 - 32=](#bookmark293) - [(g) 59 - 34=](#bookmark294) - [(i) 96-49=](#bookmark295) - [(k) 156-88=](#bookmark296) - [(m) 199-90=](#bookmark297) - [(o) 225 - 120=](#bookmark298) - 2\. Fill in the boxes : - [(a) 445 + 50-32=](#bookmark299) - [(b) 625 - 25 + 75=](#bookmark300) - [(c) 595 - 70 + 5=](#bookmark301) - [(d) 362 - 62 + 25=](#bookmark302) - [(e) 241 -20-21=](#bookmark303) - 3\. Write 36 in 3 different ways using : - (a) + sign - (b) - sign - [(b) 500 - 200=](#bookmark304) - [(d) 496 - 399=](#bookmark305) - [(f) 641 - 600=](#bookmark306) - [(h) 556 - 223=](#bookmark307) - (j) 2356- 1500 = (I) 5362 - 999 = (n) 4532 -2267 = (p) 3 734- 1245 = ![](Sum Up Math-3_files/Sum20Up20Math-3-110.jpg) ##### (PultipliCdtiOD ![](Sum Up Math-3_files/Sum20Up20Math-3-111.jpg) In 2nd standard you learnt the multiplications as 10 x 10 multiplication table which helped the multiplying of one, two and three digit numbers (without regrouping) by one-digit number. In this class we will first repeat them and then learn the multiplication of four-digit numbers by one digit number (without regrouping). Now examine the fol lowing 2 groups of 3 candies each. ![](Sum Up Math-3_files/Sum20Up20Math-3-112.jpg) 3 + 3 = 6 2 threes are 6. You write it as 2 x 3 = 6 You read it as '2 times 3 equals 6' Multiplication Table upto 10 x 10 X 1 2 3 4 5 6 7 8 9 10 1 1 2 3 4 5 6 7 8 9 10 2 2 4 6 8 10 12 14 16 18 20 3 3 6 9 12 15 18 21 24 27 30 4 4 8 12 16 20 24 28 32 36 40 5 5 10 15 20 25 30 35 40 45 50 6 6 12 18 24 30 36 42 48 54 60 7 7 14 21 28 35 42 49 56 63 70 8 8 16 24 32 40 48 56 64 72 80 9 9 18 27 36 45 54 63 72 81 90 10 10 20 30 40 50 60 70 80 90 100 ![](Sum Up Math-3_files/Sum20Up20Math-3-113.jpg) From the tables, you get the fol lowing: - (a) 5 x 1 = 5;6 x 1 = 6,etc.Thus, A number multiplied by 1 is the number itself. - (b) 5x3 = 15 = 3x5; 6x4 = 24 = 4x6, etc. Thus, Two number can be multiplied in any order. - (c) 2 x 0 = 0; 3 x 0 = 0, etc. Thus, A number multiplied by zero is always zero. Multiplication by 1-digit number (without regrouping) Example 1: Multiply 143 by 2 Solution : 143 = 100 + 40 + 3 This is standard multiplication algorithm 200 +80+6 143 x 2 = 200 + 80 + 6 = 286 ![](Sum Up Math-3_files/Sum20Up20Math-3-114.jpg) .-. 143 x 2 = 286 Example 2 : Multiply 3120 by 3. Solution : ###### Th H T O ###### Th H T O ###### Th H T O ###### Th H T O 3 12 0 x 3 \_\_\_\_\_\_\_\_\_\_0 multiply the ones 3x0 = 0 ones 3 12 0 x 3 6 0 multiply the tens 3x2 = 6 tens 3 12 0 x 3 3 6 0 multiply the hundreds 3x1=3 hundreds 3 12 0 x 3 9 3 6 0 multiply the thousand 3x3 = 9 3120 x 3 = 9360 ![](Sum Up Math-3_files/Sum20Up20Math-3-115.jpg) ##### . CXEHC1SE19 । - 1\. Multiply : ![](Sum Up Math-3_files/Sum20Up20Math-3-116.jpg)![](Sum Up Math-3_files/Sum20Up20Math-3-117.jpg) Multiplication by 1-digit number (with regrouping) - (a) Multiplication of 1-digit number by 1-digit number. You know that: 10 ones = 1 ten 10 tens = 1 hundred 10 hundreds = 1 thousand ###### Example 1 : Multiply : 14 by 4. Solution : ![](Sum Up Math-3_files/Sum20Up20Math-3-118.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-119.jpg)1 1 4 x\_\_4 6 Multiple the ones 4x4 = 16 ones 1 4 2<\_\_4 5 6 Multiple the tens 4x1=4 tens ;. 14x4 = 56. ###### Example 2 : Multiply : 36 by 3. Solution: n ![](Sum Up Math-3_files/Sum20Up20Math-3-120.jpg)1 3 6 x 3 1 3 6 >< 3 Multiply the ones 3x6 = 18 ones = 1 tens + 8 ones carry the tens /. 36 x 3 = 108. 1 0 8 Multiply the tens 3x3 = 9 tens 9 tens 1 tens (carried tens) = 10 tens = 1 hundred + 0 tens ##### (B EXERCISE 20 , 1\. Multiply: ![](Sum Up Math-3_files/Sum20Up20Math-3-121.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-122.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-123.jpg) (xv) ![](Sum Up Math-3_files/Sum20Up20Math-3-124.jpg) - ###### (b) Multiplication of 3-digit number by 1-digit number. Example 1: Multiply 226 by 2. Solution : ###### H T O ![](Sum Up Math-3_files/Sum20Up20Math-3-125.jpg) ###### H T O 1 2 2 6 2 1 2 2 6 4 5 2 ![](Sum Up Math-3_files/Sum20Up20Math-3-126.jpg) Multiply the ones and regroup 2x6 = 12 ones = 1 tens x 2 ones carry the tens 226 x 2 = 452 Multiply the tens and add the carrying tens 2x2=4 tens 4 tens + 1 tens = 5 tens Multiply the hundreds 2x2 = 4 hundreds Example 2 : Multiply : 297 by 3. Solution : ![](Sum Up Math-3_files/Sum20Up20Math-3-127.jpg) ###### H T O H T O #### I2 9 7 1 Multiply the ones and regroup 3 x 7 = 21 ones = 2 tens 1 ones carry the tens. 2 2 #### |2 9 7 X 3 9 1 Multiply the tens and add the carrying tens 3 x 9 = 27 tens 27 tens + 2 tens = 29 tens 2 hundred + 9 tens 2 2 02 9 7 x 3 8 9 1 Multiply the hundreds and add the carrying hundreds 3x2 = 6 hundreds 6 hundreds + 2 hundreds = 8 hundreds 297 x 3 = 891 Verification by standard multiplication algorithm : 297 = 200 + 90 + 7 \_\_\_\_\_\_\_\_\_\_x 3 600 + 270 + 21 2 9 7 x 3 = 600 + 2 70 + 21 = 891 ##### |J. EXERCISE 21 g - 1\. Multiply: - [(a) 1 7 9 (b) 2 4 4 (c) 1 1 7 (d)3 2 9](#bookmark339) [x3 x3 x 4x4](#bookmark340) [(e) 1 6 8 (C 3 3 9 (g) 4 8 1 (h)2 19](#bookmark341) [x5 x2 x5x6](#bookmark342) 3 0 7 O') 2 8 8 x 7 x 3 1 4 7 <n> 18 9 x 7 x 4 [(k) 4 i 6 06 0 5](#bookmark343) [x 6x 5](#bookmark344) [(o) 5 2 5 (P)3 5 8](#bookmark345) [x 5x 7](#bookmark346) ###### Continued Multiplication Example 1: 98 x 5 x 4 Solution : First multiply 98 by 5 : Then multiply 490 by 4 : .’. 98 x 5 x 4 = 1960 4 9 8 x 5 4 9 0 3 4 9 0 x 4 19 6 0 ##### ^. EXERCISE 22 v 1\. Multiply: (a) 6 2 5 (b) 5 4 8 x 5 x 3 (c) 4 3 2 x 7 (d) 3 5 6 x 8 [(e) 3 9 5 (f)2 0 9](#bookmark352) [x 6x 9](#bookmark353) [(g) 7 6 8 (h)19 8](#bookmark354) [x 4 x9](#bookmark355) cd 5 7 7 x 7 (j) 48 x 3 x 4 = (k) 57 x 2 x 3 = (I) 268 x 4 x 5 = ###### Multiplication by 10,100 and 1000 Example 1: 225 by 10. Solution: 225 x 10 = 225 x 1 tens = (225 x 1 ) tens = 225 tens = 2250 To multiply by 10, put one zero to the right of the number, you will get result. - Example 2: Multiply 42 by 100. Solution: 42 x 100 = 42 x 1 hundred = (42 x 1) hundreds = 42 hundreds = 4200 To multiply by 100, put two zero to the right of the number, you will get the result. - Example 3: Multiply 8 by 1000. Solution : 8 x 1000 = 8 x 1 thousand = (8 x 1) thousands = 8 thousands = 8000 To multiply by 1000, put three zero to the right of the number, you will get the result. 1\. Multiply: (a) 54 x 100 = (b) 38 x 100 = (c) 4 x 1000 (d) 295 x 10 = (e) 67 x 100 = (f) 6 x 1000 (g) 146 x 10 = (h) 78 x 100 = (i) 8 x 1000 (j) 565 x 10 = (k) 95 x 100 = (I) 9 x 1000 ###### Multiplication by 20,300 etc. Example 1: 33 by 20. Solution: 20 = 2 tens /. 33 x 20 = 33 x 2 tens = (33 x 2) tens = 66 tens = 660 To multiply 33 by 20, first you multiply 33 by 2 and then put one zero to the right of that number. - Example 2: Multiply 26 by 300. Solution: 300 = 3 hundreds .’. 26 x 300 = 26 x 3 hundreds = (26 x 3) hundreds = 78 hundreds = 7800 To multiply 26 by 300, first you multiply 26 by 3 and then put two zeros to the right of that number. ^X»®^ ##### JM. EXERCISE 24"^-------------- Multiply: - 1\. (a) 15 x 2 = \] (b) 15 x 20 = (c) 15 x 200 = - 2\. (a) 22 x 3 = ZU (b) 22 x 30 = O (c) 22 x 300 = 3\. (a) 12x5 = (b) 12 x 50 = \_ (c) 12 x 500 = 4\. (a) 14x4 = (b) 14x40 = \_ (c) 14 x400 = 5\. (a) 20 x 30 = \_ \_ (b) 30 x 40 = \_ (c) 40 x 50 = 6\. (a) 30 x 30 = (b) 40 x 40 = \_ (c) 50 x 50 = 7\. (a) 18 x 400 = (b) 15 x 500 = \_ (c) 14 x 600 = 8\. (a) 30 x 6 x 40 = (b) 50 x 7 x 60 = (c) 70 x 12 x 80 = ![](Sum Up Math-3_files/Sum20Up20Math-3-128.jpg) - 9\. Puja has 18 packets of toffees. Each packet has 20 toffees in it. How many total toffees are there in 18 packets? - 10\. Riya has collected 36 fifty-rupee notes. How much money has she collected? ###### Multiplication by two-digit number. Example 1: 52 by 16. Solution: In praticethis is arranged as fol lows: 5 2 [x 16](#bookmark367) [3 1 2 ^ 52 x6](#bookmark368) [5 2 0 ^ 52 x10](#bookmark369) [8 3 2 52 x16](#bookmark370) 52 x 16 = 832 Multiply by ones and then by tens and add in last. - Example 2: Multiply 178 x 36. Solution: 1 7 8 x 3 6 10 6 8 5 3 4 0 6 4 0 8 /. 1 78 x 3 6 = 6408 First multiply by ones (6) and then by tens (30) and add both. ![](Sum Up Math-3_files/Sum20Up20Math-3-129.jpg) Multiply: ![](Sum Up Math-3_files/Sum20Up20Math-3-130.jpg) - 2\. Fill in the blanks: (a) 55 x 15 = (b) 39 x 39 = (c) 73 x 32 = (d) 82 x 44 = (e) 77 x 33 = (f) 94 x 43 = 1 (g) 49 x 39 = (h) 58 x 28 = (i) 66 x 54 = (j) 169 x 24 = (k) 199 x 45 = (I) 237 x 34 = (m) 345 x 18 = (n) 472 x 23 = (o) 499 x 13 = (p) 523 x 19 = (q) 641 x 16 = (r) 298 x 12 = In a multiplication sum, the number to be multiplied is called 'multiplicand', the number by which multiply is called 'multiplier' and the result of multiplication is called the 'product'. [Forexample, in . n](#bookmark371) r ' 4 2 —»This is multiplicand [x 15](#bookmark372) - 2 1 0 ^ This is multiplier - [4 20](#bookmark373) - 6 3 0 ^ This is product ###### Properties of multiplication - 1\. Multiply: - (a) 54 x 12 ![](Sum Up Math-3_files/Sum20Up20Math-3-131.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-132.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-133.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-134.jpg) You noticed that, The product of two numbers does not change when we interchange the order of the multiplicand and the multiplier. (a) Multiply26,6and4. You can multiply two numbers atatime 26 x 6 x 4 = 26 x 24 = 624 or 26 x 6 x 4 = 156 x 4 = 624 You get the same result (product) in both cases, (b) Multiply8,15and6andfill in the blanks. You can multiply two numbers atatime 8x15x6 8x6x15 = 120 x 6 = 48 x 15 Do you get the same result in both cases?............. Note • The product of three numbers remains the same when the grouping of the numbers is changed. (c) Multiply each of 235, 555 and 3435 by 1 : 235 x 1 = 235 555 x 1 = 555 343 5 x 1 = 343 5 Note • The result (product) of a number and 1 is the number itself. (d) Multiply each of 72,255 and 1286 by 0 : 72 x 0 = 0 255 x 0 = 0 1286 x 0 = 0 ###### Note • The result (product)of number and zero is always zero. Q. EXERCISE 26 /------------ 1\. Multiply: Without actual multiplication, fill in the blanks: (a) 26 x = 27 x 26 (b) 35 x = 45 x 35 (c) 78 x 89 = 89 x J (d) 62 x 58 = x 62 (e) 138 x = 75 x 138 (f) 5x6x18= x5x6 (g) 25 x 36 x 48 = 48 x x 25 (h) 39 x x 59 = 59 x 49 x 39 (i) 345 x 1 = (j) 2562 x 0 = ###### Word problems on multiplication. Example 1: A pencil box costs? 48. Find the cost of36pencil boxes. Solution : Cost of 1 pencil box = 48 .-. Cost of 36 pencil boxes = ? 48 x 36 = ? 1728 jj. EXERCISE 27“/-------------- - 1\. There are 12 classes in a school. Each class has 72 students. Find the total number of students in the school. - 2\. There are 24 sugarcanes in a bundle. Find the number of sugarcanes in 58 bundles. - 3\. A box contains 24 pencil. Find the number of pencils in 67 boxes. - 4\. The price of a school bag is? 395. Find the total priceof 18 bags. - 5\. A truck can carry 128 bags of cement. How many bags can be carried by 56 trucks? - 6\. There are456 mangoes in atree. How many mangoes are there in 29 similartrees? ![](Sum Up Math-3_files/Sum20Up20Math-3-135.jpg) - 7\. There are 36 gems in a packet. Find the total number of gems in 59 packets? - 8\. There are 400 pages in a copy. How many pages will be in 24 copies? - 9\. The price of a copy is? 92. Find the price of 36 copies. - 10\. The cost of a tricycles is ? 756. Last week, Ashok sold 8 tricycles. How much amount did he receive last week? - 11\. There are 108 beads is a necklace. How many beads are there in 24 necklaces? - 12\. A remote control toy car costs? 595. Find the price of 18 such toy car. - 13\. There are 45 biscuits in a packet. How many biscuits are there in 32 packets? - 14\. There are 48 sweets i n 1 kg. How many sweets wi 11 be i n 18 kg? - 15\. In a school, there are 48 students can stand in a row. How many students can stand i n 13 row at a time? ###### Mental Drills 1\. Fill in the blanks : (a) (b) (c) (d) (e) (f) 5+5+5+5=4x5= 3 + 3 +3+3 + 3= x 3 = 15 8 + 8 + 8 = 3x =24 16 + 16 + 16 + 16 = x 16 = 30 + 30 + 30 + 30 + 30 = x 5 = 7 x 100 = ![](Sum Up Math-3_files/Sum20Up20Math-3-136.jpg) How many lines will be drawn in 7 rectangle? In a chess board there are 16 pawns. How many pawns will be in there 6 chess board? A human has 10 fingers. How many total fingers does 7 human beings contain? Write 72 in different ways: ![](Sum Up Math-3_files/Sum20Up20Math-3-137.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-138.jpg) - 6\. Fill in the box: - [(a) 20 x 2=](#bookmark383) - [(c) 32 x 2=](#bookmark384) - [(e) 43 x 2=](#bookmark385) - [(g) 151 x 1=](#bookmark386) - 7\. 78 x 15 = 15 x 78 = - 8\. 12x5x6 = 12x6x5 = - 9\. What is 685 x 1 = - 10\. What is 625 x 0 = - (b) 28 x 2 = - (d) 400 x 2 = - (f) 88 x 2 = - (h) 595 x 0 = ![](Sum Up Math-3_files/Sum20Up20Math-3-139.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-140.jpg) In llnd standard, you have learnt the division with different name for equal sharing among a group or repeated subtraction. Here repeat them as an example. Krish has 8 chocolates. He wants to distribute them among 4 friends in equal number. First Krish will distribute 1 chocolate to each friends. 8-4 = 4 He has distributed 4 chocolates and 4 are left. He again distributes 1 chocolate to each friends. Now, each friend has 2 chocolates. We write it as 8 = 4 = 2 8 (2 8 - -8 or 2 0 - 8 = 4 = 2 is read as eight divided by four is equal to two. In this division, 8 is called dividend, 4 is called the divisor and 2 is called quotient. Division undoes Multiplication While dividing 12 by 2, you try to find out how many times does 2 goes into 12. You know that 2x6 = 12 12 = 2 = 6 Similarly, 6x2 = 12 12 = 6 = 2 Division and multiplication are inverse of each other ###### Division Facts 3x5 = 15 /. Division facts of 3 x 5 = 15 are 15 = 3 = 5 and 15 = 5 = 3. Similarly, division facts of 6 x 3 = Ware 18 = 6 = 3 and 18 = 3 = 6. It seems that each multiplication fact gives two division facts. - Example 1: Write the division facts of 5 x 6 = 30 Solution : 5 x 6 = 30 30^5= 6 and 30 6 = 5 - Example 2 : Write the division facts of 7 x 7 = 49. Solution : v 7 x 7 = 49 /. 49 - 7 = 7 Here, both division facts are same - Example 3 : Write the multiplication facts of 72 -e- 9 = 8. Solution : v 72 - 9 = 8 /. 9 x 8 = 72 ##### i|L EXERCISE 28%®-------------- 1\. Put the mangoes in the basket (by using arrows) so that each basket has equal number of mangoes. Now fill in the boxes. ![](Sum Up Math-3_files/Sum20Up20Math-3-141.jpg)![](Sum Up Math-3_files/Sum20Up20Math-3-142.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-143.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-144.jpg)(a) 15 - 3 = (c) 60-12 = Divide by repeated subtraction and find the quotient in each case: (b) 28 - 7 = - (d) 45 - 15 = Separate dividend, divisor and quotient in each case : (example : 24 - 6 = 4; dividend = 24, divisor = 6, quotient = 4) - (a) 21 - 3 = 7 - (b) 32 - 4 = 8 - (c) 45 - 5 = 9 Write the division facts of the following multiplication facts : - (a) 7 x 5 = 35 - (b) 8 x 8 = 64 - (c) 9 x 6 = 54 - 5\. Write the multiplication fact of the following division facts : - (a) 56 - 7 = 8 - (b) 81 - 9 = 9 - (c) 13-13 = 1 Fill in the boxes: (a) 24 - 3 = (c) 45 - 5 = (e) ■-8 = 8 - (b) 36 - 4 = - (d) ■ - 7 = 9 - (f) ■ ^ 3 = 9 ###### Properties of division - (a) Subtract 6 repeatedly from 6 6 \- 6 —» First time 0 You have subtracted 6 from 6, onetime. Hence 6-6 = 1 Similarly, 9-9 = 1,10 - 10 = 1 etc. A number (except zero) is divided by itself exactly and the quotient is 1. ![](Sum Up Math-3_files/Sum20Up20Math-3-145.jpg) - (b) Subtract 1 repeatedly from 4 4 \- x 3 2 -2 1 -2 o - — » First time - — » Second time - — > Third time - — > Forth time You have subtracted 1 from 4, fourtimes. Hence 4 ^-1=4 Similarly 5^-1 =5,7-1 = 7,8 -^ 1 = 8 etc. A number is divided by 1 exactly and the quotient is the number itself, (c) Subtract 0 from 4 4 - \- 0 . - — —> First time 4 - ■ ~ —» Second time —> Third time - — ^ Forth time You have noticed that every time we subtract 0 from 4, the difference is 4. It is a neverending process. You can not get remainder as 0 when 0 is subtracted from 4 any number of times. You cannotdivideany number by zero. Therefore, you can say that 0 h- 4 = 0 When 0 is divided by any number (other than zero) the quotient is zero. ![](Sum Up Math-3_files/Sum20Up20Math-3-146.jpg) ##### £>. EXERCISE29% Fill in the boxes : (a) 7 - 1 = (b) 8 - 8 = (c) 0 - 3 = (d) 12 - 12 = (e) 0 - 8 = (f) 64-6 = (g) -9 = 1 (h) \- 1 = 36 (i) 28 - =28 ###### Division by 1-digit number (without remainder) Example 1 : Divide 60 by 2. ###### Solution : 60 4- 2 = (6 tens 4-2) = (6 4-2) tens = 3 tens = 30 Example 2 : Divide 48 by 4. Solution : 48 ^ 4 = (4 tens + 8 ones) 4-4 = (4 tens h- 4) + (8 ones 4-4) = (4^-4) tens+ (8-4) ones = 1 tens+ 2 ones = 12 Example 3 : Divide 363 by 3. Solution : 363 4- 3 = (3 hundreds + 6 tens + 3 ones) 4- 3 = (3 hundreds4- 3) + (6 tens4- 3) + (3 ones4- 3) = (3 4-3) hundreds + (64-3) tens + (3 4-3) ones = 1 hundreds+ 2 tens + 1 one = 121 Get Set Go With Sum Up Mathematics-3 In practice, it is written as : ![](Sum Up Math-3_files/Sum20Up20Math-3-147.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-148.jpg)Example 4 : Divide 7572 by 6. Solution : ![](Sum Up Math-3_files/Sum20Up20Math-3-149.jpg) ##### (J. EXERCISE 30^------------- Divide and find the quotient: (a) 40 - 2 = (b) 36 - 3 = (c) 88 - 2 = (d) 96 - 3 = (e) 84 - 4 = (f) 204 ^ 2 = (g) 360 ^ 3 = (h) 448 - 4 = (i) 348 - 2 = (j) 435 - 3 = (k) 738 - 6 = (I) 735 - 5 = (m) 444 - 3 = (n) 959 - 7 = (o) 920 - 8 = (p) 5352 - 3 = (q) 6256 - 4 = (r) 7956 - 6 = (s) 9394 - 7 = (t) 9288 - 8 = ###### Division by 1-digit number (contd.) You have solved the examples where the digit on the extreme left of the dividend was equal to or greater than the divisor. Now take up examples where the digit on the extreme left of the dividend is less than the divisor. - Example 1: Divide336by6. 6\) 3 3 6 ( Solution: ![](Sum Up Math-3_files/Sum20Up20Math-3-150.jpg) After writing as start with hundreds. - 6 does not go into 3 ![](Sum Up Math-3_files/Sum20Up20Math-3-151.jpg) Therefore, you start with tens. ![](Sum Up Math-3_files/Sum20Up20Math-3-152.jpg) 3 hundreds and 3 tens = 33 tens 6 goes into 33 by 5 times. So, you write 5 in the tens place in the quotient and subtract 30from 33. You bring down 6 ones from the dividend to the right of the remainder 3 making 36 ones. Now 6 goes into 36 by 6 times. You write 6 in the units place in the quotient and subtract 36 from 36, leaving 0 remainder. Hence 336 = 6 = 56 - Example 2: Divide 5752 by 8. Solution: After writing we start with thousands. 8 does not go into 5. 8) 5 7 5 2 Therefore, we start with hundreds. Now 5 thousand and 7 hundreds = 57 hundreds - 8 goes into 57 by 7 times. So you write 7 in the hundred's place in the quotient and subtract 56 from 57. You bring down 5 tens from the dividend to the right of the remainder 1, making 15 tens. ![](Sum Up Math-3_files/Sum20Up20Math-3-153.jpg) Now 8 goes into 15 by 1 time. So you write 1 in the ten's place in the quotient and subtracts from 15 You bring down 2 ones from the dividend to the right of there remainder 7, making 72 ones. Now 8 goes into 72 by 9 times. So you write 9 in the one's place in the quotient and subtract 72 from 72 leaving 0 as remainder. Hence, 5752 = 8 = 719 ![](Sum Up Math-3_files/Sum20Up20Math-3-154.jpg) ##### . EXERCISE 31 s Divide and find the quotient : (a) 315-5 = (b) 528 - 8 (d) 372 - 6 = (e) 693 - 7 (g) 504-7 = (h) 855 - 9 (j) 2256 - 4 = (k) 3390 - 6 (m) 5852 - 7 = (n) 2792 - 8 - (c) 231 - 3 - (f) 384 - 4 (i) 1645 -5 - (I) 2997 - 9 (o) 1974 -2 ###### Division by 1-digit number (with remainder) You have seen the questions where the given number (dividend) was exactly divisible by the divisor. Now you will solve the questions where the dividend is not exactly divisible by the divisor. It has remainder. (a) Put 11 flowers into groups of 3 each : ![](Sum Up Math-3_files/Sum20Up20Math-3-155.jpg)When divided the flowers into group of 3 you get 3 groups of flowers and 2 flowers remain as they do not make a complete group. ^^ Dividend Divisor <----3)^(3 ----► Quotient -9 2------► Remainder - (b) Put 20 fish into group of 6 each : ![](Sum Up Math-3_files/Sum20Up20Math-3-156.jpg) When 20 fishes are divided into group of 6 you get 3 groups of fish and 2 fishes are left as they do not make a complete group. ![](Sum Up Math-3_files/Sum20Up20Math-3-157.jpg) Divisor < ![](Sum Up Math-3_files/Sum20Up20Math-3-158.jpg)> Quotient Dividend ![](Sum Up Math-3_files/Sum20Up20Math-3-159.jpg) 2------► Remainder From above solution, you get: Dividend = Divisor x Quotient + Remainder Example 1: ![](Sum Up Math-3_files/Sum20Up20Math-3-160.png) Divide 268 by 3. Solution : You know that, Dividend = Divisor x Quotient + Remainder. According to the solution, Here, Dividend = 268, Divisor = 3, Quotient = 89 Remainder = 1 Examp|e 2: 8777777344 [Divide 2758 by 8.2 4](#bookmark408) [Solution :](#bookmark71) [Dividing as explained before, you get3 2](#bookmark409) [Quotient = 3443 8](#bookmark410) [Remainder = 6](#bookmark411) [To verify the answer,——](#bookmark412) Dividend (2 758)= Divisor (8) x Quotient (344) + Remainder (6) 2758 = 2752 + 6 = 2758 ###### Division by 10 Example 3 : ![](Sum Up Math-3_files/Sum20Up20Math-3-161.png) ![](Sum Up Math-3_files/Sum20Up20Math-3-162.jpg) Divide 518 by 10. Solution : Quotient = 51 Remainder = 8 ###### Example 4 : Divide 1927 by 10. Solution : i oJmK192 -1 o 9 2 -90 2 7 -2 0 7 Quotient = 192 Remainder = 7 ##### ^. EXERCISE 32 J 1\. Divide and find the quotient and remainder : Quotient Remainder Quotient Remainder (a) 497 -2 = (b) 269 - 3 = (c) 309-4 = (d) 637 - 5 = (e) 226-3 = (f) 299 - 7 = (g) 459 - 6 = (h) 799 - 9 = (i) 3537 - 2 = (j) 2689 - 3 = (k) 5578 - 6 = (I) 4787 - 5 = (m) 6978 - 8 = (n) 5987 - 7 = (o) 7958 - 9 = (p) 2987 - 4 = - 2\. Find the quotient and remainder in each case and verify the answer: - (a) 225 - 4 (b) 327 - 5 (c) 3579 - 8 (d) 4797 - 7 - 3\. Find the quotient and the remainder when each of the following number is divided by 10: - (a) 74 (b) 320 (c) 885 (d) 5432 - 4\. If 7 is subtracted repeatedly from 269, what will be left? ![](Sum Up Math-3_files/Sum20Up20Math-3-163.jpg) Word Problems - Example 1: Bheem has 45 laddoos and he wants to share these laddoo equally among 5 children. How many laddoos will be given to each child. Solution: a---- 5)45(9 Divide45 by 5 ? 4 5 45 - 5 = 9 —q .-. Each children has 9 laddoos Example!: There are 258 students in a class having 6 sections. Find the number of students in each section if each section has equal number of students. Solution : Divide 258 by 6 6) 2 5 8 (43 258 - 6 = 43 -24 /. Each section has 43 students. ^ $ \- 1 8 00 Q EXERCISE 33 %\*------------ - 1\. There are 378 plants in 6 rows in a garden. How many plants are there in each row? - 2\. A man earns ? 434 in a week. How much does he earn in a day? - 3\. There are 56 marbles. 7 children divided equally these marbles among themselves for a game. How many marbles will each child have? - 4\. A poultry farm sold 2254 eggs in a week. Find the number of eggs sold each day. - 5\. Ramu's mother distributed 477 toffees among 9 children on his birthday. How many toffees does each child get? - 6\. 272 glasses are to be placed equally in 8 trays. Find the number of glasses in each tray. ![](Sum Up Math-3_files/Sum20Up20Math-3-164.jpg) - 7\. There are 2295 mangoes which are packed equally in 9 boxes. Find the number of mangoes in each box. - 8\. The price of 6 books is? 726. Find the price of one book. - 9\. A milk man sells 595 litresof milk in aweek. Findthesaleofmilkinoneday. - 10\. 5 children picked 395 flowers in a garden. If each child picked the same number of flowers, find the numberof flower picked by them. - 11\. A car goes 9 kilometres in 1 litre of petrol. How much petrol will it require to travel 657 kilometres? - 12\. There are 5 exercise books of the same kind. Find the number of pages in each exercise book if the total number of pages are 480. - 13\. Anshu has 990 beads for making 10 necklace. Find the number of bead for 1 necklace. ###### Simlification You have learnt addition, subtraction, multiplication and division of numbers. Now use these for simplification of numbers. Example 1: Simplify (20 - 4) + (18 - 3). Solution: (20 - 4) + (18 - 3) = (5) + (6) = 11 Note - • () It is called brackets. First simplify the terms within the brackets. - Example 2: Simplify:(45 + 36) - (28-19). Solution: (45 + 36) - (28-19) = (81)-;-(9) = 9 ![](Sum Up Math-3_files/Sum20Up20Math-3-165.jpg) (45 + 36) - (28-19) =9 ###### Example3: Simplify: 120-(125 ^ 5). Solution: 120-(125 - 5) = 120-(25) = 95 Example 4: Simplify: (120 x 6) + (86 - 2). Solution: (120 x 6) + (86 - 2) = 720 + 43 = 763 ##### {J- EXERCISE 34^------------- Simplify fill in the blanks : - 1\. (15 - 3) + (16 - 4) = - 3\. (25 x 5) - (35 x 2) = - 5\. (45 x 3) - (45 x 2) = - 7\. (177 - 3)-(15 x 3) = - 9\. (9 x 9) + 400 = - 11\. (25 - 1)-(4 x 4) = - 13\. (125 - 5) + 65 x 10 = - 15\. (35 x 2) + 238 = - 17\. (117 x 2)-(120 - 2) = - 19\. (450 - 5)-(111 - 3) = - 21\. (22 x 6) - (22 x 3) = - 23\. (138 x 2) + (125 x 3) = - 25\. (0 - 5) + (6 x 7) = - 27\. (224 - 8) + (9 x 9) = - 29\. (81 - 9) - (36 - 6) = - 2\. (81 - 9) - (16 - 4) = - 4\. (50 - 10) + 85 = - 6\. (62 x 2) - (94 - 2) = - 8\. (17x3) + (88 - 4) = - 10\. 25 x 4 + (126 - 6) = - 12\. (63 x 2) - (84 - 3) = - 14\. 152-8 = - 16\. (2 5 x 2 5) + 2000 = - 18\. (205 - 5) + (27 x 3) = - 20\. (36 - 9) + (63 - 7) = - 22\. (5 x 5) + (49 - 7) = - 24\. (45 x 3) - (25 x 3) = - 26\. (200 - 50) + (8 x 8) = - 28\. (354 - 6) + (20 x 20) = - 30\. (7 x 7) - (9 x 0) = Answer the questions that fol low the picture : There are 9 jars of green candies containing 9612 candies. Pinky bought 3 jars of candies for the birthday party. How many candies are left? Rohit purchased 3 boxes of biscuits for ? 147. If Ragini wants to buy 7 boxes of biscuits then how much money she needs to pay? A crate of eggs is sold for ![](Sum Up Math-3_files/Sum20Up20Math-3-166.jpg) ? 36. Gurang buys 11 crates of eggs for his restaurant. How much did he pay to the general stores? - 4\. 7 boxes of namkeen weights 112 kg. Daddan pahalwan can lift 4 such boxes. How much weight can be lifted by Daddan Pahalwan? ###### Mental Maths - 1\. Fill in the blanks : (a) 50-2 = (b) 39-3 = (c) 450 - 10 = — (d) 595 - 5 = — (e) 345 - 1 = (f) 467 - 467 = (g) 0-35 = (h) 250 - 250 = (i) 479 - 479 = (j) 900 - 10 = (k) (585 - 5)+ 13 = (I) (640 - 8) - 15 = (m) (5 X 5) + (8 X 7) = (n) (248 - 4)-(165 - 5) = - 2\. Seperate dividend, divisor and quotient in each case. ![](Sum Up Math-3_files/Sum20Up20Math-3-167.jpg)36 — 6 = 6 (b) 72 - 9 = 8 ![](Sum Up Math-3_files/Sum20Up20Math-3-168.jpg) ® fKildW ![](Sum Up Math-3_files/Sum20Up20Math-3-169.jpg) You have learnt the method of dividing a number by 1 digit number in previous chapter. This method also helps you to divide a given number of objects equally. For example, you have 14 apples and you want to divide them between two friends equally. You will divide 14 by 2 to get the number of apples forthem. Now you will learn todivide ifyou have just one thing (apple). Now study the following statements: - 1\. I have half piece of a biscuit. - 2\. Rohan takes quarter of an hourto finish hishomework. - 3\. Rashmi finished three-fourths ofa glass of juice. Words like half, quarter, three fourths, two thirds etc. represents a fraction. Part ofawholeobjectoracollection of objects iscalled fraction. ![](Sum Up Math-3_files/Sum20Up20Math-3-170.jpg) Fraction as a part of whole Sonam has an apple, she divides it into two equal so that she can give equal pieces to her two brothers, part is cal led one half. One-half is written as — . It means there are two halves in a whole. Here is a cucumber. It is divided into two equal parts. Each part is one half of the whole. Each of the above 2 parts is divided further into 2 equal parts. Each part is called one-fourth of the whole. It is written as — . 4 This figure is divided into three equal parts. ![](Sum Up Math-3_files/Sum20Up20Math-3-171.jpg) One part is coloured. Coloured part represents one third. It is writtensas — . 3 It means there are 3-one third in a whole. ##### Q. EXERCISE 35% - 1\. Colour one half of each figure : ![](Sum Up Math-3_files/Sum20Up20Math-3-172.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-173.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-174.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-175.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-176.jpg) - 3\. Colour seperately which represents two-thirds : ![](Sum Up Math-3_files/Sum20Up20Math-3-177.jpg) - 4\. Tick the figure which are divided into equal parts : ![](Sum Up Math-3_files/Sum20Up20Math-3-178.jpg) - 5\. Tick the figure which is half coloured : ![](Sum Up Math-3_files/Sum20Up20Math-3-179.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-180.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-181.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-182.jpg)7\. Colour the portion which represents three fourths : ![](Sum Up Math-3_files/Sum20Up20Math-3-183.jpg)Yes/No Yes/No Yes/No Yes/No Yes/No - 9\. (a) How many one-halves are in a whole? - (b) How many one-thirds are in a whole? - (c) How many one fourths are in a whole? 10\. Match the fraction with correct option : ![](Sum Up Math-3_files/Sum20Up20Math-3-184.jpg) - (a) One third/y 3 - (b) Three-fourth/y - (c) One-half/ y 2 - (d) Two-thirds/y 1 - (e) One-fourth/y ![](Sum Up Math-3_files/Sum20Up20Math-3-185.jpg) ###### Representation of Fractions Earlier, you have seen that if you colour 2 parts out of 3 equal parts, it . 2 represents —. 3 3 Similarly, — represents that 3 parts out of 4 equal parts. This figure has 5 equal parts with two coloured parts. Coloured parts represents 2 -zr . It reads as "two fifths" or "two by five or "two over five". 5 ![](Sum Up Math-3_files/Sum20Up20Math-3-186.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-187.jpg) ##### g. EXERCISE 36% In the following, write the answer in the blank space. - 1\. (a) In how many equal parts is the figure divided? - (b) How many fractions are coloured? - (c) How many parts are coloured? - 2\. (a) In how many equal parts is the figure divided? - (b) Write the fraction for the uncoloured portion. - (c) Write the fraction for the coloured portion. - 3\. (a) How many parts are there in this figure? - (b) How many parts are not coloured. - (c) How many parts are coloured? — part of each of the following figure : o ![](Sum Up Math-3_files/Sum20Up20Math-3-188.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-189.jpg) 3 5\. Colour — part of each of the following figures : ![](Sum Up Math-3_files/Sum20Up20Math-3-190.jpg) 6\. Write the fraction for the coloured part in each figure : ![](Sum Up Math-3_files/Sum20Up20Math-3-191.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-192.jpg) ###### Fraction as a part of a collection There are collection of 8 toy cars. 3 cars are separated. The seperated cars on the left represent the fraction Now here is the collections of caps. Four of them are of red colours. ![](Sum Up Math-3_files/Sum20Up20Math-3-193.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-194.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-195.jpg) The red colour caps collection represents y of the whole collection. ![](Sum Up Math-3_files/Sum20Up20Math-3-196.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-197.jpg) ##### . EXERCISE 37 , - 1\. (a) How many marbles arethere in the collection? - (b) How many marbles are coloured? - (c) Write the fraction for the uncoloured marbles? ![](Sum Up Math-3_files/Sum20Up20Math-3-198.jpg) Write the fraction for the colured part? ![](Sum Up Math-3_files/Sum20Up20Math-3-199.jpg) 3\. Write the fraction which represents the uncoloured part in the following collections of figures: ![](Sum Up Math-3_files/Sum20Up20Math-3-200.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-201.jpg)OOO0O ^5 4\. Colour to show the given fraction? ![](Sum Up Math-3_files/Sum20Up20Math-3-202.jpg) ###### Numerator and Denominator Look at the fractions represented by coloured parts in the fol lowing figure: One part coloured = J\_ —> Numerator Denominator 2 equal parts 2 —> Three part coloured 8 equal parts ![](Sum Up Math-3_files/Sum20Up20Math-3-203.jpg)Numerator Denominator ## △△△△ Five parts coloured 12 equal parts 12 -> Numerator Denominator Thus each fraction has two numbers seperated by a rule: (a) The number above the rule iscalled numerator. (b) The number belowthe rule is called denominator. 2 2 is read as 'one by two' or 'one upon two' or 'one overtwo'. V is read as 'three by eight' or 'three upon eight' or 'three over eight'. 8 5 is read as 'five by twelve' or 'five upon twelve' or 'five over twelve'. Note 1\. — is a fraction in which numerator is 0 3 2\. when the numerator and denominator are equal the fraction represents the ![](Sum Up Math-3_files/Sum20Up20Math-3-204.jpg) ###### Example 1 : Find the numerator and denominator in the fol lowing fractions: (a) ![](Sum Up Math-3_files/Sum20Up20Math-3-205.jpg) (b) — 8 ###### Solution : - (a) Numerator = 1; Denominator = 6 - (b) Numerator = 5; Denominator = 8 (c) Numerator = 7; Denominator = 13 ##### ^. EXERCISE 38 । 1\. Write the following fractional numbers : (a) One by three (b) Sixteen upon nine (c) Nine by thirteen (d) Thirteen by twenty one (e) Thirteen upon Nineteen (f) Seven by Seventeen 2\. Write the numerator of the following fractions : 5 i—i .0 (a) 9 — (b) 5 — ic) 10 — (d) n 13 (e) — (f) — 19 9 (g) — 21 (h) y 16 3\. Write the denominator of the following fractions : (a) y |\_\_ (b) y \_\_ w 4 (d) \_8 15 (e) 2 (f) 2 13 7 (g) 15 19 (h) 1Z 21 ![](Sum Up Math-3_files/Sum20Up20Math-3-206.jpg) - 4\. Write the fraction whose numeratorsand denominators are given below: ![](Sum Up Math-3_files/Sum20Up20Math-3-207.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-208.jpg) Numerator Denominator (a) 5 11 (b) 7 13 (c) 8 15 (d) 6 17 (e) 0 3 Timmy cuts a cake in 14 pieces. She distributed 9 pieces of cake to her friends. What fraction ofcakedid shedistribute to herfriends? A shopkeeper has 37 eggs. 11 eggs are broken. Now what fraction of eggs does he has? - 7\. A fruit seller has 13 baskets of apples out of which 2 baskets of apples are rotten. Now what fraction of baskets of apples are left for sei I i ng? - 8\. Raunak invited 22 friends on his birthday party. Only 14 friend came to attend the party. What fraction of the friends did not attend the party. - 9\. There are 25 rose flowers. 11 roses were dry. What fraction of roses were left? ![](Sum Up Math-3_files/Sum20Up20Math-3-209.jpg) ##### 09oney ![](Sum Up Math-3_files/Sum20Up20Math-3-210.jpg) When you purchase any item from a shop, you pay money to the shopkeeper for exchange rate. In previous classes you have already learnt money in the form of coinsand notes. That is 50 P, ? 2, ? 5 and ? 10, ? 5, ? 20, ? 100 and ? 500 notes are in use in our country these days. Note of ? 2000 also used here, which is shown below: ![](Sum Up Math-3_files/Sum20Up20Math-3-211.jpg) ###### Writing of rupees and Paise. Seema has 10-rupee note and a 50-paisa coins. In words this amount is expressed as "? ten and paise fifty". In figure it is expressed as "10 rupees 50 paise or ? 10.50". Some amounts are expressed in words and figures below: In words In figures Long form Short form 1\. Rs Twenty seven and fifty Paise 27 rupees 50 paise ? 27.50 2\. Rs Nine 9 rupees ?9.00 3\. Rs Thirty and five paise 30 rupees 5 paise ? 30.05 4\. Eighty five paise 85 paise ?0.85 Note - • A dot between rupees and paise seperate both terms. - • After the dot two digits always represent paise. ![](Sum Up Math-3_files/Sum20Up20Math-3-212.jpg) U- EXERCISE 39 ^------------ - ###### 1. Write the following in long form : (a) ?565 (b)? 75.00 (c) ? 0.65 - ###### 2. Write the following in short form: - (a) 34 rupees 15 paise (b) 7 rupees 18 paise (c) 75paise - ###### 3. Write the following in words: - (a) ? 17.19 (b)?4.07 (c)?0.70 ###### Conversion (Rupees into paise) You know that, 1 Rupee = 100 paise Now solve a few examples. - ###### Example 1: Convert ? 9 into paise. ###### Solution: ? 9 = 9 x 10Op = 900 paise - ###### Example 2: Convert ? 84.07 and ? 0.95 into paise ###### Solution: ? 84.07 = ? 84 + 7 paise = 84 x 100 paise + 7 paise = 8400 paise + 7 paise = 8407 paise ? 0.95 = 95 paise ![](Sum Up Math-3_files/Sum20Up20Math-3-213.jpg) EXERCISE 40%®---- - 1\. Convert the fol lowing rupees into paise: (a) ?7 (b) ?82 (c) ? 8.25 (d) ? 19.80 (h) ?0.07 ![](Sum Up Math-3_files/Sum20Up20Math-3-214.jpg) - (e) ? 78.04 (f) ? 90.19 (g) ? 94.65 ###### Conversion (Paise into rupees) To convert paise into rupees or into rupees and paise, seperate the ones and tens digits from the given number of paise. The number formed by ones and ten digits gives the paise and the remaining number gives the rupees. Example 1: Convert 1525 p and 920 p into rupees. Solution : 1525 p = 1500 p + 25 p = ? 15 and 25 p = ? 15.25 920 p = 900 p + 20 p = ? 9 and 20 p = ? 9.20 ^. EXERCISE Hl ^------------ 1. Convert the following paise into rupees: (a) 800 p (b) 1300p (c) 738 p (d) 820 p (e) 1318p (f) 8405 p (g) 4005 p (h) 707 p Addition of money Addition without regrouping Example 1: Add ? 15.25 and ? 7.73 ###### Solution: /----------------------X or ? P 15 . 25 \+ 7 . 73 22 . 98 ? p 15 25 \+ 7 73 22 98 Add paise to paise and rupees to rupees Write the amounts with dots (points) column wise add like whole numbers Sum = ? 22.98 ![](Sum Up Math-3_files/Sum20Up20Math-3-215.jpg) Addition with regrouping ![](Sum Up Math-3_files/Sum20Up20Math-3-216.jpg) or ? P 11 [4782](#bookmark472) [+ 4565](#bookmark473) [9347](#bookmark474) Add paise to paise (82 + 65) P = 147P = Re 1 + 47P carry Re 1 to rupees Add rupees to rupees (1 + 47 + 45) Rs = Rs 93 ? 47.82 + ? 45.65 = ? 93.47 Other method ? P 11 Add paise and regroup into rupees then add rupees 47 . 82 \+ 45 . 65 <\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_y 93 . 47 <\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_y - ###### Example 3: Suruchi bought a pen for ? 12.30, a pencil for ? 4.75 and a copy for ? 18.95. How much did she spend forthese items? Solution: Cost of pen = 12.30 Costofpencil = 7.75 Cost of copy = 18.95 Total Cost = 39.00 Suruchi spent ? 39.00 ![](Sum Up Math-3_files/Sum20Up20Math-3-217.jpg) ##### ^. EXERCISE M2 J (a) (d) ![](Sum Up Math-3_files/Sum20Up20Math-3-218.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-219.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-220.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-221.jpg) (g) ![](Sum Up Math-3_files/Sum20Up20Math-3-222.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-223.jpg) - 2\. Add ? 75.26,? 12.48and ?8.15. - 3\. Add ? 36.10,? 14.39and ?0.35 - 4\. Rani bought a skirt for? 82.60 and a pair of ear ring for ? 8.92. How much did she spend? - 5\. Arjun bought a book for ? 56.50 and colour for ? 25.18 and 9 pencil for ? 12.00. How much did he give to shopkeeper? ![](Sum Up Math-3_files/Sum20Up20Math-3-224.jpg) Rajni's mother bought a box of toffees for ? 56.25 and a packet of biscuit for ? 22.00 and a packet of namkin for ? 21.44. How much did she spend? ![](Sum Up Math-3_files/Sum20Up20Math-3-225.jpg)7\. Anmors father purchased a toy car for ? 65.40 and a Ludo set for ? 36. 65. How much did he give to shopkeeper? - 8\. Today Namita gave ? 26.50 to milk man and ? 44.30 to green grocer. How much money did she give them today? 9\. Find the total cost of the following: A toy car A ball ? 49.10 ? 20.00 A shuttle cocks ? 12.50 An Ice-cream ? 23.65 Total cost Subtraction of Money Subtract without borrowing (decomposing) Example 1 : Subtract ?23.14from ? 56.38. Solution : ![](Sum Up Math-3_files/Sum20Up20Math-3-226.jpg)Subtract paise from paise and rupees from or rupees ? P 56 . 38 \- 23 . 14 \\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_/ 33 . 24 \\\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_/ Write the bigger amounts with dots and below the other then subtract like whole numbers. Subtract with borrowing (decomposing) Example 2 : Subtract ? 24.68 from Solution : ![](Sum Up Math-3_files/Sum20Up20Math-3-227.jpg) ? 48.46 First to subtract paise, you cannot subtract 68 p from 46p. So borrow Re 1 (100p) from Rs 48 Now 146 p - 68 p = 78 p .-. ? 48.46-? 24.68 = ? 23.78 Then subtract rupees since you borrowed ? 1 from ? 48. You are left with ? 47. Now ? 47 - ? 24 = ?23 ![](Sum Up Math-3_files/Sum20Up20Math-3-228.jpg) Other method = [? P 731](#bookmark479) 48 . 16 \- 24 . 68 [XZ](#bookmark480) 23 . 78 [XZ](#bookmark481) Example 3 : Ranu had ? 90.00 with her. She spent ? 50.25 on make up kits. How much money has she now? Solution : p 89 100 90 . 00 \- 50 . 25 \_\_\_\_\_\_\_\_z 39 . 75 x \_\_\_\_z .-. Ranu has? 39.75 ![](Sum Up Math-3_files/Sum20Up20Math-3-229.jpg) ##### EXERCISE 43 ![](Sum Up Math-3_files/Sum20Up20Math-3-230.jpg) 1\. Subtract: (a) ------. 86 67 P 85 43 (b) ? 94 78 ![](Sum Up Math-3_files/Sum20Up20Math-3-231.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-232.jpg) P 64 22 ![](Sum Up Math-3_files/Sum20Up20Math-3-233.jpg) 58 26 P 20 38 ![](Sum Up Math-3_files/Sum20Up20Math-3-234.jpg) 2\. ? 42.75from? 65.25 3\. ? 28.58 from ? 44.20 4\. ? 64.38from? 85.50 5\. ? 72.40from ? 95.62 - 6\. Ramu bought egg for ? 36.00 and a packet of bread for ? 12.50. He gave the shopkeeper a 100 rupee note. How much money did heget back? ![](Sum Up Math-3_files/Sum20Up20Math-3-235.jpg) - 7\. Suman has a 100 rupees note. She bought sugar for ? 32.25, tea leaves for ? 35.10 and milkfor ? 24.00. Now how much money does she have? - 8\. Nirali got ? 36.40 from her mother. She bought an ice-cream for ? 12.25 and a chocolate for ? 10.00. How much money was left with her? - 9\. Prem bought a tooth brush for ? 16.00 and 9 toothpaste tube costing ? 24.75. He gave a 50 rupees note to a shopkeeper. How much money would the shopkeeper return? ###### Multiplication of rupees and paise by a number ###### Example 1: Multiply: (a) ? 4 x 4 ###### Solution: - (a) ? 4 x 4 = ? 16 - (b) 20 p x 8 (b) 20px8 = 160p = ?1.60 ###### Example 2 : Multiply: (a) ###### Solution : (a) ?5.25 x 10 (b) ? 6.50 x 4 ? P 5.25 x 1 0 5 2.50 (b) ? 6.50 x 4 = ? P 6.50 x 4 2 6.00 X,\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ To multiply money, you do it the same way as you multiply numbers, but put a point leaving two digits from the right. - ###### Example 3: The cost of a ball is ? 18.60. What will be the cost of 3 balls? Solution : ? P 18.60 x 3 5 5.80 ![](Sum Up Math-3_files/Sum20Up20Math-3-236.jpg) Cost of 3 balls is? 55.80 - ###### Example 4: Costof a marble is 85 paise. How much will 8 marbles cost? Solution: ? P 0.85 X 8 6.80 Costof8 marbles is? 6.80 ###### Making Bills When you go to buy some items from the market, the shopkeeper gives you a bill. Each bill has (a) The name of the shop, (b) Bill number and date, (c) Items sold, (d) Quantity sold, (e) Price of each item and the total cost. We can see an example for this: Examples: Amish bought a Ludo set for ? 36.45, 2 shuttle cocks each for ? 12.40 and 2 dart each for? 3.30 from Suman Sports House. Make a bill and find the total cost. Solution: Cash Memo Suman Sports House Bill No-416 Date: 22.07.2013 Item Qty- Rate Rs P Ludoset 1 36.45 36 45 Shuttlecocks 2 12.40 24 80 Dart 2 3.30 6 60 Total 5 67 85 ? Sixty seven and eighty five paise only. ##### ... EXERCISE 44 s - 1\. Multiply and fill in the boxes: - (a) ? 14 x 5 x 4 = - (c) ? 5.45 x 4 = (b) 75P x 9 = (d) 7.65 x 9p = ![](Sum Up Math-3_files/Sum20Up20Math-3-237.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-238.jpg) - 2\. If one jar of jam costs ? 45.00, find the cost of 3 jars of jam? - 3\. Ifone kilogram tomatoes cost ? 15.30, find the cost of 6 kilogram tomatoes. - 4\. A packet of sketch pen costs? 15.50. Find the cost of 7 packets of sketch pen. - 5\. Anil buys 9 shuttle cocks. Ifone shuttle cock cost ? 15.75, what does he pay to the shopkeeper? - 6\. Sangeeta went to vegetable market. She bought 5 lemon for 50 paise each, 1 bottle gourd for 15 rupees 2 kilogram of onion for ? 18.50 each kilogram and 1 kilogram of tomato for ? 22.25. How much money does she give them? The articles are on sale in Raghav shop. Raghav Shop ![](Sum Up Math-3_files/Sum20Up20Math-3-239.jpg) Solve the question (¡-¡v) according to the above given prices. - (i) Find the total cost ofthe following articles: - (a) A bat, a ball and a hockey stick. - (b) Atoy car and a toy plane. - (c) A teddy bear and a doll. - (ii) Make separate bill for each ofthe fol lowing and find the total cost: - (a) 3 Racket and 2 hockey sticks. - (b) 4 Magic set, 5 balls, 1 bat. - (iii) Which is costlierand by how much? - (a) A doll or a teddy bear. - (b) A hockey stick or a racket. - (iv) Which is cheaper and by how much? - (a) Atoy car or a toy plane. - (b) A racket or a magic set. ###### Division of Rupees and Paise by A Number You have learnt addition, subtraction or multiplication of rupees and paise in the same way as you did in case of numbers similarly, division of money can be done in the same way as we divide numbers. It can be understood by following examples. - Example 1: Divide: (a) 93Pby3 (b) ? 120 by 4 Solution : (a) 93P ^ 3 = 31 P (b) ? 120-4=? 30 ###### Example 2 : Divide: (a) ? 15.00by4 (b) ? 16.16 by 4 Solution : 4 15.00 3.75 12 3 0 28 = ?3.75 2 0 2 0 x ###### Solution : (b) ? 16.16 by 4 4 16.16 4.04 = ?4.04 Example 3 : 6 packets of chocolates cost ? 43.92. What is the cost of one packet of chocolate? Solution : 6 43.92 7.32 -42 19 \- 18 12 \- 12 x = ? 7.32 One packet of chocolate ? 7.32 ![](Sum Up Math-3_files/Sum20Up20Math-3-240.jpg) Divide and fill in the boxes : - [(a) ? 45 -h 5 =?](#bookmark508) - [(c) 64 p 4- 4 =?](#bookmark509) - [(e) ? 165 - 3 =?](#bookmark510) - [(g) ? 45.45 - 9 =?](#bookmark511) (b) ? 60 - 10 (d) 125 p - 5 (f) ? 112 - 7 (h) ?57 - 6 ![](Sum Up Math-3_files/Sum20Up20Math-3-241.jpg) - 2\. Three pineapple cost ? 99.90. Find the cost of one pineapple. - 3\. Four packet of cookies cost ? 89.20. What is the cost of one packet of cookies? - 4\. A set of 6 cup costs ? 150.00. Find the cost of one cup. - 5\. 4 kilogram of mangoes costs ? 142.40. What is the cost of 1 kilogram of mangoes? ![](Sum Up Math-3_files/Sum20Up20Math-3-242.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-243.jpg) ##### ÿ <Ved5UR6ment—Length ![](Sum Up Math-3_files/Sum20Up20Math-3-244.jpg) In previous class, you learnt about non-standard and standard unit of length for measuring small distance and thing. Here in this chapter, first review the previous work in brief and then learn for measuring longdistance. Non-standard unit of length is finger, a hand span, a cubit and a pace. For measuring they do not have the same result. So, the mathematicians, discovered the standard units of length. The standard unit of length is metre. In this picture a tailor is measuring the cloths with a measuring tape. In another picture a girl is measuring her height by a metre scale. There are different types of metre scales. ![](Sum Up Math-3_files/Sum20Up20Math-3-245.jpg) Above is the figure of metre rod. It is divided into 100 equal parts. The length of each part represents one centimetre. 1 metre = 100 centimetres ###### Note - • The short form for metre is m and the short form for centimetre is cm. ![](Sum Up Math-3_files/Sum20Up20Math-3-246.jpg) This is a ruler. It is used for measuring iiiii|iiii|iiii|iiii|iiii|iiii|iiii|iiii|iiii|iiii|iiii|iiii|iiH small lengths and objects such as length of a r \\ । . . . . iiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii penci I, a piece of paper, a crayon etc. Small lengths are generally measured in centimetres and big lengths are measured in metres. You will find on the road side signboards as shown here. Distance between 2 cities is written or measured in kilometres not in centimetres or metres. The short form of kilometre is km. 1 km = 1000 m Bowling speed of a player and speed of running vehicles etc is measured in kilometres. Conversion of Units of Length With the help of above relationship between metre and centimetre, kilometre and metre, you can convert metre to centimetres and ki lometres to metres. - (a) To convert metres into centimetre You know that 1 m = 100 cm So, to convert metres into centimetres, multiply the number of metres by 100 - Example 1: Convert into centimetres: (i) 8 m (ii) 2m 60 cm Solution: - (i) 8m = 8 x 100cm = 800cm Metre (m) are changed to centimetre (cm) by putting 2 zeros to the right of the number of metre (m) - (ii) 2m 60 cm = 2 x 100 + 60 = 2 60 cm - (a) To convert kilometre into metres You know that 1 km = 1000 m So, to convert kilometres into metres, multiply the number of kilometres by 1000. - Example 2: Convert into metres: (i) 4 km (ii) 2 km 560 m Solution: - (i) 4km =4 x 1000m = 4000m kilometre (km) are changed to m by putting 3 zeros to the right of the number of km. - (ii) 2 km 560 m = 2 x 1000 m + 560 m = 2560 m Convert km into m and then add the given number of m. Get Set Go With Sum Up Mathematics-3 ##### . EXERCISE 46 f - 1\. Convert into centii - (a) 8m = c - (c) 5 m 30 cm = - (d) 8 m 4 cm = - (e) 16m 80 cm = - (g) 7 m 49 cm = - 2\. Convert into metre - (a) 5 km = - (c) 8 km 66 m = - 3\. Guess the bowling metres and fill in the blanks : :m (b) 15 m = cm = x + cm = cm + cm = cm = x cm + cm = cm + cm = cm = cm (f) 27 m 75 cm = cm = cm (h) 13 m 30 cm = cm m (b) 1 km 545 m = m (d) 9 km 9 m = speed of the following cricketers. (a) Harbhajan Singh (b) Ashish Nehra To convert centimetres into metres To convert centimetres into metres or into metres and centimetres, we separate the ones and ten digits from the given number of centimetres. The number thus formed by ones and tens digits represents the centimetres and remaining number represents the metres. ###### Example 1 : Convert into m and cm (a) 500 cm Solution : (a) (b) ![](Sum Up Math-3_files/Sum20Up20Math-3-247.jpg) - (b) 468 cm (c) 815 cm 500 cm = 500 cm + 0 cm = 5 m 468 cm = 400 cm + 68 cm = 4 m + 68 cm 815 cm = 800 cm + 15 cm = 8 m + 15 cm ###### To convert metres into kilometres To convert metres into kilometres or into kilometres and metres, we separate the ones, tens and hundreds digits from the given number of metres. The number thus formed by ones, tens and hundreds digits represents the metres and the remaining number represents the kilometres. - Example 2 : Convert into km and m: (a) 7000 m (b) 5638 m (c) 2040 m. Solution : - (a) 7000 m = 7km + 0m = 7km - (b) 5638 m = 5000 m + 638 m = 5 km 638 m - (c) 2040 m = 2000 m + 40 m = 2 km 40 m ![](Sum Up Math-3_files/Sum20Up20Math-3-248.jpg) ##### EXERCISE 47 ^------------- - 1\. Convert into metres and centimetres and fill in the blanks: - (a) 600 cm = - (b) 525 cm = - 2\. Convert into metres and centimetres: - (a) 607 cm = - (b) 1707 cm = (c) 5490 cm = - 3\. Convert into kilometres and metres and fill in the blanks: - (a) 6540 m = - (b) 8016 m = m m m = 6 km m = 8 km m m - 4\. Convert into kilometresand metres: (a) 1430 m (b) 5604 m (c) 7058 m ###### Measuring in Centimetres To measure the length of small objects, put the one end of the objects on the zero mark of the ruler and read the number corresponding to the other end of the object. For example: ![](Sum Up Math-3_files/Sum20Up20Math-3-249.png) cm 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 9 9 1z £ 2 T 0 ![](Sum Up Math-3_files/Sum20Up20Math-3-250.jpg) The pencil measures 6 cm. ![](Sum Up Math-3_files/Sum20Up20Math-3-251.jpg)The paint brush measures 13 cm ![](Sum Up Math-3_files/Sum20Up20Math-3-252.jpg) ##### EXERCISE MS । ![](Sum Up Math-3_files/Sum20Up20Math-3-253.jpg) Addition of units of length Addition without regrouping. Example 1 : Add 32 m 25 cm and 46 m 14 cm Solution : m cm 32 25 \+ 46 14 78 39 Sum = 78 m 39 cm ![](Sum Up Math-3_files/Sum20Up20Math-3-254.jpg) Add cm to cm and m to m. Like paise, we write cm as 2-digit numbers. For example, to write 2 cm we write 02 cm. Then add metres and centimetres like whole numbers. Example! : Add 2 km 35 m and 4 km 413 m. Solution : Add m to m and km to km km m 2 035 \+ 4 413 6 448 Write m as 3-digit numbers for example 35m is written as 035m and 5m as 005m. Then add km and m like whole numbers. Sum = 6 km 448 m Addition with regrouping Example 3: Add 44 m 68 cm and 45 m and 45 cm Solution: Add cm to cm (68 + 45) cm = 113 cm = 1 m 13 cm, carry 1 m to metres ![](Sum Up Math-3_files/Sum20Up20Math-3-255.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-256.jpg) Add m to m (1) + 44 + 45 = 90 m Sum = 90 m 13 cm ![](Sum Up Math-3_files/Sum20Up20Math-3-257.jpg) ###### Example 4: Add 4 km 575 m and 3 km 764 m. Solution: .-. Sum = 8 km 339 m Examples: km m 1 4 575 + 3 764 , ’ 8 1339 ' A boy for tent house bought 56 m 88 cm blue ribbon and 29 m 63 cm red ribbon for decoration. How much ribbon did he buy? Solution: m cm 11 1 56 88 \+ x\_\_\_\_ 29 63 86 51 .’. He bought 86 m 51 cm. ![](Sum Up Math-3_files/Sum20Up20Math-3-258.jpg) ##### EXERCISE 49 J (a) (d) ![](Sum Up Math-3_files/Sum20Up20Math-3-259.jpg) (b) m cm 85 58 (c) \+ 9 05 ![](Sum Up Math-3_files/Sum20Up20Math-3-260.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-261.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-262.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-263.jpg) m cm 16 09 72 58 \+ 11 11 - 7 (f) (g) km cm 609 372 (h) km 3 cm 456 345 ![](Sum Up Math-3_files/Sum20Up20Math-3-264.jpg)668 cm 775 ![](Sum Up Math-3_files/Sum20Up20Math-3-265.jpg) Write in columns and add : (a) (b) (c) 29 m 57 cm and 43 m 69 cm. 33 m 46 cm and 52 m 29 cm. 2 km 679 cm and 4 km 582 cm. Shalu bought 5 m 75 cm red lace and 3 m 15 cm yellow lace. How much total lace she bought? A shopkeeper sold 14 m 32 cm cotton clothsand 11 m 54 cm silk cloth. How much total cloth did he sell today? Anil travelled 3 km 565 m by bus and 2 km 356 m by car. How much total distance did hetravel? ![](Sum Up Math-3_files/Sum20Up20Math-3-266.jpg) Subtraction Subtraction without decomposing Example 1: Subtract 36 m 68 cm from 68 m 88 cm. Solution : m cm 68 88 \- 36 68 32 20 Subtract cm from cm and m from m 68 m 88 cm - 36 m 68 cm = 32 m 20 cm. ###### Example 2: Subtract 3 km 215 m from 6 km 429 m. Solution: .-. 6 km 429 m - 3 km 215 m = 3 km 214 m Get Set Go With Sum Up Mathematics-3 km m 6 429 \- 3 215 Subtract m from m and km from km 3 214 ![](Sum Up Math-3_files/Sum20Up20Math-3-267.jpg) ###### Subtraction with Decomposing Example 3: Subtract 15 m 76 cm from 32 m 08 cm. ###### Solution: m 31 cm 108 32 15 08 76 16 32 Subtracting centimetres You cannot subtract 76 cm from 8 cm. So you have to borrow 1 m from m column. Now you have 1 m + 8 cm = 108 cm (108-76) cm = 32 cm You have borrowed 1 m from m column. So you are left with (32 -1) m 31 m /. 32 m 08 cm -15 m 76 cm = 16 m 32 cm Subtracting metres Example 4: Subtract 2 km 649 m from 7 km 313 m. Solution: ![](Sum Up Math-3_files/Sum20Up20Math-3-268.jpg) /. 7km 13 3 m-2 km 649 m = 4 km 664 m Examples: Sunil bought 68 m 59 cm rope. He used 32 m 67 cm of rope. Now, how much rope is left? Solution: ![](Sum Up Math-3_files/Sum20Up20Math-3-269.jpg)35 m 92 cm rope is left. ![](Sum Up Math-3_files/Sum20Up20Math-3-270.jpg)m 67 cm 159 ##### £>. EXERCISE50"J ![](Sum Up Math-3_files/Sum20Up20Math-3-271.jpg) (b) m 57 24 cm 15 (e) (h) ![](Sum Up Math-3_files/Sum20Up20Math-3-272.jpg) (c) (f) ![](Sum Up Math-3_files/Sum20Up20Math-3-273.jpg) - 2\. Write in column and subtract: - (a) 14 m 85 cm from 22 m 36 cm. - (b) 2 km 425 m from 5 km 758. - 3\. A tailor bought 47 m 59 cm cloth. He used 21 m 32 cm for making dress. How much cloth is left? - 4\. Shivani had 36 m 40 cm lace. She gave 12 m 15 cm lace to his friend. How much lace is left? - 5\. Rahul went 7 km 378 m by car and 2 km 120 m by scooter. How much distance did he travel more by car? ![](Sum Up Math-3_files/Sum20Up20Math-3-274.jpg) ##### ^ CVeasuRement—<Y?ti5s (Weight) ![](Sum Up Math-3_files/Sum20Up20Math-3-275.jpg) You have learnt in llnd standard, the need for standard units of weight. The standard unit of weight is kilogram and gram. In kilograms, heavier things are weighed like vegetables, grainsand other things. But lighter things are weighed in grams like chocolates chips etc. The short form of ki logram is kg and the short form of gram is g. 1 kg = 1000 g A balance is used to weigh things. There are different types of balances used for weighing. Few types of balances are shown below: ![](Sum Up Math-3_files/Sum20Up20Math-3-276.jpg)Picture of some weights are given below: ![](Sum Up Math-3_files/Sum20Up20Math-3-277.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-278.jpg)500g 200g 100g 50g ![](Sum Up Math-3_files/Sum20Up20Math-3-279.jpg)20g 10g To weight one kilogram of mangoes, put mangoes in one side of pan of the balance and in the other side of pan put two weights of 500 grams. .-. 1 kg = 500 g + 500 g = Two 500 g There is a balance shown in which one side has 4 blackberries and in other side we have put 500 g. Do the blackberries weigh 500 g? Is the weight of the blackberries less than 500 g? ![](Sum Up Math-3_files/Sum20Up20Math-3-280.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-281.jpg) Is the weight of the blackberries more than 500 g? Look at this picture, here we have used 1 kg in one side of pan of a balance and a papaya in other pan. Does the papaya weighs 1 kg? Isthe weight of papaya less than 1 kg? Isthe weight of papaya more than 1 kg? ![](Sum Up Math-3_files/Sum20Up20Math-3-282.jpg) Conversion of unit of mass (weight) With the help of the relation which is shown above 1 kg = 1000 g. You can convert kilograms into grams and grams into kilograms. - (a) To convert kilograms into grams To convert kilograms into gram multiply the number of kilograms by 1000. Example 1: Convert into grams: (a) 2 kg (b) 4 kg (c) 9 kg. Solution: - (a) 2kg = 1000 x 2g = 2000g - (b) 5 kg = 1000 x 4g = 4000g - (c) 9 kg = 1000 x 9 g = 9000 g To convert kg into g put 3 zeros to the right ofthe number of kg. Example 2: Convert into grams: (a) 3 kg 420 g (b) 5 kg 25 g (c) 7 kg 6 g. Solution: (a) 3kg420g = 1000 x 3g + 420g = 3000 g + 420 g = 3420 g (b) 5 kg25 g = 1000 x 5 g + 25 g = 5000 g + 25 g = 5025 g (c) 7 kg 6 g = 1000 x 7 g + 6 g = 7000 g + 6g = 7006 g - ###### (b) To Convert grams into kilograms To convert grams into kilograms or into kilograms and grams. Seperate the ones, tens and hundreds digits from the given number of gram. The number thus formed by ones, tens and hundreds digits represent the grams and the remaining number represents the ki lograms. ![](Sum Up Math-3_files/Sum20Up20Math-3-283.jpg)Example 1 : Convert into kg and grams (a) 4000 g (b) 5460 g (c) 2090 g Solution: - (a) - (b) (c) 4000 g = 4 kg + 0 g = 4 kg 5460 g = 5000 g + 460 g = 5 kg 460 g 2090 g = 2000 g + 90 g = 2 kg 90 g ![](Sum Up Math-3_files/Sum20Up20Math-3-284.jpg) ##### EXERCISE 51 । 1\. Fill in the blanks to make equal weights on both sides: 2\. (a) 1 kg = 500 g + 500 g = 5 00 g - (b) 100g + 200g + 200g + 500 g - (c) \_\_ 100 g = 1 kg (d) = 1 kg = 200 g + 100g + 200g = 1 kg (e) 500 g- 100g (f) Convert the fol lowing into grams: 500 g = 200 g + three 100 g (a) 3 kg (b) 5 kg (c) 8 kg (d) 2 kg425 g (e) 4 kg 570 g (f) 7 kg 10g Convert into kilogramsand grams: (a) 5000 g (b) 3400 g (d) 2509 g (e) 3067g (g) 6 kg 45 g (h) 5 kg 5 g (c) 6789 g (f) 7007 g ###### Addition-kilograms and grams (a) Addition without regrouping (grams into kilograms) - Example 1 : Add 4 kg 265 g and 3 kg 534 g. Solution : ![](Sum Up Math-3_files/Sum20Up20Math-3-285.jpg)Sum = 7 kg 799 g kg g 4 265 Add kg to kg and g to g seperaterly \+ 3 534 7 799 - ###### Example 2 : Add 6 kg 485 g and 2 kg 6 g. Solution : Sum = 8 kg491 g kg g 1 6 485 \+ 2 006 X\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_/ ' 8 491 ' Write grams in 3 digits before adding like 6 g as 006,2 6 as 02 6 g. (b) Adding with regrouping (gram into kilograms) ###### Example 3 : Add 4 kg 639 g and 2 kg 567 g. Solution : Sum = 7 kg 206 g Example 4 : kg g 1 11 4 639 \+ 2 567 7 206 Renu bought 1 kg 125 g moong dal, 2 kg 775 chana dal and 3 kg 350 g rajma. How much grains did she buy? Solution : .-. Renu bought 7 kg 250 g grains. kg g 1 125 \+ 2 775 \+ 3 350 X\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_^ ' 7 250 ' ![](Sum Up Math-3_files/Sum20Up20Math-3-286.jpg)1\. Add : ##### EXERCISE 52 । (a) ![](Sum Up Math-3_files/Sum20Up20Math-3-287.jpg) kg g 4 278 \+ 1 456 ![](Sum Up Math-3_files/Sum20Up20Math-3-288.jpg) (c) ![](Sum Up Math-3_files/Sum20Up20Math-3-289.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-290.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-291.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-292.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-293.jpg) (f) ![](Sum Up Math-3_files/Sum20Up20Math-3-294.jpg) - 2\. Write in column and add : - (a) 1 kg 565 g and 3 kg 8 g. - (b) 3 kg 770 g and 5 kg 108 g. - (c) 2 kg 5 g and 7 kg 540 g. - (d) 3 kg 1 7 g and 9 kg 235 g. - (e) 5 kg 250 g and 8 kg 760 g. - 3\. Arun carries a bag weighing 3 kg 70 g and his father carries a bag weighing 8 kg 115g. Find the differences in the weights. - 4\. A baby weighs 2 kg 750 g at the birth time. After 6 month her weight is 8 kg 420g. How much weightdid she gain? - 5\. Mala weighs 6 kg 450 g and his brother weighs 9 kg 999 g. Who is heavier and by how much? - 6\. Suman bought 5 kg 685 g vegetable and Rita bought 2 kg 200 g vegetable. Who bought more vegetable and by how much? - 7\. Sunita has 2 kg 5 g fruits and Anita has 1 kg 125 g fruits. Who has more fruits and by how much? ![](Sum Up Math-3_files/Sum20Up20Math-3-295.jpg) ##### 10 ##### (VeasuRcment—Capacity ![](Sum Up Math-3_files/Sum20Up20Math-3-296.jpg) In llnd standard, you have discussed about the nonstandard and standard units of measuring liquid. The standard unitof measuring liquids is litre. 1 litre = 1000 millilitres. Milk, oil and petrol are measured in litres but medicinal liquids are measured in millilitres. The short form of litre is / and the short form of millilitres is ml. The standard sized containers are given below which are used for measuring liquids. First kind of containers: ![](Sum Up Math-3_files/Sum20Up20Math-3-297.jpg) Upper containers are generally used for measuring milk. Whereas lower containers are used for measuring petrol and oil. You have learnt that a metre is bigger than a centimetre and a kilogram is heavier than agram. Similarly, a litre is more than a millilitre. So if you have to measure one litre milk you have to use 1 litre container for one time and 500 ml container for two times. /. 1 litre = Two 500 ml Similarly, 1 litre = Five 200 ml or 1 litre = one 500 ml + two 200 ml + one ml ![](Sum Up Math-3_files/Sum20Up20Math-3-298.jpg) or 1 litre = ten 100 ml Get Set Go With Sum Up Mathematics-3 ![](Sum Up Math-3_files/Sum20Up20Math-3-299.jpg)Conversion of unit of Capacity Using the relation 1 litre = 1000 millilitres, we can convert litre into millilitre & millilitre into litre. - ###### (a) To convert litres into millilitres Multiply the number of litres by 1000 to convert litres into millilitres. - Example 1: Converts litres, 7 litre and 10 litres into millilitres. Solution: 3 litres = 1000 x 3 millilitres = 3000 ml 7 litres = 1000 x 7millilitres = 7000ml 10 litres = 1000 x 10 millilitres = 10000 ml - Example 2: Convert 4 litres 343 ml into ml. Solution: 4 litres 343 ml = 4 litres + 343 ml = 1000 x 4 litres + 343 ml = 4000 litres + 343 ml = 4343 ml To convert I itres i nto mi 11 i I itres, put 3 zeros to the right side of the number of I itres. - ###### (b) Conversion of millilitres into litres Conversion of ml into 1 or into 1 and ml is done in the same way as you did in the case of grams into kilograms or into kilogramsand grams. Example 3: Convert into litresand millilitres: - (a) 5000 ml - (b) 6745 ml - (c) 7015 ml Solution: - (a) 5000 ml = 51 + 0 ml = 51 - (b) 6745 ml = 6000 ml + 745 ml = 61745 ml ![](Sum Up Math-3_files/Sum20Up20Math-3-300.jpg) - (c) 7015 ml = 7000 ml + 15 ml = 7115 ml ##### J. EXERCISE 53% ![](Sum Up Math-3_files/Sum20Up20Math-3-301.jpg) - 1\. Fill in the boxes to make equal measures on both sides : (a) (b) 11 = 500 ml + ml = two ml 500 ml + 200 ml + 100 ml + 100 ml + 100 ml 200 ml + 100 ml = 500 ml + (c) 11 = 100 ml (e) 21 = 500 ml (f) 21 = 500 ml (d) 21 = 200 ml 200 ml one 100 ml + one litre (g) (h) 500 ml = 500 ml = 200 ml + 100 ml 100 ml - 2\. Convert into millilitres : (a) 7 litres - (d) 1 litres 35 ml (b) 5 litres - (e) 6 litres 10 ml (c) 2 litres 156 ml - 3\. Convert into litres and millilitres : (a) 3000 ml (b) 4583 ml (d) 1640 ml (e) 4050 ml (g) 5006 ml (h) 7508 ml (c) (f) 6500 ml 2009 ml ###### Addition-Litres and Millilitres (a) Addition without regrouping (millilitres into litres) ###### Example 1 : Add 2 litres 547 ml and 5 litres 246 ml. ###### Solution : ml 2 547 Add 1 to 1 and ml to ml 246 7 793 Sum = 71793 ml ![](Sum Up Math-3_files/Sum20Up20Math-3-302.jpg) ###### Example 2 : Add 4 I ¡très 75 ml and 4 I itres 5 ml. Solution : 1 ml 4 075 \+ 4 005 8 080 Write ml in 3 digits before adding e.g. 75 ml as 075 ml and 5 ml as 005 ml. Sum = 81080 ml - (b) Addition with regrouping (militres into litres) Example 3 : Add 5 litres 585 mland 2 Iitre437 ml. Solution : 1 ml 1 11 5 585 \+ 2 437 Sum = 81022 ml ( o Add caried Itoi ##### {B EXERCISE 5R । - 1\. Add : (a) 1 ml 2 380 \+ 4 759 ![](Sum Up Math-3_files/Sum20Up20Math-3-303.jpg) 4 348 \+ 3 763 ![](Sum Up Math-3_files/Sum20Up20Math-3-304.jpg) (b) 1 ml 5 678 \+ 3 300 (e) 1 ml 6 499 \+ 3 375 (c) 1 ml 1 009 \+ 7 785 (f) 1 ml 5 647 \+ 1 756 ![](Sum Up Math-3_files/Sum20Up20Math-3-305.jpg) - ###### 2. Arrange in columns and add : ![](Sum Up Math-3_files/Sum20Up20Math-3-306.jpg) - (a) 3 litres 46 ml and 2 litres 58 ml. - (b) 1 litres 55 ml, 3 litres 107 ml, 3 litres 227 ml. - (c) 6 litres 513 ml and 2 litres 357 ml. - 3\. Sonali purchased 3 litres 125 ml of refined oil and 5 litres 250 ml mustard oil. How much total oil did she purchased? - 4\. A milkman sells 5 litres 250 ml, 2 litres 500 ml and 1 litres 115 ml milk to his three customers. How much total milkdoes he sell them? - 5\. Sonam filled 31 500 ml and his friend filled 41 250 ml petrol in their cars. How much total petrol did they fill? ###### Subtraction-litres and millilitres Remember: Subtraction of capacity measures is carried out in the same way as we do the subtraction of weight measures. - (a) Subtraction without decomposing (litres into millilitres) Example 1: Subtract 2 litres 345 ml from 6 litres 896 ml Solution: 1 ml 6 896 \- 2 345 4 551 Subtract ml from ml and 1 from 1 Difference = 41551 ml - (b) Subtraction with decomposing (litres into millilitres) Example 2: Subtracts litres 689 mlfrom 9 litres235 ml Solution : 1 ml 8 11 9 235 \- 3 689 <\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_/ 91235 ml-31689 ml = 51546 ml 5 546 ![](Sum Up Math-3_files/Sum20Up20Math-3-307.jpg) ##### . EXERCISE 55 । - 1\. Subtract: (a) (d) ![](Sum Up Math-3_files/Sum20Up20Math-3-308.jpg) 1 ml 6 510 9 678 \- 3 356 ![](Sum Up Math-3_files/Sum20Up20Math-3-309.jpg) \- 1 897 ![](Sum Up Math-3_files/Sum20Up20Math-3-310.jpg)1 ml 7 234 \- 3 798 ![](Sum Up Math-3_files/Sum20Up20Math-3-311.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-312.jpg) - 2\. Write in columns and subtract: - (a) 4 litres 502 ml from 9 litres 713 ml. - (b) 3 litres 437 ml from 6 litres 879 ml. - (c) 1 litres 995 ml from 5 litres 495 ml. - (d) 6 litres 775 ml from 9 litres 250 ml. - 3\. A bucket contains 9 litres 775 ml waters. 1 litres 50 ml is wasted due to a leak in the bucket. How much water is left in the bucket? - 4\. Sunita had 3 litre 250 ml mustard oil. Last week she used 1 litre 50 ml oil. How much oil is left with her now? - 5\. A shopkeeper has 9 litre 975 ml milk. He sell 5 litre 500 ml milk in a hour. How much milk is left after an hour? ![](Sum Up Math-3_files/Sum20Up20Math-3-313.jpg)You already know about time. We have read about time in llnd standard. Some of you may be tel I ing time from a clock also. Let us recal I the parts of a clock. A clock has two hands. Some clocks have three hands. The shorter hand is the hour hand. The longer hand is the minute hand. The hour hand shows time in hours and the minute hand shows time in minutes. ![](Sum Up Math-3_files/Sum20Up20Math-3-314.jpg) The face of the clock is called dial. There are 12 equal parts in it. They are marked as 1, 2, 3... 11,12. Between two successive numbers, there are 5 equal divisions. So, there are 60 small divisions in all. Each smaller division shows one minute and each big division representsone hour. In one hour the hour hand moves from a number to the next number. In one hour, the minute hand makes one round of the dial. Thus; 1 hour = 60 minutes. ![](Sum Up Math-3_files/Sum20Up20Math-3-315.jpg) ###### How to read Time? In this figure, the hour hand is at 7. The minute hand is at 12. The time is 7 o'clock. It is written as 7:00. Lab Activity Let us make a model of a clock. Take a piece of cardboard. With the help of a plate draw a circle on it. Mark 1,2, 3, ...11,12 inside the circle. Take two drinking straws of different colours. Cut them in two sizes. With a thumb pin fix the straws to make minute hand and hour hand. Your clock is ready. Make a position of straws and ask a friend to tel I the time. ##### EXERCISE 56 f - 1\. Read the time and write in two ways : ![](Sum Up Math-3_files/Sum20Up20Math-3-316.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-317.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-318.jpg) 5 O'clock 5:00 One hand of the clock is missing. Draw them to show the time given below the figure : ![](Sum Up Math-3_files/Sum20Up20Math-3-319.jpg)3\. Read the time and then draw hands and fill in the blanks : ![](Sum Up Math-3_files/Sum20Up20Math-3-320.jpg)O'clock O'clock O'clock ###### Reading time in Half Hours and Quarter Hours Look at this figure : The hour hand is between 12 and 1 The minute hand is at 6. The time is "half past 12". It is written as 12:30. It is read as "twelve thirty." ![](Sum Up Math-3_files/Sum20Up20Math-3-321.jpg) 120 ###### Look at this figure : ![](Sum Up Math-3_files/Sum20Up20Math-3-322.jpg) The hour hand is between 9 and 10. The minute hand is at 3. The time is "quarter past 9." It is written as 9:15. It is read is "nine fifteen". Look at this figure : The hour hand is between 5 and 6. ![](Sum Up Math-3_files/Sum20Up20Math-3-323.jpg) The minute hand is at 9. The time is "quarter to 6." It is written as 5:45. It is read as "five forty five." ##### EXERCISE 57 - 1\. Read the time and write in two ways : ![](Sum Up Math-3_files/Sum20Up20Math-3-324.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-325.jpg) Half past three 3:30 O'clock ![](Sum Up Math-3_files/Sum20Up20Math-3-326.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-327.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-328.jpg) Quarter past twelve 12:15 O'clock ![](Sum Up Math-3_files/Sum20Up20Math-3-329.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-330.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-331.jpg) Quarter to seven 6 : 45 O'clock 2\. Match the following : ![](Sum Up Math-3_files/Sum20Up20Math-3-332.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-333.jpg) (a) 2:45 (b) 11:15 (c) 3:00 (d) ~930~~ ###### Reading Time in Hours and 5 minute Correctness Look at this figure: The hour hand is between 6 and 7. The minute hand is at 2. The time is "10 pastó". It is written as 6:10. It is read as "ten past six". 2 multiplied by "5 is 10". ![](Sum Up Math-3_files/Sum20Up20Math-3-334.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-335.jpg) ##### EXERCISE 58 ^------------ Read the time and write in two ways : ![](Sum Up Math-3_files/Sum20Up20Math-3-336.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-337.jpg) 20 minutes past 7 7:20 O'clock ![](Sum Up Math-3_files/Sum20Up20Math-3-338.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-339.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-340.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-341.jpg) Draw the missing hand in these clocks : ![](Sum Up Math-3_files/Sum20Up20Math-3-342.jpg)![](Sum Up Math-3_files/Sum20Up20Math-3-343.jpg) 4\. Read the first clock. Write the time and then draw hands in next clock. Get up in morning. ![](Sum Up Math-3_files/Sum20Up20Math-3-344.jpg)6:10 Look at the watches on the left and write times to complete the sentence. Then draw hands on the watch on the right. ![](Sum Up Math-3_files/Sum20Up20Math-3-345.jpg) 9:30 is 30 minutes after 9:00 ![](Sum Up Math-3_files/Sum20Up20Math-3-346.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-347.jpg) is 30 minutes after is 30 minutes after is 30 minutes after ![](Sum Up Math-3_files/Sum20Up20Math-3-348.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-349.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-350.jpg) ###### (6. ![](Sum Up Math-3_files/Sum20Up20Math-3-351.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-352.jpg) is 30 minutes after ![](Sum Up Math-3_files/Sum20Up20Math-3-353.jpg) Draw hands and write time when : ![](Sum Up Math-3_files/Sum20Up20Math-3-354.jpg) You go to school 7:30 You come back home Your father goes to office ![](Sum Up Math-3_files/Sum20Up20Math-3-355.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-356.jpg) ###### Estimating Time Everytime we don't need to look at a clock to know or tell time. You get ready in 10 minutes. The prayer in school takes 5 minutes. You take 10 minutesto finish lunch. Your grandmother take 1 hour for prayer. ##### EXERCISE 59% - 1\. Tick (/) against the time suited to you. - (a) Finishing breakfast - (b) Sharpeningapencil - (c) Finishing homework - (d) Sleeping at night - (e) Watching a cartoon film - (f) Singingasong 5 hours/5 minutes. - 1 hour/1 minute. - 2 hour/2 minute. - 8 hours/8 minutes. - 2 hours/2 minutes. - 5 hours/5 minutes. - 2\. Write three activities which take less than one hour: - (a) .......................................................................... - (b) .......................................................................... (c) .......................................................................... - 3\. Write three activities which take more than one hour: - (a) ..................................................................................... - (b) ..................................................................................... (c) ..................................................................................... ###### Conversion of Time You know that 1 hour = 60 minutes The time from one mid-nightto next mid-night is called one day. The hour hand makes two rounds in a day. The hour hand completes 12 hours in one round. So, the hour hand completes 24 hours in two rounds. Thus, ![](Sum Up Math-3_files/Sum20Up20Math-3-357.jpg)There is no school/on Sunday. Monday comes after Sunday. Tuesday comes after Monday. Saturday comes after Friday. Sunday comes after Saturday. 1 month = 4 weeks. 1 year = 12 months. ![](Sum Up Math-3_files/Sum20Up20Math-3-358.jpg) ###### Months of the year Month No. of Days Month No. of Days 1\. January 31 7- July 31 2\. February 28 or 29 8\. August 31 3\. March 31 9\. September 30 4\. April 30 10\. October 31 5\. May 31 11\. November 30 6\. June 30 12\. December 31 1 month = 30 days 1 year = 365 days. Four months of a year have 30 days each. Seven months of a year 31 days each. February has 28 or 29 days. Republic Day comes in January. Independence Day comes in August. - Example 1: Convert into minutes (a) 1 hour (b) 3 hours Solution: - (a) 1 hour = 60 minutes. - (b) 1 hour = 60 minutes. 3 hours = 60 x 3 = 180 minutes. - Example 2: Convert in weeks (a) 2 months (b) 6 months Solution: - (a) 1 month = 4 weeks /. 2 months = 4x2 = 8 weeks. - (b) 1 month = 4 weeks .’. 6 months = 4 x 6 = 24 weeks. ![](Sum Up Math-3_files/Sum20Up20Math-3-359.jpg) To convert into minutes, multiply hours by 60 ![](Sum Up Math-3_files/Sum20Up20Math-3-360.jpg) To convert into weeks multiply months by 4. ![](Sum Up Math-3_files/Sum20Up20Math-3-361.jpg) - ###### Example 3: Convert into months (a) 3 years (b) 5 years. Solution: - (a) 1 years = 12 months /. 3 years = 12x3 = 36 months. - (b) 1 years = 12 months .-. 5 years = 12 x 5 = 60 months. ##### j. EXERCISE 60S1------------- - 1\. Answerthe questions: - (a) Which day comes after Thursday? - (b) Which day comes before Sunday? - (c) Which day is between Saturday and Monday? - (d) How many days are there in a week? ........ - (e) How many hours are there in a day? - (f) Which is the shortest month? - (g) Howmany months have 30 days? - (h) Which is the first month of the year? - (i) In which month we celebrate Independence Day? - (j) Your birthday comes in which month? ........ - (k) Which month is the summer vacation for you? - (I) Which month comes afterJune? - 2\. Fill in the blanks: - (a) There are months in a year. - (b) There are days in August. - (c) There are..................weeks in a month. - (d) There are days in a month. - 3\. Look at the calender of this year and fill in the blanks: ![](Sum Up Math-3_files/Sum20Up20Math-3-362.jpg) - (a) How many Sunday are there in July? - (b) New year day falls on which day of the week? - (c) Republic day ¡son which day of the week? - (d) Yourbirthday comeson which day of the week? .............................. ![](Sum Up Math-3_files/Sum20Up20Math-3-363.jpg)Convert: - (a) 5 hours into minutes. - (b) 4 years into months. - (c) 7 months into weeks. - (d) 4 weeks into days. - (e) 2 years intodays. - (f) 6 months intodays. ![](Sum Up Math-3_files/Sum20Up20Math-3-364.jpg) 12 Geometry ###### Basic Shapes Triangle Look at this figure. It has three sides and three vertices. It is a triangle. It is written as AABC. The sides of the triangle are AB, BC and AC. The vertices of the triangle are A, B and C. ###### Square Look at this figure. It has four sides and four vertices. All sides are equal. It is a square. The sides of the square are AB, BC, CD and AD. AB = BC = CD = AD. BD is the diagonal of the square ABCD AC is also a diagonal of the square ABCD. ![](Sum Up Math-3_files/Sum20Up20Math-3-365.jpg)Vertex ![](Sum Up Math-3_files/Sum20Up20Math-3-366.jpg)Side Rectangle Circle Get Set Go With Sum Up Mathematics-3 Rectangle Look at this figure. It has four vertices and four sides. Opposite sides are equal. It is a rectangle. AB = DC AD = BC AC and BD are diagonals of rectangle ABCD. ###### Circle Look at this figure. It has no side and no vertex. ###### Drawing Shapes Triangles can be made by matchsticks or drinking straws. ![](Sum Up Math-3_files/Sum20Up20Math-3-367.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-368.jpg) You can also use ruler or wooden or plastic blocks to draw triangles. Squares and rectangles can be made by matchsticks or drinking straws. Square can be made by a dice or by a Rubik's cube. Rectangle can be made by a book or a pencil box. ![](Sum Up Math-3_files/Sum20Up20Math-3-369.jpg) Circle can be made by a coin or a bangle or a plate. ![](Sum Up Math-3_files/Sum20Up20Math-3-370.jpg) ###### Lab Activity Paper Folding Let us make a triangle, a square and a rectangle by folding paper. Take a sheet of paper. Fold the shorter side of paper onto the longer side, as shown. ![](Sum Up Math-3_files/Sum20Up20Math-3-371.jpg)You get a triangle Unfold the paper. ![](Sum Up Math-3_files/Sum20Up20Math-3-372.jpg)You get a square and a rectangle. ![](Sum Up Math-3_files/Sum20Up20Math-3-373.jpg)###### Using a Dot Paper ![](Sum Up Math-3_files/Sum20Up20Math-3-374.jpg) You can make a triangle, a rectangle and a square using a dot paper. This is a triangle. ![](Sum Up Math-3_files/Sum20Up20Math-3-375.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-376.jpg) This is a rectangle. This is a square. ![](Sum Up Math-3_files/Sum20Up20Math-3-377.jpg) ###### Using a grid You can make a triangle, a rectangle and a square using a grid. ![](Sum Up Math-3_files/Sum20Up20Math-3-378.jpg)This is a square. Get Set Go With Sum Up Mathematics-3 ![](Sum Up Math-3_files/Sum20Up20Math-3-379.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-380.jpg)This is a rectangle. ![](Sum Up Math-3_files/Sum20Up20Math-3-381.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-382.jpg) Look at the figure, count and fill in blanks : (a) There are..............circles. (b) (c) (d) There are There are There are triangles. squares. .....rectangles. Colour the picture as indicated : Orange Blue ![](Sum Up Math-3_files/Sum20Up20Math-3-383.jpg)Red Yellow Answer these questions : ![](Sum Up Math-3_files/Sum20Up20Math-3-384.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-385.png) ![](Sum Up Math-3_files/Sum20Up20Math-3-386.png) - (a) Can you make a triangle with three different sized sticks? - (b) How many vertices are there in a triangle? - (c) How many sides are equal in a square? - (d) How many sides are there in a circle? - (e) How many diagonals are there in a rectangle? Name two objects which are triangular in shape? Name two objects which are rectangular in shape? Name two objects which are circular in shape? 7\. Match the shapes : - (a) Sun - (b) Black board - (c) Chessbord - (d) Pizza piece ![](Sum Up Math-3_files/Sum20Up20Math-3-387.jpg) 136 - 8\. Fill in the blanks : - (a) There are..............sides and..............vertices in a triangle. - (b) There are sides and vertices in a square. - (c) There are sides and vertices in a rectangle. - (d) There are..............sides and vertices in a circle. - 9\. Use a grid paper to draws a triangle, a rectangle and a square. ###### Plane and curved surfaces Look at this figure. ![](Sum Up Math-3_files/Sum20Up20Math-3-388.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-389.jpg) The whole length of ruler touches the book. The top of the book is a plane surface. Look at this picture. ![](Sum Up Math-3_files/Sum20Up20Math-3-390.jpg) The whole length of ruler does not touch the top of the ball. The ball has a curved surface. ###### Cuboid A cuboid has 6 surfaces. Surface of a cuboid is called face. Each face in a cuboid is rectangular. Opposite faces of cuboid are equal. Each side of a cuboid is called edge. There are 8 corners in a cuboid. ###### Cube A cube looks like a cuboid. All faces of a cube are equal. All edges of a cube are equal. ![](Sum Up Math-3_files/Sum20Up20Math-3-391.jpg)Cuboid Cube ![](Sum Up Math-3_files/Sum20Up20Math-3-392.jpg) Cylinder Cylinder A cylinder has a curved face. A cylinder has two flat (plane) faces. A cylinder has two circular edges. ![](Sum Up Math-3_files/Sum20Up20Math-3-393.jpg) ###### Sphere A sphere has one curved face. A sphere has no flat (plane) face. A sphere has no vertex. ###### Straight and Curved Lines Plane Edge Curved Face wzzzzw ###### Cone A cone has a curved face and one flat (plane) face. A cone has one vertex. A cone has one circular edges. ![](Sum Up Math-3_files/Sum20Up20Math-3-394.jpg) Make a (/) against curved lines and (X) against straight lines : ![](Sum Up Math-3_files/Sum20Up20Math-3-395.jpg) Open and closed figures. Makea (/) against open figures and (X) against closed figures: ![](Sum Up Math-3_files/Sum20Up20Math-3-396.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-397.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-398.jpg) ###### (1. ##### X. EXERCISE 62 f A cuboid has how many faces? A cube has how many faces? - 3\. A cylinder has how many curves? - 4\. A cone has how many faces? - 5\. A cylinder has how many edges? - 6\. A ball has how many edges? - 7\. A cube has how many vertices? - 8\. Name two objects which looks like a cube? - 9\. Name two objects which looks like a sphere? 10\. Name one object which looks like a cone? ![](Sum Up Math-3_files/Sum20Up20Math-3-399.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-400.jpg) A cell Sideview Top view ![](Sum Up Math-3_files/Sum20Up20Math-3-401.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-402.jpg)Almirah Front view Side view Mirror Images and Mirror Lines Trace this figure on a paper and make a cut out. Fold along the dotted line. One half of the figure completely covers another half. This is true for both halves. Each half is a mirror image of other half. The dotted line is 'mirror line'. Get Set Go With Sum Up Mathematics-3 ![](Sum Up Math-3_files/Sum20Up20Math-3-403.jpg) ###### Do it yourself Fold a paper in two halves. Make these shapes and cut out. Unfold to see the complete shape. ![](Sum Up Math-3_files/Sum20Up20Math-3-404.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-405.jpg) EXERCISE 63 s ![](Sum Up Math-3_files/Sum20Up20Math-3-406.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-407.jpg) ##### patteRns ![](Sum Up Math-3_files/Sum20Up20Math-3-408.jpg) When a shape or drawing is repeated in a figure it is called pattern. Sometimes same figure is repeated. Sometimes figures change in set pattern. Geometrical Patterns: Number Patterns ![](Sum Up Math-3_files/Sum20Up20Math-3-409.jpg) 10 20 30 40 50 60 70 2 4 6 8 10 12 14 5 10 15 20 25 30 35 24 32 40 48 56 64 72 ##### EXERCISE 64 , 1\. Complete the following patterns : (a) 7 10 13 16 (b) 35 45 55 65 (c) 7 9 11 13 (d) 99 97 95 93 ![](Sum Up Math-3_files/Sum20Up20Math-3-410.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-411.jpg) ###### Even and Odd Numbers Even numbers are divisible by 2. Example: 4,14,16,28, etc. are even numbers. Odd numbers are notdivisibleby2. Example: 3,1 7,19, 57, etc. are odd numbers. Addition properties of even and odd numbers Even + Even = Even Sum of two even numbers is even. Example: 12 \+ 16 = 28 1 JL ; Even Even Even Odd + Odd = Even Sum of two odd numbers is even. ![](Sum Up Math-3_files/Sum20Up20Math-3-412.jpg) Even + Odd = odd Odd + Even = odd Sum of an even numbers and an odd number is odd. Example: 12 + 11 = 33 ; ^ ; Even + Odd = Odd 17 + 16 = 33 ; ^ ; Odd + Even = Odd - 1\. Encircle even numbers in the following : 503, 76, 312, 479, 873, 522 - 2\. Encircle odd numbers in the following : 604, 75, 319, 794, 387, 252 - 3\. Fill in the boxes : (a) 26 + 42 = (b) 27 + 26 = ^ ; ; Even Even Odd Even (c) 57 + 49 = (d) 27 + 48 = ^ ; ; Odd Odd Odd Even - 4\. Write 'T' for True and 'F' for False : - (a) Two even numbers add up to an even number. - (b) Two odd numbers add upto an odd number. - (c) One even number and another odd number add up to an even number. ##### 14 ##### Delhi Handling ![](Sum Up Math-3_files/Sum20Up20Math-3-413.jpg) Data is shown in the form of (a) Tables (b) Pictographs (c) Bar graphs. Pictographs use pictures or symbols to show data. This makes the data easy to understand. ###### Tallies and Vertical Bars Tallies are used for counting the number of an object in data. Tallies are written as fol lows: - [1 |6](#bookmark658) - [2 II](#bookmark659) - [3 III](#bookmark660) - [4 Illi](#bookmark661) - [5 HU10](#bookmark662) ![](Sum Up Math-3_files/Sum20Up20Math-3-414.jpg) Let us take another example of vegetables given here. 5 Tomatoes ![](Sum Up Math-3_files/Sum20Up20Math-3-415.jpg) 10 Potatoes 1 Brinjal 7 Carrot 8 Cauliflowers Let's count them as fol lows: 44\] Vegetable ![](Sum Up Math-3_files/Sum20Up20Math-3-416.jpg) Tallies ### rw rw nu mn n IHI III ###### Number 5 10 1 7 8 Get Set Go With Sum Up Mathematics-3 Now, it can be shown by given pictograph. ![](Sum Up Math-3_files/Sum20Up20Math-3-417.jpg) Let us take another example. Rohit has madeatally of histoys. This is shown in the table below: ![](Sum Up Math-3_files/Sum20Up20Math-3-418.jpg) Tallies ![](Sum Up Math-3_files/Sum20Up20Math-3-419.jpg) ###### Number 7 4 6 10 3 This table can be displayed in pictograph as follows: ![](Sum Up Math-3_files/Sum20Up20Math-3-420.jpg)^ 7 cars ^4 Aeroplanes 6 balls ![](Sum Up Math-3_files/Sum20Up20Math-3-421.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-422.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-423.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-424.jpg)^ 10 darts In these examples, the numbers are small and hence easy to show in pictograph. Now, suppose that numbers are large, then one picture can stand for 5 items or 10 items or 100 items. Let us take an example of collection of old coins which Rahul has. Coins 25p 50p 5p IP No of Coins 25 30 45 50 Here all numbers are in multiples of 5. So, let us show 5 items by 1 picture. The pictograph will look like this figure. ![](Sum Up Math-3_files/Sum20Up20Math-3-425.jpg)Here 1 coin standsfor 5 coins Reading and Interpreting a Pictograph Let us try to interpret the given pictograph. ![](Sum Up Math-3_files/Sum20Up20Math-3-426.jpg)![](Sum Up Math-3_files/Sum20Up20Math-3-427.jpg)—> 7 Snails ![](Sum Up Math-3_files/Sum20Up20Math-3-428.jpg)—» 10 Crubs ![](Sum Up Math-3_files/Sum20Up20Math-3-429.jpg)![](Sum Up Math-3_files/Sum20Up20Math-3-430.jpg)While readingthis pictograph, we should answerthese questions : - (a) Which animals are seen? - (b) How many snails can be seen? (c) How many crabscan be seen? - (d) How many fish can be seen? - (e) How many frogs can be seen? - (f) What is the total number of animals? ##### L EXERCISE SS J - 1\. What is the number of fruits in the basket: Fruits Tallies Number ![](Sum Up Math-3_files/Sum20Up20Math-3-431.jpg)![](Sum Up Math-3_files/Sum20Up20Math-3-432.jpg) - 2\. Find the number of birds on a tree. ![](Sum Up Math-3_files/Sum20Up20Math-3-433.jpg) Birds Tallies Number Make tallies for different types of candies shown here : OOLAOOOOOAAA oooooo□D D Dao Show this by pictograph. 4\. Make a pictograph for following data : Items Pencil Pen Eraser Toffee Pastry Number 8 6 7 4 3 The following pictograph shows number of vehicles in a parking lot: <iiu <iu fk <1^ fi\* ^Bp fl?^F “mi ^?|^pf 5 Buses 8 Cars 10 Cycles ![](Sum Up Math-3_files/Sum20Up20Math-3-434.jpg) 4 Scooters f< Ù ^^^^^^^^^^^^^^^^^^ ^ 9 Motorcycles \[148 ![](Sum Up Math-3_files/Sum20Up20Math-3-435.jpg) From the above pictograph answerthese questions : - (a) There are buses. (b) There are cars more than buses. (c) Numberof scooters is less than motorcycles. - (d) Total number ofvehicle is - 6\. The following pictograph shows numberof students in different game teams: Skating Tennis -7 Ta 7F 7 SA ' ¿H / ¿H T 1« ' Ji / J\* ![](Sum Up Math-3_files/Sum20Up20Math-3-436.jpg) Cricket Basketball —» ![](Sum Up Math-3_files/Sum20Up20Math-3-437.jpg) Volleyball —> ![](Sum Up Math-3_files/Sum20Up20Math-3-438.jpg) Here 1 shows 5 students. On the basis of above pictograph answerthese questions : - (a) How many students are in skating team? - (b) How many students are in cricket team? - (c) How many students in volleyball team? - (d) How many students are in tennis team? - (e) How many students are in basketball team. ![](Sum Up Math-3_files/Sum20Up20Math-3-439.jpg) FORMATIVE ASSESSMENT-i (Chapter 1 to 3) Time: 1 hr.F.M. 20 - 1\. Write the number names: 5607, 6750, 7005, 8709, 2955. - 2\. Write the place values of both 7's in 5797 and find their difference. - 3\. Add: 804 + 92 3 + 149 - 4\. There are 3245 students in a school. If the number of girls are 1343, find the number of boys. - 5\. Write the following numbers in expanded form: (a) 8706 (b)7709 - 6\. What is the difference between 875 and 735 ? - 7\. One packet of candies contain 120 candies. How many candies are there in 15 such packets? - 8\. Write in figures: - (a) Two thousand eight hundred ninety two. - (b) Seven thousand five hundred seventy six. - 9\. Write the place value of two 3' in 3230 and find their difference. - 10\. Solve: 5 780-3052 + 2895 - 1 786 ![](Sum Up Math-3_files/Sum20Up20Math-3-440.jpg) Time: 1 hr. F.M. 20 - 1\. 15 T-shirts cost Rs. 1230. What is the price of 1 T-shirt? - 2\. A snail travels 12 inches in a day. How much distance the snail travels in a week? - 3\. The product of two numbers is 8253. If one of them is 9, find the other number. - 4\. In following fractions, separate the numerator and the denominator. - (a) (b) A (c) L 3 7 9 - 5\. Priceof apen is Rs.27. What is the price of 54 pens? - 6\. Raju got 236 chocolates. He can give 4 chocolates to one person. To how many persons can he distribute chocolates ? - 7\. Raina purchased cauliflower for Rs.17.85 and tomatoes for Rs.28.25. He gave a fifty rupees note to the shopkeeper. How much money is returned by the shopkeeper? - 8\. An egg cost Rs. 3.50. What is the price of 24 eggs? - 9\. On an average each student of a class gets Rs.154 as pocket money. Find the total pocket money for 43 students. - 10\. Add: Rs.9.53, Rs.17.85 and Rs. 36.30. ![](Sum Up Math-3_files/Sum20Up20Math-3-441.jpg) Time: 1 hr. F.M. 20 - 1\. Add: 150 m 13 cm and 162 m 53 cm. - 2\. A grocer had 230 kg 750 g of potatoes. He sold 78 kg 250 g on a day. How much potatoes are left with him? - 3\. Add 2 kg 20 gm and 5 kg 70 gm. - 4\. A container has 15 litre and 500 mZ milk. 2 litre and 250 mZ milk is taken out from this. How much milk is left in the container? - 5\. How many minutes are there in 3 hours 20 minutes? - 6\. Subtract 3 m 35 cm from 11 m 60 cm. - 7\. Convert: - (a) 7 days into hours. - (b) 7 months into weeks. - 8\. Baba Ramdev travelled 2 73 km 5 3 m on foot. Baba Balkrishn travelled 568 km 3 3 m on foot. What is the total distance travelled by them? - 9\. Golu slept for 7 hours 18 minutes. For how many minutes he slept? - 10\. A tailor bought 47 m cloth. He used 21 m 32 cm for making dress. How much cloth is left? ![](Sum Up Math-3_files/Sum20Up20Math-3-442.jpg) Time: 1 hr. F.M. 20 1\. The following pictograph shows number of items in a shop. ![](Sum Up Math-3_files/Sum20Up20Math-3-443.jpg)Here, 1 4- stands for 10 items. Based on the above pictograph fill in the blanks - (a) There are - (b) There are - (c) There are - (d) There are watches. cameras, mobile phones, total items. - 2\. Answer the following questions. - (a) How many vertices are in a triangle? - (b) How many sides are in a square? - (c) How many curved surfaces are in a ball? - (d) How many curved surfaces are in a cylinder? 3\. The following table shows pets of class 3 students. 4 4 4 4 44 4 À X X X X X X ![](Sum Up Math-3_files/Sum20Up20Math-3-444.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-445.jpg)- (a) Which is the most popular pest? - (b) Which is the least popular pest? - (c) How many students keep snails as a pet? - (d) How many students have octopus as pet? - 4\. Fill in the blanks: - (a) A rectangle has..............sides. - (b) A cube has..............faces. - (c) A cuboid has..............corners. - (d) A cone has..............vertex. - 5\. The following table shows number of animals in a zoo. Make a pictograph from this data. Animals Lion Zebra Deer Bear Monkey Numbers 12 8 9 2 7 ![](Sum Up Math-3_files/Sum20Up20Math-3-446.jpg)![](Sum Up Math-3_files/Sum20Up20Math-3-447.jpg) ##### RnsweR Sheet ![](Sum Up Math-3_files/Sum20Up20Math-3-448.jpg) - 1\. (a) 3231, (b) 4122, (c) 3631, (d) 4302, (e) 3241, (f) 5023, (g) 3042, (h) 2251, (i) 4003. - 2\. (a) 1002,1003,1004,1005. (b) 2322,2323,2324, 2325. (c) 5478, 5479, 5480, 5481. - 3\. (a)4321,(b) 6438, (c) 7550. 4. (a) 4577, (b) 7770, (c) 8694. - 5\. (a) 8473, 8474, 8475, (b) 6590, 6591,6592, (c) 7856, 7857, 7858. - 6\. (a) 7750, 7752, 7754, (b) 6407, 6409, 6411. 7. (a) 2613, 2620, 2627, (b) 5726, 5733, 5740. - 8\. (a) 6530, 6540, 6550, (b) 8787,8797, 8807. 9. (a) 4126,4226,4326, (b) 3335, 3435, 3535. - 10\. (a)6318,7318,8318,(b) 7520,8520,9520. 11. (a) 3220, 3224, 3228, (b) 4619,4516, 441 6, - (c) 4820, 3820,2820. 12. (a) 99, (b) 999, (c) 9999. 13. (a) 10, (b) 100, (c) 1000. Exercise-2\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) Two thousand one hundreds fifty seven, (b) Four thousand two hundreds sixty eight, (c) Seven thousand three hundreds seventy three, (d) Eight thousand four hundred five, (e) Nine thousand twenty seven. 2. (a) 2322, (b) 3056, (c) 4509, (d) 7230, (e) 1692, (f) 9009. - 3\. (a) 7651, (b) 6934, (c) 3562. 4. (a) 2367, (b) 9456, (c) 3758. Exercise-3--------------------------------------------------------- - 1\. (a) 2, 7,1,9, (b) 3, 8,2, 6, (c) 5,0, 7,2, (d) 7,4,0, 3, (e) 9, 6,2,0. - 2\. (a) 3000 + 700 + 30 + 9, (b) 7000 + 300 + 6, (c) 5000 + 70 + 2, (d) 4000 + 900 + 60, (e) 6000 + 300 + 20 + 1, (f) 8000 + 70 + 6. 3. (a) 5672, (b) 3906, (c) 8082, (d) 7006, (e) 2601. Exercise-R--------------------------------------------------------- Thousands Hundreds Tens Ones 3816 3000 800 10 6 7634 7000 600 30 4 609 600 0 9 8058 8000 0 50 8 2\. 4\. 342 = 40, 76 = 6, 4792 =90, 469 = 60, 289 = 9, 7645 = 600, 5632 = 5000, 3912 = 3000, 6782 = 700. 3. 72 = 70, 679 = 70, 8637 = 7, 5788 = 700,4070 = 70, 2700 = 700. 6564 6564 t t 5\. 6000 Place value of 6 = 6000 7464 60 Place value of 6 = 60 7464 400 Get Set Go With Sum Up Mathematics-3 4 ![](Sum Up Math-3_files/Sum20Up20Math-3-449.jpg) Place value of 4 = 4. Place value of 4 = 400 Difference: 400 \- 4 = 396 396 6\. 4312. 7\. 4060. 8\. c 9\. Do it yourself. Exercise-5--------------------------------------------------------- 1\. (a) =, (b) <, (c) <, (d) >, (e) <, (f) >, (g) <, (h) <, (i) <, (j) =, (k) =, (I) >, (m) <, (n) =, (o) A block is less houses, (p) Boys are more in number. Exercise-6--------------------------------------------------------- 1\. (a) 625, (b) 615, (c) 9782. 2. (a) 196, (b) 596, (c) 3412. - 3\. (a) 95, 565, 965,1561,1865, (b) 681,795, 805,1645, (c) 981,1206,1565, 2100, 3289. - 4\. (a) 1362,926,427,157, (b) 1751,1201,981,351, (c) 5525,4321,3789,1234. - 5\. (a) Ascending order, (b) Ascending order, (c) Ascending order, (d) Descending order. - 6\. (a) 566, (b) 2452, (c) 1957. 7. (a) 747, (b) 3241, (c) 4545. - 8\. Smaller-56, Greater = 65. - 9\. (a) Smallest number = 235, Greatest number = 532. - (b) Smallest number = 167, Greatest number = 761. - 10\. Smallest number = 2348, Greatest number = 8432. - 11\. (a) Smallest number = 30, Greatest number = 93. - (b) Smallest number = 45, Greatest number = 75. - 12\. (a) Smallest number = 245, Greatest number = 542. - (b) Smallest number = 347, Greatest number = 743. - 13\. (a) Smallest number = 1346, Greatest number = 6431. - (b) Smallest number = 2678, Greatest number = 8762. Mental Drills. - 1\. (a) 4235, (b) 307, (c) 100, (d) 5637, (e) Predecessor, (f)4267, (g) Ascending order. - 2\. (a) No, (b) Yes, (c) Yes, (d) Yes, (e) Yes. Exercise-7\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 683, (b) 867, (c) 786, (d) 8566, (e) 91 54, (f) 9977, (g) 6977, (h) 9797, (i) 8353, (j) 6879, (k) 8465, (I) 9859, (m) 6616, (n) 7799, (o) 8786, (p) 9668, (q) 7988, (r) 4997, (s) 6967, (t) 7978, (u) 8898, (v) 9989. - 2\. (a) 8987, (b) 6897, (c) 8969, (d) 7898. Exercise-8\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 14,1,4, (b) 12, 5, (c) 16,8,1,6, 8, (d) 16,1,6, (e) 5,1 7, 7, 6, 7, 7, (f) 16,8, 5,18, 7, 5,1,8, 7, 5. Exercise-9\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ ![](Sum Up Math-3_files/Sum20Up20Math-3-450.jpg) (a) 1420, (b) 773, (c) 1247, (d) 1425, (e) 1541, (f) 833, (g) 1243, (h) 1356, (i) 1280, (j) 1449, (k) 943, (1)845, (m) 1244, (n) 1440, (o) 1126, (p) 1203, (q) 1074, (r) 1241, (s) 968, (t) 1373, (u) 1345, (v) 834^ (w) 1 553, (x) 1283. - 2\. (a) 1000; sum = One thousand, (b) 1404; sum = One thousand four hundred four, (c) 1 722; Sum = One thousand seven hundred twenty two. Exercise«)----------------------------------------------------- - 1\. (a) 724, (b) 845, (c) 1031, (d) 965. - 2\. (a) 844; Sum = Eight hundred forty four, (b) 1021; Sum = One thousand twenty one, (c) 811; Sum = Eight hundred eleven, (d) 916; Sum = Nine hundred sixteen. - 3\. (a) 689, (b) 622, (c) 712, (d) 776, (e) 643, (f) 920, (g) 805, (h) 832, (i) 423, (j) 830, (k) 830, (I) 651, (m) 720, (n)894, (o) 741. Exercise-11\_\_\_\_\_\_\_\_ — 1\. Total fruits = 477. 2\. Total beads = 427. 3\. Total bricks = 5377. 4\. Total marbles = 633. 5\. Total people = 8337. 6\. Total oil = 9235. 7\. Total things 957. 8\. Total seeds = 1237. 9\. Total litres of milk = 901. 10\. Total items = 656 11\. Total 560 items. 12\. Total numberofcoins = 563. Exercise-12-------------------------------------------------------- - 1\. (a) 265, (b) 387, (c) 738, (d) 595, (e) 295, (f) 314, (g) 989, (h) 578, 625, (i) 707, (j) 41 3, 818. Mental Drills. - 1\. (a) 20, 92, (b) 80, 318, (c) 68,243. - 2\. (a) True, (b) True, (c) False, (d) False, (e) False, (f) True, (g) True. Exercise-13---------------------------------------------------------- - 1\. (a) 222, (b) 333, (c) 434, (d) 441 3, (e) 4554, (f) 2445, (g) 3323, (h) 3224, (i) 1 31 3, (j) 5652, (k) 5533, - (I) 2655, (m) 7161, (n) 2411, (o) 4222. - 2\. (a) 6163, (b) 4433, (c) 2252, (d) 4111, (e) 3264. - 3\. (a) 4 6 8 9 (b) 9 7 5 3 - \- 2 3 5 4 - 6 2 4 1 2 3 3 5 3 5 1 2 Exercise-M----------------------------------------------------- - 1\. (a) 14, (b) 3, (c) 52, (d) 4, (e) 3, (f) 10, (g) 10,14. Exercise-15\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 14, 2, 5, (b) 13, 5. - 2\. (a) 218, (b) 31 7, (c) 225, (d) 507, (e) 305, (f) 237, (g) 223, (h) 338, (i) 236, (j) 482, (k) 182, (I) 261, (m) 254, (n) 261, (o) 181, (p) 352, (q) 219, (r) 225, (s) 304, (t) 1 75. - 3\. (a) 4 7 1 (b) 5 5 5 (c) 7 5 3 -233 -391 -549 238 164 204 ![](Sum Up Math-3_files/Sum20Up20Math-3-451.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-452.jpg)- 4\. (a) 178, (b) 218, (c) 307, (d) 47, (e) 324, (f) 118, (g) 164, (h) 386, (i) 106, (j) 279, (k) 478, (I) 160, (m) 258, (n) 169, (o) 401, (p) 275, (q) 490, (r) 256, (s) 149, (t) 225. Exercise-16\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1\. 168. 2\. 118\. 3\. 49\. 4\. 190\. 5\. 27 6\. 267\. 7\. 162. 8\. 179\. 9\. 178\. 10\. 267\. 11\. 469 12\. 1357\. 13\. 416. 14\. 188\. 15\. 144\. Exercise-17 \---------------------------------------------------------------■ 1\. 7. 2\. 20\. 3\. 6\. 4\. 12\. 5\. 8 6\. 7\. 7\. 52. 8\. 19\. 9\. 47\. 10\. 35\. Exercise-18\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. Do it yourself. 2. Do it yourself. - 3\. (a) 410, (b) 579, (c) 516, (d) 634, (e) 592, (f) 446, (g) 434, (h) 283, (i)446, (j) 288. Mental Drills. - 1\. (a) 32, (b) 30, (c) 22, (d) 97, (e) 33, (f) 41, (g) 25, (h) 333, (i) 47, (j) 856, (k) 68, (I) 4363, (m) 109, (n) 2265,(0) 105, (p) 2489. - 2\. (a) 463, (b) 675, (c) 530, (d) 325, (e) 200. Exercise-19\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 888, (b) 626, (c) 369, (d) 996, (e) 6884, (f) 6639, (g) 4840, (h) 9396, (i) 9999, (j) 5055, (k) 8206, (I) 9690, (m) 8088, (n) 6660, (o) 7070, (p) 9999, (q) 8080. Exercise-20\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (i) 75, (ii) 75, (iii) 70, (iv) 42, (v) 80, (vi) 117, (vii) 119, (viii) 74, (ix) 132, (x) 135, (xi) 154, (xii) 125, (xiii) 90, (xiv) 156, (xv) 111, (xvi) 201, (xvii) 240, (xviii) 284, (xix) 320, (xx) 304, (xxi) 190, (xxii) 198, (xxiii) 231, (xxiv) 285, (xxv) 116, (xxvi) 207, (xxvii) 198, (xxviii) 1 57, (xxix) 294, (xxx) 1 71. Exercise-21\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 537, (b) 732, (c) 468, (d) 1316, (e) 840, (f) 678, (g) 2405, (h) 1314, (i) 2149, (j) 864, (k) 2496, (I) 3025, (m) 1029, (n) 756, (o) 2625, (p) 2507. Exercise-22\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 3128, (b) 1644, (c) 3024, (d) 2548, (e) 2370, (f) 1881, (g) 3072, (h) 1 782, (i) 4039, (j) 576, (k) 342, (1)5360. Exercise-23\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1\. (a) 5400, (b) 3800, (c) 4000, (d) 2950, (e) 6700, (f) 6000, (g) 1460, (h) 7800, (i) 8000, (j) 5650, (k) 9500, (I) 9000. ![](Sum Up Math-3_files/Sum20Up20Math-3-453.jpg)![](Sum Up Math-3_files/Sum20Up20Math-3-454.jpg) Exercise-îH--------- - 1\. (a) 3 0, (b) 3 00, (c) 3 000. - 4\. (a) 5 6, (b) 5 60, (c) 5 600. - 7\. (a) 7200, (b) 7500, (c) 8400. 9\. 360. - 2\. (a) 66, (b) 660, (c) 6600. 3. (a) 60, (b) 600, (c) 6000. - 5\. (a) 600, (b) 1200, (c) 2000. 6. (a) 900, (b) 1600, (c) 2500. - 8\. (a) 7200, (b) 21000, (c) 67200. 10\. 1800. Exercise-25 - [1. (a) 4 8 (b) 3 7 (c)6 8](#bookmark673) [x 1 2 x25x36](#bookmark674) [96“ 1 8 54 0 8](#bookmark675) [480 7402040](#bookmark676) - 2\. (a) 825, (b) 1521, (c) 233, (d) 3505, (e) 2541, (f) 4042, (g) 1 911, (h) 1 624, (i) 3364, (j) 4056, (k) 8955, (I) 8058, (m) 6210, (n) 6856, (o) 6487, (p) 9937, (q) 10256, (r) 3576. Exercise-26 1\. (a) 27, (b) 45, (c) 78, (d) 58, (e) 75, (f) 18, (g) 36, (h) 49, (i) 345, (j) 0. Exercise-27-------------------------------------------------------- 1\. 564\. 2. 1392. 3. 1608. 4. 7110. 5. 7168. 6. 13224. 7\. 2124\. 8. 9600. 9. 3312. 10. 6048. 11. 2592 12. 10710. 13\. 1440\. 14. 864. 15. 624. Mental Drills. 1\. (a) 5, (b) 5, (c) 8, (d) 4, 64, (e) 30,150, (f) 700. 2. 21. 3. 96. 4. 70. 5\. 39 x 2,26 x 3,13 x 6, 9 x 8, 8 x 9, 72 x 1. 6. (a) 40, (b) 56, (c) 64, (d) 800, (e) 86, (f) 11 76, (g)151,(h)0. 7. 1170. 8. 3 60. 9. 68 5. 10.0. Exercise-28-------------------------------------------------------- 1\. (a)3,(b)4. 2. (a)5,(b)4,(c)5,(d)3. - 3\. (a) (21 - 3 = 7; dividend = 21, Divisor = 3, Quotient = 7) , (b) (32 -s- 4 = 8; dividend = 32, Divisor = 4, Quotient = 8), (b) (45 h- 5 = 9; dividend = 45, Divisor = 5, Quotient = 9). - 4\. (a) 35 - 7 = 5 and 35 - 5 = 7, (b) 64 - 8 = 8, (c) 654 - 9 = 6 and 54 - 6 = 9. - 5\. (a) 7 x 8 = 36, (b) 9 x 9 = 81, (c) 13 x 1 =13. - 6\. (a) 8, (b) 9, (c) 9, (d) 63, (e) 64, (f) 27. Exercise-29\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 7, (b) 1, (c) 0, (d) 1, (e) 0, (f) 1, (g) 9, (h) 36, (i) 1. Exercise-30-------------------------------------------------------- (a) 20, (b) 12, (c) 44, (d) 32, (e) 21, (f) 102, (g) 120, (h) 112, (i) 174, (j) 145, (k) 123, (I) 127, (m) 148, (n) 1 37, (o) 11 5, (p) 1 784, (q) 1 564, (r) 1 326, (s) 1 342, (t) 1161. ![](Sum Up Math-3_files/Sum20Up20Math-3-455.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-456.jpg) Exercise-31 - (a) 63, (b) 66, (c) 77, (d) 62, (e) 99, (f) 96, (g) 72, (h) 92, (i) 329, (j) 564, (k) 565, (I) 333, (m) 836, (n) 349, (o) 987. Exercise-32\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) Q = 248; R = 1, (b) Q = 89; R = 2, (c) Q = 77; R = 1, (d) Q = 127; R = 2, (e) Q = 75; R = 1, (f) Q = 42; R = 5, (g) Q = 76; R = 3, (h) Q = 88; R = 7, (i) Q = 1 758; R = 1, (j) Q = 896; R = 1, (k) Q = 929; R = 4, (I) Q = 957; R = 2, (m) Q = 872; R = 2, (n) Q = 855; R = 2, (o) Q = 884; R = 2, (p)Q = 746; R = 3. - 2\. (a) Quotient = 56; Remainder = 1 ; Dividend (225) = Divisor (4) x Quotient (56) + Remainder (1 ); 225 = 224 + 1 = 225. - (b) Quotient = 65; Remainder = 2; 327 = 5 x 65 + 2 = 325 + 2 = 327. - (c) Quotient = 44 7; Remainder = 3; 3 5 79 = 8 x 44 7 + 3 = 3 5 76 + 3 = 3 5 79. - (d) Quotient = 685; Remainder = 2; 4797 = 7 x 685 + 2 = 4795 + 2 = 4797. - 3\. (a) Quotient = 7; Remainder = 4, (b) Quotient = 32; Remainder = 0, - (c) Quotient = 88; Remainder = 5, (d) Quotient = 543; Remainder = 2. 4. 3. Exercise-33\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1\. 63. 2. 62\. 79\. 3\. 8. 11\. 73. 4\. 12\. 322\. 96\. 5\. 13\. 53\. 9\. 6\. 34\. 7\. 255\. 8\. 121\. 9\. 85. 10. Exercise-34 1\. 9. 2. 5\. 3\. 55. 4\. 90\. 5\. 45\. 6\. 77\. 7\. 14\. 8\. 73\. 9\. 48. 10. 12\. 11\. 41. 12\. 108\. 13\. 675\. 14\. 19\. 15\. 308\. 16\. 2625\. 17\. 74. 18. 122\. 19\. 23. 20\. 13\. 21\. 66\. 22\. 32\. 23\. 65\. 24\. 60 25\. 42. 26. 68. Answer the questions. 1\. ? 6408. 27\. 100. 2\. ? 393. 28\. 459. 29\. 3\. 3\. ? 396. 30\. 40\. 4\. 64 kg. Mental Drills. - 1\. (a) 25, (b) 13, (c) 45, (d) 119, (e) 345, (f) 1, (g) 0, (h) 1, (i) 1, (j) 90, (k) 130, (I) 65, (m) 81, (n) 29. - 2\. (a) Dividend = 36, Divisor = 6 and Quotient = 6. - (b) Dividend = 72, Divisor = 9 and Quotient = 8. Exercise-35 ![](Sum Up Math-3_files/Sum20Up20Math-3-457.jpg) 2\. 4\. 6\. ![](Sum Up Math-3_files/Sum20Up20Math-3-458.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-459.jpg)9\. (a) There are 2 one-halves in a whole, (b) There are 3 one-thirds in a whole, (c) There are 4 one-thirds in a whole. - 10\. (i). (c), (ii). (e), (iii). (a), (iv). (b), (v). (d). Exercise-36-------------------------------------------------------- - 1\. (a) Four, (b) Two, (c) Two. 2. (a) Eight, (b) Four, (c) Four. 3. (a) Six, (b) Three, (c) Three. ![](Sum Up Math-3_files/Sum20Up20Math-3-460.jpg)2 3 3 4 6\. (a)^-,(b)^-,(c)^-,(d)^. Exercise-37\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ [? R"7](#bookmark677) - 1\. (a) Nine, (b) Four, (c) Five. 2. (a) Two-=-, (b) Five-—, (c) Five-—, (d) Seven-—. [5 6 89](#bookmark678) [4 2 21](#bookmark679) - 3\. Four-g-,Two-g-,Two-^-, One—. 4. Do ityourself. Exercise-38-------------------------------------------------------- - 1\. (a) 4-, (b) 4-, (c)^, (dÆ (e) (0 77 • 2. (a) 5, (b) 0, (c) 7, (d) 11, (e) 15, (f) 2, (g) 1 7, (h) 13. - 3\. (a) 7, (b) 11, (c) 5, (d) 15, (e) 13, (f) 7, (g) 19, (h) 21. 4. (a) ^ (b)^-, (c)^-, (d)^, (e) A. 5\. 9. 6. 26. 7. 11. 8. 8. 9. 14. Exercise-39-------------------------------------------------------- - 1\. (a) Five hundred sixty five rupees, (b) Seventy five rupees, (c) Sixty five paise. - 2\. (a) 34.15, (b) 7.18, (c) 0.75. 3. (a) Seventeen rupees and nineteen paise, (b) Four rupees and seven paise, (c) Zero rupees and Seventy paise. Exercise-RO\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1\. (a) 700, (b) 8200, (c) 825, (d) 1980, (e) 7804, (f) 9019, (g) 9465, (h) 7. Exercise-Rl-------------------------------------------------------- 1\. (a) 8, (b) 13, (c) 7.38, (d) 8.20, (e) 13.18, (f) 84.05, (g) 40.05, (h) 7.07. Exercise-RZ-------------------------------------------------------- - 1\. (a) 67 51 p, (b)85 94 p, (c) 70 (h) 79 03 p. - 2\. 95 89 p. 3. 50 84 p. - 7\. 92 79 p. 8. 70 80 p. 25 p, (d) 76 16 p, (e) 78 82 p, (f) 28 03 p, (g) 59 1 5 p, - 4\. 91 52 p. 5. 93 58 p. 6. 99 79 p. - 9\. Total cost 105.25. Exercise-43-------------------------- ![](Sum Up Math-3_files/Sum20Up20Math-3-461.jpg) - 1\. (a) 9 42p,(b)16 42p,(c)44 67p,(d)31 82 p. Get Set Go With Sum Up Mathematics-3 ![](Sum Up Math-3_files/Sum20Up20Math-3-462.jpg)2\. ? 12.50. 6\. ? 51.50. 3\. ? 15.62. 4\. ?21.12. 5. ?23.22. 7\. ?8.65. 8\. ?14.15. 9\. ?9.25. Exercise-1«\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) ? 70, (b) ? 6.75, (c) ? 21.80, (d) ? 6885, (e) ? 60.60, (f) ? 47.25. - 2\. ? 90.00 3. ?91.80 4. ? 108.50. 5. ? 141.75. 6. ? 69.75. - 7\. (i)(a)? 109.55, (b)? 100.15, (c)? 99.40. (ii) (a)? 207.50, (b)? 247.55. (iü) (a) ? 4.60, (b) ? 24.10. (iv) (a) ? 23.85, (b) ? 16.35. Exercise-MS\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 9, (b) 6, (c) 0.16, (d) 25, (e) 55, (f) 16, (g) 5.05, (h) 26.25. - 2\. ? 533.30. 3. ? 22.30. 4. ? 25.00. 5. ? 35.60. Exercise-Hô\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 800, (b) 1 500, (c) 5, 100, 30, 500, 30, 530, (d) 8, 100, 4, 800, 4, 804, (e) 16 80, (f) 2775, (g) 7049, (h) 1330. 2. (a) 5000, (b) 1545 m, (c) 8066, (d) 900 m. 3. Do ityourself. Exercise-H7\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1\. (a) 6cm + 0cm = 6 m, (b) 6 m + 0cm = 6 m. 2. (a) 6 m 7cm, (b) 1 7m 7cm, (c) 54 m 90cm. - 3\. (a) 6000m + 540m = 6km + 540m, (b)8000m + 16m = 8km + 16m. - 4\. (a) 1 km 430 m, (b) 5 km 604 m, (c) 7 km 58 m. Exercise-\*«\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ Do ityourself. Exercise-\*« - 1\. (a) 82 m 94 cm, (b) 94 m 63 cm, (c) 53 m 71 cm, (d) 43 m 73 cm, (e) 99 m 78 cm, (f) 88 m 24 cm, (g) 8 m 981 cm, (h) 8 m 801 cm, (i) 8 m 443 cm. 2. (a) 73 m 26 cm, (b) 85 m 75 cm, - (c) 7 km 261 cm. 3. 8 m 90 cm. 4. 25 m 56 cm. 5. 5 km 92 m. Exercise-50\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 25 m 31 cm, (b) 32 m 78 cm, (c) 33 m 49 cm, (d) 14 m 80 cm, (e) 21 m 82 cm, (f) 28 m 64 cm, (g) 3 km 282 m, (h) 5 km 678 m, (i) 4 km 565 m. 2. (a) 7 m 51 cm, (b) 3 km 333 m. 3\. 26 m 27cm. 4. 24 m 25 cm. 5. 5 km 258 m. Exercise-51-------------------------------------------------------- - 1\. (a) two, (b) two, one, one, (c) ten, (d) five, (e) 5, (f) one. - 2\. (a) 3000 g, (b) 5000 g, (c) 8000 g, (d) 2425 g, (e) 4570 g, (f) 7010 g, (g) 6045 g, (h) 5005 g. - 3\. (a) 5 kg, (b) 3 kg 400 g, (c) 6 kg 789 g, (d) 2 kg 509 g, (e) 3 kg 67 g, (f) 7 kg 7 g. Exercise-52\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 5 kg 768 g, (b) 5 kg 734 g, (c) 8 kg 556 g, (d) 8 kg 157g, (e) 9 kg 782 g, (f) 8 kg 767g. ![](Sum Up Math-3_files/Sum20Up20Math-3-463.jpg) - 2\. (a) 4 kg 573 g, (b) 8 kg 878 g, (c) 9 kg45 g, (d) 12 kg 25 g, (e) 14 kg 10 g. - 3\. 5 kg 45 g. - 4\. 5 kg 670 g. - 5\. Make brother is heavier by 3 kg 548 g. - 6\. Suman bought more vegetable by 3 kg485 g. - 7\. Sunita has 880 grams fruits more than Anita. Exercise-53\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 500, (b) 1,1,3,1, (c) 10, (d) 10, (e) 4, (f) 1,2, (g) 2, (h) 5. - 2\. (a) 7000 ml, (b) 500 ml, (c) 2156 ml, (d) 1035 ml, (e) 6010 ml. - 3\. (a) 3 1, (b) 41583 ml, (c) 61 500 ml, (d) 1 1640 ml, (e) 4150 ml, (f) 219 ml, (g) 516 ml, (h) 71508 ml. Exercise-54\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 71139 ml, (b) 81978 ml, (c) 81794 ml, (d) 81111 ml, (e) 91874 ml, (f) 71403 ml. - 2\. (a) 51104 ml, (b) 71389 ml, (c) 81870 ml. - 3\. 51625 ml. 4. 81865 ml. 5. 71750 ml. Exercise-55\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 3 1326 ml, (b) 41613 ml, (c) 61322 ml, (d) 41008 ml, (e) 31436 ml, (f) 1 1558 ml. - 2\. (a) 51211 ml, (b) 31442 ml, (c) 3 1500 ml, (d) 21475 ml. - 3\. 81725 ml. 4. 21205 ml. 5. 41475 ml. Exercise-56\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (b) 6 O'clock, 6:00, (c) 9 O'clock, 9:00. - 2\. (a)Z?p\\ (b)Z!p\\ (c) /fT\\ 3. (a) 7 O'clock, (b) 5 O'clock, (c) 8 O'clock. Exercise-57-------------------------------------------------------- - 1\. (a) Half past eight; 8:30 o'clock, (b) Half past nine; 9:30 o'clock, (c) quarter past six; 6:15 o'clock, (d) Quarter past ten; 10:15 o'clock, (e) Quarter to one; 6:45 o'clock, (f) Quarter to three; 2:45 o'clock. - 2\. (i)(d), (ii)(b), (iii)(a), (iv)(c). Exercise-58-------------------------------------------------------- - 1\. (a) 40 minutes past 3; 3:40 o'clock, (b) 20 minutes past 8; 8:25 o'clock, (c) 35 minutes past 3; 3:35 o'clock, (d) 5 minutes past 5; 5:05 o'clock, (e) 50 minutes past 4; 4:50 o'clock. - 2\. (a) (b) Zir\\ (c) 3. (i) (e), (ii) (c), (iii) (d), (iv) (b), (v) (a). 4\. 7:10,12:10. Exercise-59\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ Do ityourself. Exercise-60\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1\. (a) Friday, (b) Saturday, (c) Sunday, (d) 7, (e) 24, (f) February, (g) 4 months, (h) Juanry, (i) August, (j) Do ityourself, (k) Do ityourself, (I) Do ityourself. 2\. (a) 12,(b)31,(c)4,(d)30. - 3\. Do ityourself. - 4\. (a) 300 minuets, (b) 48 months, (c) 28 days, (d) 730 days, (e) 180 days. ![](Sum Up Math-3_files/Sum20Up20Math-3-464.jpg) ![](Sum Up Math-3_files/Sum20Up20Math-3-465.jpg)Exercise-61\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ 1\. (a) 6, (b) 3, (c) 4, (d) 4. ^’ /\\ O ^’ (b) 3, (c) 4, (d) No sides, (e) 2. - 4\. Do ityourself. ■■ 5. Do ityourself. 6. Do ityourself. - 7\. (a)(iv),(b)(iii),(c)(ii),(d)(i). 8. (a) 3,3, (b) 4,4, (c) 4,4, (d) 0,0. Exercise-62-------------------------------------------------------- - 1\. 5. 2. 8. 3. 1. 4. 1. 5. 2. 6. 0. 7. 8. - 8\. Doityourself. 9. Doityourself. 10. Doityourself. Exercise-63-------------------------------------------------------- - 1\. (a), (e), (h). 2. Do ityourself. Exercise-64\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. (a) 19, (b) 75, (c) 15, (d) 91, (e) ::, (f) A, (g) , (h) $$oo, (0 ® ■ Exercise-65\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_ - 1\. 76,312,387. 2. 75,319,387. 3. (a) 68, Even, (b) 53, Odd, (c) 106, Even, (d) 75, Odd. - 4\. (a) T, (b) F, (c) T. Exercise-66-------------------------------------------------------- - 1\. (a) 5, (b) 10, (c) 6, (d) 3. 2. (a) 8, (b) 10, (c) 7, (d) 4. 3. Do ityourself. - 4\. Do ityourself. 5. (a) 5, (b) 3, (c) 6, (d) 5 + 8 + 10 + 4 + 9 = 36. 6\. (a) 5, (b) 9, (c) 10, (d) 7, (e) 6. ![](Sum Up Math-3_files/Sum20Up20Math-3-466.jpg)Get Set Go With Sum Up Mathematics-3