---
title: "Sum Up Math 5"
book: "xxxxx"
category: "MA"
publisher: "Ratan Prakashan Mandir Pvt. Ltd."
type: "Educational Material"
---
MRP: ' 470
BRANCHES
ISBN: 978-93-7899-395-4
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. Jublee Inter College, Baxipur, Gorakhpur. Ph.: 0551-2337178, Mob. : 9719004925,9451686798
: 504, M. G. Road, Opp Kothari Market, Indore.
Ph.: 0731-2432479, Mob. : 9827233199, 9719004951
: 1632, Chordia Bhawan, Sonthliwalon Ka Rasta, Choura Rasta, Jaipur.
Mob. : 9783358000, 9719004930
: Tilak Hall Lane, Meston Road, Kanpur. Mob.: 9336106323
: 129-A, Mukta Ram Babu Street, Kolkata. Ph. : 033-22193306, Mob. : 9830466360
: Indira Market, Opp. Mahila College, Aminabad, Lucknow.
Mob. : 9719004924, 9450422840
: Shop No.2, Sunil Complex, Western Kutchery Road, Meerut. Ph.: 0121-2641622, Mob. : 9719004929
: Plot No. 124, D-2, Bhagyodaya C.H.S. Ltd. Swami Vivekanand Nagar, Nr Vasant Vihar Club, Pokhran Road No. 2, Thane (West), Mumbai. Ph. 022-21730175, Mob. : 9930537375
: Shop No. GS-22, Shyam Palace, Opp. Shivaji Science College, Congress Nagar, Nagpur. Ph.: 0712-2452361, Mob. : 9822086148, 9823385600
: D-159, Sector-7, Near Vasundhara Enclave Check Post, Noida.
Ph.: 0120-4541101,02, Mob.: 9891179480
: Chunni Lal Market, BM Dass Road, Patna.
Ph.: 0612-6456562, Mob. : 9931568925
© All rights reserved with publishers. Revised Edition
Printed by:
Ravi Offset Printers & Publishers (P) Ltd.
5/169/1, Lata Kunj, Agra-Mathura Road, Agra-282002. Ph. : 0562-2650100, 2650109
Typeset & Illustrated at : Typeface
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
## (K
'^C.O.UTEUTS
S. No. Chapters
Number & Number Names
Addition & Subtraction
5
20
- [3. Multiplication & Division](#bookmark2)
- [4. Factors & Multiples](#bookmark3)
- [5. Common Fractions](#bookmark4)
6\. Decimals 77
7\.
Money
96
8\.
Measurement of Length
105
9\.
Measurement of Weight
117
10\.
Measurement of Capacity
123
11\.
Measurement of Time
130
12\.
Geometry
142
13\.
Area & Volume
162
14\.
Perspective View & Net of a 3d-Object
174
15\.
Pattern
181
16\.
Data Handling
190
Get Ready for Examination
202
Put on Your Thinking Cap
211
Formative Assessment 1 to 5
213
Answers
218
Numbexs and hiumkR Niâmes
You already know about 5-digit numbers. Now you are going to learn about 6-digit and 7-digit numbers and their number names.
###### Patterns of Numbers
4 digit number 5 digitnumber 6digitnumber 7 digitnumber
###### Smallest
1000
10000
100000
1000000
###### Greatest
9999
99999
999999
9999999
In this pattern you can also see the following:
When 1 is added to the greatest 4 digit number, you get the smallest 5 digit number.
9999 + 1 = 10000
Similarly, when 1 is added to the greatest 5 digit number you get the smallest 6 digit number.
99999 + 1 = 100000
The number name for 100000 is one lakh.
Similarly, when 1 is added to the greatest 6 digit number you get the smallest 7 digit number.
999999 + 1 = 1000000
The number name for 1000000 is ten lakh.
Now look at the fol lowing pattern
10001
100001
Ten thousand + one
One lakh + one
1000001 = Ten lakh + one
The number name for 100001 is one lakh one.
There are 1 lakh, 0 thousands, 0 hundreds, 0 tens and 1 ones in this number.
The number name for 1000001 is ten lakh one.
There are 10 lakhs, 0 thousands, 0 hundred 0 tens and 1 ones in this numbers.
The greatest 7 digit number 9999999 has 99 lakhs, 99 thousands, 9 hundreds, 9 tens and 9 ones.
The number name for 9999999 is ninety nine lakh ninety nine thousand nine hundred
nine nine.
(Note: lakh is also written as lac)
Example 1:
Write the successor of each ofthese numbers:
(a) 5675432 (b) 400000
(c) 234678 (d) 399999
Solution:
A number coming just after a number is successor of the number.
(a) 5675433 (b) 400001
(c) 234679 (d) 400000
A number coming just before a number is # predecessor of the number.
- ###### Example 2:
Write the predecessor of each ofthese numbers:
- (a) 78426 (b) 30956 (c) 799999 (d) 100000
Solution:
(a) 78425 (b) 30955 (c) 799998 (d) 99999
Example3:
Counting by thousands, write next three numbers starting from 753192.
Solution:
The numbers are— 753192, 754192, 755192 and 756192.
- Example 4:
Write the numbers between 463415 and 463419; in ascending order.
Solution:
The numbers are—463416,46341 7 and 463418.
##### {J. EXERCISE 1 ^--------------
- 1\. Write the successor of each of these numbers :
- (a) 815067 (b) 708919 (c) 299999
- 2\. Write the predecessor of each of these numbers: (a) 815906 (b) 3000000 (c) 265196
- 3\. Counting by tens, write four numbers starting from 213506.
- 4\. Counting by hundreds, write next three numbers, starting from 30521 7.
Counting by lakhs, write next three numbers, starting from 276819.
Write in ascending order, numbers between : (a) 708605 and 708609 (b) 223116 and 223120
Write the smallest number of 6 digits.
Write the greatest number of 7 digits.
Write a number greater than 56427 and 56429.
###### Representation of Numbers on Spike Abacus
We are learning about 6 digit and 7 digit numbers, so we need an abacus with 7 spikes. For example 431287 and 3215674 can be shown on the spike as follows:
Writing of Numbers in Figures and Words
- I. By using spike abacus
Example:
Write the numbers given on each spike abacus in figure and words.
(a)
(b)
###### Solution :
- (a) There are 3 lakhs, 6 ten-thousands, 4 thousands, 8 hundreds, 5 tens and 7 ones in this number. It is written as 364857 in figures. It is written as three lakh sixty four thousand eight hundred fifty seven in words.
- (b) There are three ten lakhs, one lakh, four ten thousands, two thousands, zero hundreds, 7 tens and zero ones. It is written as 3142070 in figures. It is written as thirty in lakh forty two thousand seventy in words.
- ###### II. By using place value table
Following example shows how to use the place value table.
Example:
###### Solution:
- (a) There are 3 lakhs, 5 ten thousands, 8 thousands 6 hundreds, 0 tens and 2 ones in this number. It is written as 358602 in figure. It is written as three lakh fifty eight thousand six hundred two in words.
- (b) There are 7 ten lakhs, 2 lakhs, 9 ten thousands, 5 thousands, 4 hundreds, 3 tens and 1 ones in this number. It is written as 7295431 in figures. It is written as seventy two lakh ninety five thousand four hundred thirty one in words.
Reading Numbers
- © The number is divided into periods starting from right.
- © The first period has three digits. It is called the units period.
- © Next period hastwodigits. It is called the thousands period.
- © Next period also has two digits. It is called the lakhs period.
- © Periods are separated by comma.
Example:
Read and write the number names of these numbers:
(a) 413040
Solution:
(b) 328562 (c) 7310205 (d) 4000210
(a)
(b)
4,13,040 = Four lakh thirteen thousand forty.
3,28,562 = Three lakh twenty eight thousand five hundred sixty two.
73,10,205 = Seventy three lakh ten thousand two hundred five.
40,00,210 = Forty lakh two hundred ten.
###### Example:
Write these numbers in figures:
- (a) Five lakh fourthousand three hundred two.
- (b) Thirty five lakh sixty seven thousand three hundred nineteen.
c
(75
—1
IZ>
C n5 tn
O
■^
C
c
in
O
H
</>
C
ZZ5
I
t/>
o
Number
(a)
5
0
4
3
0
2
504302
(b)
3
5
6
7
3
1
9
3567319
###### Example:
How many numbers are there with 6 digits.
Solution:
Greatest 6-digit number = 999999
Greatest 5-digit number = 99999
Numberof 6-digit numbers = 900000
##### U EXERCISE 2^---------
- 1\. Read these numbers from spike abacus and write them in figures and words.
(a)
(b)
- 2\. Read these numbers from table and write them in figures and words.
Lakhs
Thousands
Units
T-L
L
T-Th
Th
H
T
O
(a)
2
6
5
2
0
1
(b)
8
7
6
2
7
8
9
- 3\. Read these numbers and write their number names.
(a) 521310 (b) 206301 (c) 3280371 (d) 3901014
- 4\. Write the following numbers in figures:
- (a) Seven lakh eighteen thousand six hundred twelve.
- (b) Eight lakh seventy three thousand four hundred fifty seven.
- (c) Twenty six lakh sixty thousand nineteen.
- (d) Thirty nine lakh fifty four thousand two hundred sixty eight.
- 5\. Make the number which has :
- (a) 5 lakhs, 7 ten thousands, 2 thousands, 4 hundreds, 5 tens and 3 ones.
- (b) 42 lakhs, 2 ten thousands, 3 thousands, 3 hundreds, 6 tens and 2 ones.
- (c) 7 ten lakhs, 2 lakhs, 5 ten thousands, 4 thousands, 2 hundreds, 8 tens and 4 ones
- 6\. There are 53801 7 potatoes, 302509 onions and 73892 oranges in a shop. Write these numbers in words.
- 7\. Write in figures :
- (a) The population of Buland Shahar is twelve lakh sixty two thousand four hundred twenty five.
- (b) There are five lakh thirty four thousand six hundred seventy three females in Buland Shahar.
- 8\. Look at the patterns and write next three numbers:
(a) 625419,635419,645419 (b) 325679,335679,345679
- 9\. How many numbers are there with :
- (a) 5 digits (a) 7digits
###### Place Value and Expanded Form
We can use place value chart to find the place value of a digit.
Example:
Find the place value of 3 in these numbers. Use place value chart for this.
(a) 630526 (b) 5300614 (c) 3085296
Solution:
Numbers
Lakhs
Thousands
Units
T-L
L
T-Th
Th
H
T
O
630526
6
3
0
5
2
6
5300614
5
3
0
0
6
1
4
3085296
3
0
8
5
2
9
6
(a) Place value of 3 is 3 ten thousands or 30000.
(b) Place value of 3 is 3 lakhs or 300000.
(c) Place val ue of 3 is 3 ten lakhs or 3000000.
###### Example:
Write these numbers in expanded form and find the place value ofthe digit 5 in words and in figures.
- (a) 757942 (b) 6506702
Solution:
- (a) 75 7942 = 700000 + 50000 + 7000 + 900 + 40 + 2
.•. Place val ue of 5 is fifty thousand or 50,000.
- (b) 6506702 = 6000000 + 500000 + 6000 + 700 + 2
.•. Place value of 5 isfive lakh or 5,00,000
Example:
Find theplacevalueofthedigitsgiven in boxes:
- (a) 2 3 2569 (b) 2 43679
Solution:
- (a) The place value of 3 is 30000 (b) The place value of 2 is 200000
Example:
Write these numbers in short form:
- (a) 700000 + 60000 + 2000 + 300 + 50 + 6
- (b) 8000000 + 600000 + 30000 + 4000 + 700 + 80 + 9
Solution:
- (a) 7,62,356 (b) 86,34,789
##### ^. EXERCISE 3 ■/--------------
- 1\. Write these numbers in the place value chart and find the place value of digit 6 in each case:
- (a) 563 7920 (b) 6074280 (c) 260034 (d) 8652693
- 2\. Find the place value of 5 in 35201 59 in figuresand words.
Write these numbers in expanded form :
(a) 760354 (b) 304800 (c) 8720076 (d) 505965
Write these numbers in expanded form and find the place value of the digit 7 in each
case :
- (a) 720651 (b) 7055320 (c) 475406 (d) 7030520
Find the place value of digits in boxes:
- (a) 42 3 5601 (b) 7 2 8952 (c) 8 69541
Find the digits in the required place in these numbers:
- (a) Ten lakhs place in 8509073 (b) Lakhs place in 2597860
Write these numbers in short form:
- (a) 600000 + 80000 + 6000 + 400 + 80 + 6
- (b) 7000000 + 400000 + 70000 + 3000 + 600 + 90 + 2
- (c) 9000000 + 200000 + 10000 + 6000 + 400 + 20 + 6
###### Order Relation
If two numbers have different numbers of digits then the number with greater less numberof digits isgreaterthan the number with less numberof digits.
Examples:
52 > 9; 684 > 46; 3000 > 876;
32456 > 4256; 120456 > 20456
If two numbers have the same number of digits then we start comparing the digit from leftmost position.
Example:
Which is greater: 342786 or 256876.
Solution:
342 786 has 6 digits.
256876 has 6 digits.
Compare the digits at the leftmost positions.
Thedigiton the leftmost position in 342 786 is 3.
The digit on the leftmost position in 2 5 68 76 is 2.
- 3 > 2
###### Example:
Which is greaterof 7865321 and 7864321 ?
Solution:
7865321 has 7digits.
7864321 has 7digits.
Thedigiton the leftmost position in 7865321 is 7.
Thedigitonthe leftmost position in 7864321 is 7.
.•. Let us compare the next digit. Thedigitnextto 7 in 7865321 is8. The digit nextto 7 in 7864321 is 8. But8 = 8.
.-. Let us compare the next digit. Thedigitnextto8 in 7865321 is6. The digit nextto 8 in 7864321 is 6. But 6 = 6.
.-. Let us compare the next digit. Thedigitnextto6 in 7865321 is5. The digit nextto 6 in 7864321 is4. 7 5 > 4
/. 7865321 > 7864321
Example:
Arrange the given numbers in ascending order:
188596, 723800, 62752, 500232
Solution:
62752 is the smallest number. The next number greater than 62752 is 188596. After that 500232 and 723800 are greater in the same order.
.-. Numbers arranged in ascending order are:
62752,188596,500232, 723800
Example:
Arrange the given numbers in descending order:
501316, 6280031,502316, 5362298
Solution:
Numbers arranged in descending order are : 6280031,5362298,502316, 501316
Get Set Go With Sum Up Mathematics-5
###### Formation of Greatest and Smallest Numbers
You know howto make greatest and smallest numbers of 5-digits. Same rule is used in making greatest and smallest numbers of 6-digitsand 7-digits.
- (a) Repetition of digits not allowed
Example:
Make greatest and smallest number of 6-digits using the digits 2, 1,7, 0, 6 and 9 only once.
Solution:
To make greatest number:
Keep the greatest digit on the leftmost place.
Followwith othernumbers in descending order.
.•. The greatest 6-digit number is 976210
To make smallest number:
Keep the smal lest digit (but not zero) at the leftmost place.
Followwith zero.
Followwith othernumbers in ascending order.
.-. The smallest 6-digit number is 102679.
- (b) Repetition of digit is allowed
Example:
Write greatest and smallest 6-digits number by usingthe digits 1,9Z 6, Oand 3.
Solution:
To make greatest number:
Repeat the greatest digit at the leftmost place.
Followwith othernumbers in descending order.
.•. Greatest 6-digit number is 996310
Write the smallest number.
Keep the smal lest digit (but not zero) at the leftmost place.
Follow by repeating zeroes.
Follow by othernumbers in ascending order.
.-. Smallest 6-digits number is 100369
1\. Compare these numbersand put > or < inboxes:
(a)
250795
98854
(b)
54004
592003
(c)
708607 \_
\_ 697060
(d)
237605 \_
\_ 245605
(e)
787878 \_
\_ 788778
(f)
5009730 \_
\_ 5069370
##### ^. EXERCISE M
- 2\. Find the smallest and the greatest numbers from the following:
- (a) 523723,52315,640195,800201
- (b) 9121512,2191512,99999,999999
- 3\. Arrange these numbers in ascending order:
- (a) 534198,852002,799651,300902
- (b) 204019,229725,540020,307578
- (c) 2195738, 2095738, 2345958,2459958
- 4\. Arrange these numbers in descending order:
- (a) 7885923, 7785923, 7985923, 7685923
- (b) 521365,512365,532365,562365
- (c) 259625,289625,279625,229625
- 5\. Write the smallest and greatest numbers using each of these digits only once: (a) 2, 3,4, 5,0,8 (b) 0,1,4, 6, 7, 9
- 6\. By using 0, 3, 5, 7 and 9 make the greatest and smallest 6-digit number.
- 7\. By usingO, 1,5, 7 and 9 make the greatest and smallest 7-digit number.
###### International System of Writing Numbers in Words
In international system each period is made of three digits.
1, 000, 000
Units
Thousands
Millions
UNITS
International System
Indian System
Ones
Tens Hundreds
Ones
Tens Hundreds
THOUSAND
Thousands Ten thousands Hundred thousands
Thousands Ten-thousands Lakhs
Millions
Ten Lakhs
While writing a number in international system, periods are separated by putting commas (,) afterevery three digit.
Example:
Write in words, in international system :
- (a) 403129 (b) 3490956
Solution:
- (a) 403129 = 403,129
= Four hundred three thousand one hundred twenty nine.
- (b) 3490956 = 3,490,956
= Three million four hundred ninety thousand nine hundred fifty six.
Example:
Write in figures
Five million three hundred twenty six thousand five hundred twenty three.
Solution:
Millions
Thousands
Units
The number is 5,326,523
##### EXERCISES“/----
- 1\. Write these numbers in words (International System): (a) 3025708 (b) 8805610
(c) 513507
(f) 5040203
(d) 800700 (e) 2030790
- 2\. Write these numbers in figures :
- (a) Three million five hundred thirty thousand two hundred fifty six.
- (b) Six hundred seventy five thousand four hundred.
- (c) Eight million three hundred sixty two.
- (d) One million one hundred five thousand two hundred forty two.
- (e) Seven million five thousand twenty four.
- (f) Nine million seven hundred twenty four thousand nine.
###### Roman Numerals
You read that there are seven basic Roman numerals as given below: I V X L C D and M.
These basic Roman numerals stands for fol lowing Arabic numbers:
Roman Numerals
\_\_\_\_\_\_\_ArabicNumbers\_\_\_\_\_\_I
The compounding of Roman numerals shows the other Arabic numbers.
To show the Arabic numbers by compounding the Roman Symbol are given below-(a) X when written to the left of L or C, it is subtracted from the numeral.
Example:
XL^ 50-10 = 40
XC^100-10 = 90
- (b) I is when written to the left of V, it is subtracted from the numeral.
Example:
IV^5-1 =4
- (c) X when written to the right of L or C, it is added to that numeral.
Example:
LX ^50 + 10 =60
LXX ^ 50+10 + 10 = 70
LXXX -+50+10 + 10+10 = 80
[CX ^100 + 10=110](#bookmark49)
[CXX -+ 100 + 10 + 10= 120](#bookmark50)
[CXXX -+ 100 + 10 + 10 + 10 =130](#bookmark51)
- (d) I is written tothe right of adigitto add 1.
Example:
VI -+5 + 1=6
[VII -+ 5 + 2 =7](#bookmark52)
[VIII -+ 5 + 3 =8](#bookmark53)
[XI -+ 10 + 1 =11](#bookmark54)
Example 1:
Write the following numbers in Roman Numerals:
(a) 20
Solution :
(b) 45 (c) 49 (d) 97 (e) 89
(a) 20 =
10+10 (b) 45 = 40 + 5
X + X = XL + V
XX = XLV
(c) 49 =
40 + 9 (d) 97 = 90 + 7
XL + IX = XC + VII
XLIX = XCVII
(e) 89 =
80 + 9 LXXX + IX LXXXIX
Example 2 :
Write following in Hindu-Arabic numerals :
(a) XXV
Solution :
(b) XLII (c) XXXVII (d) LXXV (e) XCVII I
(a) XXV
= X + X + V (b) XLII = XL + I + I
= 10 + 10 + 5 =40+1+1
=25 =42
- (c) XXXVII = X + X + X + V + l + l V
= 10+10 + 10 + 5 + 1+1 10 + 5
= 37
- (e) XCVIII = XC + VIII
= 90 + V + I + I + I
##### EXERCISE 6 f
= 50 + 10 +
= 75
1\.
Write the following in Roman numerals :
(d) 49
(e)
(j)
37
91
(a) 41
(f) 61
(b) 52 (c)
(g) 95 (h)
59
81
(i)
79
2t
Write the following in Hindu-Arabic numerals :
(a) XXXIX (b) XLIV (c) XCVI (d)
DL
(
e)
DXLV
3\.
(f) LVI
Compare th
(a) XXV
(c) XL
(e) XC
(g
5 foil
) LXV (h) owing using <, LI LX CX
CXLV
> or =
(i) LXXIX in the box :
(b) XL
(d) XXXVI
—
D
IVXXX
4\. Write the equivalent Roman Numerals in the box:
(a)
D -X =
(b)
C + X =
(c)
XV + XV =
\_\_\_\_\_ (d)
L + L =
(e)
XLV + LXV =
Addition
You have already learnt the addition of 4 and 5 digit numbers in previous class.
In this class you will learn the addition of 6 and 7 digit numbers.
- Example 1:
Add 7532531 and 6345232 and write the number sentence.
Solution:
Write the numbers in column form and then add.
- ###### Example 2:
Add 9787395 and 7695738 and write the sum in words.
Sum = One crore seventy four lakh eighty three thousand one hundred thirty three.
Addents- Addents are the numbers, which are to be added in a sum of addition.
##### EXERCISE 7 ^--------------
Add:
- 2\. Find the sum of the fol lowing and write their sum in words-
(a) (c) (e)
2378932 + 3598997
3256789 + 9873289 + 32567
3567 + 765321 + 5698921
(b) 325698 + 896329
(d) 3289789 + 9878 + 7891011
###### Word Problems on Addition
Example 1:
Amit purchased 32759 mangoes, Rahul purchased 932568 mangoes. How many total mangoes were purchased bythem? Write the solution in sentence.
Solution:
Mangoes purchased by Amit = 3 2 7 5 9
Mangoes purchased by Rahul = +932568
.•. Total Mangoes purchased by them = 965 32 7
Solution Sentence
The total number mangoes purchased bythem are 965327.
or
The total 965327 mangoes are purchased bythem.
- Example 2:
There are 2 73215 houses in Nebsarai and 40736 houses in Lajpatnagar. Calculate the total numbers of houses in Nebsarai and Lajpatnagar.
Get Set Go With Sum Up Mathematics-5 Vbf
Solution:
No. of houses in Nebsarai = 2 7 3 2 1 5
Numberof houses in Lajpatnagar = + 40736
Total no. of houses = 3 1 395 1
Solution Sentence
There are total 313951 houses in Nebsarai and Lajpatnagar.
(g. EXERCISE 8^--------------
Write the solution sentences for al I questions given below:
- 1\. There were 421 796 monkeys and 756792 bears in Ram's army. Find the total numbers of animals in hisarmy.
- 2\. There were 859621 banana trees and 1269587 guava trees in Ashok Vatika in Sri Lanka. Calculate the total number oftrees in Ashok Vatika.
- 3\. 473521 persons visited the Ramlila Maidan, situated in New Delhi, on the eve of 1st day of Durga Puja. On second day 2356789 persons visited the Ramlila Maidan. On third day 532673 persons visited there. How many persons visited the RamlilaMaidan?
- 4\. Your mathematics book have 250 pages. There are 34369 pages in English to Hindi Dictionary. Calculate the numbers of total pages in both the books.
- 5\. There were 1324987 soldiers in Kaurav's army. There were 789423 soldiers in Pandav's army. How many soldiers were in both the army?
- 6\. During the Ram Ravan war, Sugreeveate 5629321 fruits, Angad ate 963215 fruit and Ravan ate 9999999 fruits on first day of war. Find the total number of fruits ate by them in the first day of the war.
Subtraction
You have already learnt the subtraction of 4 and 5 digits in previous class. In this class you will learn the subtraction of 6 and 7digits.
- Example 1:
Subtract 3267156 from 879321 7 and check your answer.
[T-L L T-Th Th H TO](#bookmark64)
[8 7 9 3 2 17](#bookmark65)
[3 2 6 7 1 56](#bookmark66)
[5 5 2 6 0 61](#bookmark67)
Checking-
[3 2 6 7 1 56](#bookmark68)
[+ 5 5 2 6 0 61](#bookmark69)
[8 7 9 3 2 17](#bookmark70)
In a subtraction the bigger digit is known as "Minuend" and smaller digit is known as "Subtrahend".
- Example 2:
Find the difference between 9876254 and 4598762. Write the number sentence and answer in words.
Solution:
Write the digit which is greater on the top, and then subtract
[T-L L T-Th Th H TO](#bookmark71)
[16 15 1115](#bookmark72)
[9 8 7 6 2 54](#bookmark73)
-4598762
[5 2 7 7 4 92](#bookmark74)
The number sentences: 9876254-4598762 = 5277492
Answer in words - Fifty two lakh seventy seven thousand four hundred ninety two.
EXERCISE 9 f
9 0 0 0 0 0
6 8 5 2 3 6
(f) 5 2 1 0 9 8 1
j - 4 9 3 0 1 5 6
(g) 6 5 2 1 5 9 3
-4983294
(h) 8 9 3 2 1 0 5
i - 3 786284
Find the difference-
(a) 9276159-365321
(c) 7594321 -6439520
(b) 9516729-1235631
(d) 234957-139498
- 3\. Find the difference between 659321 7 and 4639521. Check the answer.
- 4\. Look the pattern of difference and write next two terms:
(a) 1023,102 7,1031, ,
(b) 520,517,514,
###### Word Problems on Subtraction
Example 1:
The sum oftwo numbers is 6593214. If one number is 593214, find the other number. Solution:
Sum oftwo numbers = 65 932 1 4
One of the number = - 5 932 1 4
The other number = 6000000
.•. Second number = 6000000
- Example 2:
There were 9523594 students in a university. 525595 got admission in other university and 2532596 students passed out. How many students were left in the university?
Solution:
Numberof student got admission in other University = 52 5 595
No. of students passed out = +2532596
Total = 30581 91
No. of total students in University = 952 3 5 94
No. ofstudentscomingout of University = -30581 91
Numberofstudents left = 6465403
Therefore, total numberof students left in the University = 64 6 540 3
##### (|. EXERCISE 10 ^-------------
- 1\. There were 8753275 monkeys in the state of Kiskindha. 2932569 went out in the search of Maa Sita. How many monkeys were left in Kishkindha?
- 2\. A factory produced 242569 bicycles in 1st years. In second it produced 394254 bicycles. Find the increase in production of bicycles.
- 3\. Numbers of soldiers in Pandava's army was 3426754 less than soldier's in Kauravs army. If numbers of soldiers in Kaurav's army was 7526982 then calculate the total numbersoldiers in Pandav's Army.
- 4\. There were 6927689 guavas in a tree. Gardener plucked 232597 guavas on Monday and 3269789 guavas on Tuesday. Calculate the number of guavas left in the tree.
- 5\. What should be added to the 289706, sothatthesum will become 8950278?
- 6\. The population of a city is 7690354 and the number of females are 3690543, what is the number of males in that city?
- 7\. The population of a city is 5768934 and the number of males are 3786531, then calculate the numberoffemales.
- 8\. The servicing of engine of an aeroplane was due after flying 5278321 km. After flying of 4219784 km. How much kilometers is left for servicing?
- 9\. Rekha wanted to buy a home. The cost of home is ? 4755695. She had ? 3527635 in hand. How much bank loan is required by herto buy home?
- 10\. There are 275206 children, 3762635 males and 3167520 females in a city. Calculate total population ofthat very city.
###### Estimating the Sum and the Difference
You have learnt the method of estimating the sum to the nearest thousands and ten thousands in previous class. In this class you will learn the estimating of sum to the nearest lakh place. For rounding a number, we will consider the number at ten thousand place. If it is 5 or more we will move up, otherwise we will move down.
###### For example-
440000
430000
420000
410000
400000
500000
490000
480000
470000
460000
450000
- (a) 456920 will be rounded upto 500000.
- (b) 63 962 5 will be rounded down to 600000.
- (c) 780259 will be rounded upto 800000.
Rule - In general for rounding, we consider the number at the right side of required number. If the number at the right side of required number is equal to 5 or more, then the required number is increased by 1 and all numbers to the right side of it becomes zero.
If number at the right side of the required number is less than five, the required number is decreased by 1 and all numbers to the right side of it become zero.
Example 1:
Find the actual and estimated sum of 450915 and 325698 to the nearest lakh.
Solution:
Actual Sum
Estimated sum
450915
500000
\+ 325698
+300000
776613
800000
Example 2:
Find the actual and estimated difference between 876252 and 553027 to the nearest lakh.
Solution:
Actual difference
Estimated difference
876252
900000
-553027
-600000
323225
300000
###### Story Writing or Framing Award Problem
In this section you will write a story for given number sentences. Some examples are given below:
Number sentence 253089 + 680539 = ?
You can write any one of the following story-
- (a) What is the sum of 253089 and 680539?
or
- (b) Anil bought 253089 mangoes and Rakesh bought 680539 mangoes. What is the number of total mangoes they bought?
or
- (c) A shopkeeper sold 253089 metres of cloth on Monday and 680539 metres of cloth on Tuesday. How much metres of cloth did he sold in there two days?
Similarly, you can write any one of the stories for the number sentence 693025 -486538 = ?
- (a) Calculate the difference between 693025 and 486538.
or
- (b) Rakesh has 693025 bags of cement. He sold 486538 bags out of them. He many bags of cement are left with him?
or
- (c) Ankit sold 486538 metres of cloth. It he had total 693025 metres of cloth. How many metres of cloth left in hisshop?
##### (J. EXERCISE 11 ■/--------------
1\. Frame word problem (or write a story) foreach ofthe number sentence :
(a)
(c)
2700000 + 292952 = ? (b) 53420 + 242035 = ?
35625 + 279555 = ? (d) 399279 + 352532 = ?
(e)
397299-256 = ? (f) 9935625-4529729 = ?
(g)
52635-225 = ? (h) 2259543-1673109 = ?
- 2\. Ina factory 354369 bags of cement produced in the month of January and it produced 679 more bags of cement in February. In March because of some problem it produced 9735 bags less than that produced in January. Calculate the total number bags it produced in three months.
- 3\. Find the smallest and greatest numbers which are rounded near to the nearest lakh as 60,00,000.
In this chapter you will learnt more about multiplication and division.
###### Multiplication
Some important properties of multiplication are given below.
- ###### 1. The product of two numbers does not change if the order of numbers is changed.
Example:
15x12 = 180 and
12x15 = 180
Therefore, 15x12 = 12x15
Similarly, 210 x 315 = 315 x 210 72 8 x 12 5 = 12 5 x 72 8 6351 x 12 = 12 x 6351
- ###### 2. The product of three numbers does not change if the grouping of numbers is changed.
Examples: (14 x 17) x 22 = 14 x (1 7 x 22) = (14 x 22) x 1 7 (235 x 1 7) x 95 = 235 x (1 7 x 95) = (235 x 95) x 1 7
- ###### 3. If any number is multiplied by 1, the product will be always the number it self, or
The product of number and 1 is the number itself, e.g., 271 x 1 = 271 2755 x 1 = 2755 4925 x 1 = 4925 344151 x 1 = 344151
- ###### 4. If any number is multiplied by 0, the product will always be 0.
Now see the products of a number tens, hundreds or thousands.
12 x 10
= 120
375 x 10
= 3750
4756 x 30
= 142680
19 x 100
= 1900
19 x 400
= 7600
Similarly, on the same pattern-product of a number when number is multiplied by thousands:
47 x 1000 = 47000
475 x 2000
= 950000
6755 x 5000
= 33775000
- ###### Example 1:
Multiply 6751 by 53
Solution:
675 1
x 53
20253 —Multiplication of 6751 by 3.
3 3 7550 —Multiplication of 6751 by 50 357803
In this problem
Multiplication of 6751 by3 + Multiplication of 6751 by 50 = Product
- Example 2:
Multiply 8422 by 705 and write the number sentence.
Solution:
8422
x 705
42110
00000 -You can avoid multiplication by zero. 5895400
593 75 1 0 '
Number sentence = 8422 x 705 = 593 7510
###### txample3:
Multiply 315 by 4569 and write the product in words.
Solution:
4569 = 4000 + 500 + 60 + 9
/. 315 x 4569 = 315(4000 + 500 + 60 + 9)
= 315 x 4000 + 315 x 500 + 315 x 60 + 315 x9
= 1260000 + 157500 + 18900 + 2835
= 1439235
It can be done I ike th is
53 1
x 4 5 6 9 2835 —531 x 9
1 8900 —531 x 60
1 5 7 5 0 0 —531 x 500
1260000 — 531 x 4000
U3 9 2 3T- 531 x 4569
Product- Fourteen lakh thirty nine thousand two hundred thirty five.
##### U- EXERCISE 12“/-------------
1\. Multiply thefollowingovally:
(a) 5647 x 10
(b)
(e)
24 x 100
(c) 4215x100
8521 x 1000
(d) 79 x 1000
795 x 1000
(f)
2\.
Multiply: Usingthe method as given in the example: (a) 5697 x 24 (b) 9723 x 75
(c)
69211 x 632
(d) 79231 x 410
(e)
15692 x 412
(f)
6962 x 305
(g) 3421 x 326
(h)
421 x 3545
(i)
124 x 5453
(j) 54551 x 412
(k)
3595 x 4520
(I)
4523 x 415
3
(m) 47510 x 630
Find the answer orally: (a) 23515 x0
(n)
(b)
3200 x 4500
345565 x 1
(c)
45225 x 10
(d) 25325 x 0 x 235
(e)
12635 x 1
(f)
253432 x 100 x
Word Problems on Multiplication
- Example 1:
There are 3526 boxes of biscuit in a wholesale shop. Each box has 85 biscuits. Find the total number biscuits.
Solution :
The total numberof biscuits will be calculated by multiplying 3526 by 85 therefore-
[3 5 26](#bookmark105)
x 8 5
[1 7 6 30](#bookmark106)
[2 8 2 0 80](#bookmark107)
[2 9 9 7 10](#bookmark108)
Total numberof biscuits = 299710
- Example 2:
If the cost of one bag of wheat is ^ 915, find the cost of 2627 such bags.
Solution:
Total cost of wheat bags will be calculated by the multiplication of total number of bags by cost of one bag.
Therefore-
[2 6 27](#bookmark109)
[x 9 15](#bookmark110)
[13 13 5 2 6 2 70](#bookmark111)
[2 3 6 4 3 00](#bookmark112)
[2 4 0 3 7 05](#bookmark113)
Total cost of 2627 bags of wheat is? 2403705.00
- Example 3:
Find the product of 835 x 45 x 19
Solution:
Firstmultiply 835 by 45
Then multiply the product by 19.
Soz
###### Product:
Seven lakh thirteen thousand nine hundred twenty five.
[3 7 5 75](#bookmark116)
x 1 9
[3 3 8 1 75](#bookmark117)
[3 7 5 7 50](#bookmark118)
[7 1 3 9 25](#bookmark119)
U- EXERCISE 13 ^------------
- 1\. There are 215 pens in one box. How many pens will be there in 4351 such boxes?
- 2\. 5791 students read in one college. How many students can read in such 212 colleges?
- 3\. Kumbhakarn used to eat 1200 quintals of grains in one day. How many quintals of grain did he ate in 365 days?
- 4\. A milkman sells 3716 litres of milk in one week. How many litres of milk will he sell in 52 weeks?
- 5\. A bag of cement weighs 102 kg. In a godown there are 6365 such bags of cement. Find the total weight of cement in that store.
- 6\. The price of a book is? 375. Calculate the cost of 72511 books.
- 7\. What will be the total weight of 9752 cartons of medicine of one carton of medicine weighs 721 kg?
- 8\. Rina paid ? 3,20,000 for purchasing suits. She bought 7321 such suits. If the price of one suit is ? 105, then how much she has to pay more?
- 9\. A cement factory can produce 7342 bags in one day. In 295 days how many bags of cement can be produced?
- 10\. Find the product and write them in words-
- (a) 87 x 372 x 540 (b) 045 x 273 x 871
(c) 342 x 2 x 0 (d) 3751 x 1 x 1 x 1 x 1
- (e) 49452 x 1 x 0 x 932500
- 11\. 375 visitors go everyday to visit a museum. How many visitors will visit the museum in one year?
- 12\. Replace \* with correct number—
8 3\*018 x 2 \*
4\*55\*90 16\*2\*360 2 0 7 \*\* 4 5 0
7 3\*198 x 1 \* 7 5\*113\*6 7\*01 \*80 7\*01 \*800
###### Division
In this class you will learn the division of a number by a 3-digit or 4-digit number. Before doing this, first of all go through the following important properties of division-
1\. When a number is divided by itself, the quotient will be always 1.
Examples:
72 - 72 = 1
235 -235 =1 5-5=1
75 94 - 75 94 = 1
6002 - 6002 = 1
2\. The quotient will be always number itself, if any number is divided by 1.
Examples:
49-1 =49
5-1 =5
235 - 1 = 235 7542 - 1 = 7542
3\. When 0 will be divided by any number, the quotient will be always 0. e.g.
Examples:
0-5=0
0-42 =0
0 - 245 =0
0 - 9125 = 0
###### Divisor x Quotient + Remainder = Dividend
In adivision sum:
Divisor
Quotient
— Dividend 5
Dividend
or
65
— = 13 <
Quotient
Remainder
4
1
Divisor
###### Division by a Two Digit Number
Example 1:
Divide 793259 by 25. Find quotient and remainder.
Solution:
yr25) 7 9 3 2 5 9 (3173 <---Quotient
Divisor 7 5
4 3 Dividend
2 5
1 8 2
1 7 5
7 5
7 5
Remainder----► 9
Check-Divisor x Quotient + Remainder = Dividend
Note: The remainder at every step would be less than divisor.
###### Division by three Digit Number
Example 2:
Divide 47219059 by 582 and find the quotient and remainder.
Solution:
Explanation
As you can see that divisor consists of three digit. Therefore, we consider the number formed by three digits on the extreme left side of the divident.
The three digit number formed on the extreme left side of the divident is 472.
But472 is less than thedivisor582.
So we will take the number consisting of four digits on the extreme left of the dividend.
- i .e. 4721. We will divide th is four digit number 4721 by 582 first of al I. Now,
582 x 8 = 4656
and 582 x 9 = 5238
Here
4656 < 4721 and 5238 > 4721
Step-1 So we multiply 582 by 8
Write 8 at the place of Quotient and write 4656 just below the 4721 and subtract 4656 from 4721. By this way you will get65.
116 4
2 3 5
Step-2 Now bringdown the nextdigit '9' that is placed right after4th digit '1'.
And multiply 582, which is divisor by 1.
Step-3 Write '1' atthe place of quotient. Put this just right after 1.
Step-4 Write 582 x 1 = 582 just below the 659 and subtract 582 from 659.
You will get remainder 77.
Remember remainder must be less than divisor at every step.
Step-5 Again bringdown the next digit "0". By this way you get '770' to be divided by 582.
Step-6 Again multiply divisor "582' by 1 and write it just below the 770. Now subtract 582 from 770. Write 1 as quotient just right after 1.
Step-7 You will get 188 as remainder.
Now bringdown the nextdigit '5'.
Step-8 You have now "1885" to be divided by 582.
Multiply 582 by 3
You will get 1 746.
Subtract this 1746 from "1885" and.
You get the "139" as remainder.
Write "3" just right-after the "1" in the quotient.
Step-9 Bringdown the lastdigit "9".
Now you have" 1399" to be divided by "582".
Multiply 582 by 2.
i.e. 582 x 2 = 1164
Write "1164" just below the 1399.
Subtract 116 from 1399. You will get "235" as remainder.
So, in this sum
Quotient = 81132
Remainder = 235
##### ^. EXERCISE 14 ^------------
- 1\. Divideandfindthequotientand remainder:
(a) 2975309 by 27
(d) 8952043 by 352
(g) 5239804 by 621
1112
(b) 530997 by 75
(e) 95263948 by 712
(h) 39804325 by 3415
(c) 3895204 by 112
(f) 2032904 by 725
(i) 95280213 by
- 2\. Divide and check the answer:
- (a) 325694 by 78 (b) 496523 by 285
- (c) Find the dividend, if the divisor is 247, quotient is 11256 and remainder is 31.
- (d) Divide the greatest number of 7-digit by the greatest numberof 3 digits.
###### Word Problems on Division
Example 1:
If a company manufactures 333610 pens in 365 days. How many pens are manufactured in one day? Write the number sentence.
Solution: 365) 3 3 3 6 1 0 (914
To calculate the no. of pens manufactured in one 3 2 8 5
[day-divide the total number pens given by number of days.^](#bookmark135)
[Therefore 914 pens are manufactured in one day.3 6 5](#bookmark136)
NumberSentence = 333610 -^ 365 = 914 1 4 6 0
Example 2: 14 6 0
[If the cost of one mobile phone is](#bookmark137)
? 1225. Then how many mobiles will be 1225) 6 2 7 2 0 0 (512
purchased in? 62 7200? 6 12 5
Solution: 14 7 0
To find the number of mobiles that can 12 2 5
be purchased in ?627200 divide it by the . , c n
/ 4 j U cost of one mobile. „ . r „
2 4 6 (J
Solution sentence- ---q—
512 mobiles can be purchased in? 62 7200.
EXERCISE 15 ^-------------
- 1\. A shopkeeper collected ? 770048 by selling 1504 bags of cement. Find the cost of one bag of cement.
- 2\. If there are 255 rows in a stadium and a total of 31875 persons can be seated in stadium. How many persons can be seated in one row?
- 3\. If a shopkeeper bought 675 watches for ? 7,56,000. How much did he pay for one watch?
- 4\. For a relief fund ? 95,43,500 collected by the students of a school. If 125 students were involved in collection. Find the amount collected by each student.
- 5\. If 3 3,75,000 litres of water can be kept in 112 5 water tanks. Find the capacity of each
tank.
- 6\. A packet of thread rolls contain 124650 metres of thread. If a roll has 225 metres of thread. How many thread rolls arethere in the packet?
- 7\. If a company collected ? 4499 7000 from its share holders. The value of each share is ? 2120. How many shares were issued?
- 8\. In a book store each almirah has the capacity to hold 165 books. There are 52800 books in the store. Find the number of almirah in that store.
34,02,000 apples are packed equally in 1620 boxes. Find the number of apples in one box.
The cost of production of one bicycles is ? 995. A company spent ? 2089500 in one year on the pro duotion of bicycles. How many bicycles were produce in one year?
The production cost of one computer set is ? 8215. If a company spent? 1,72,51,500. Find the number of computer sets produced.
- 12\. If one number is 628 and the product of two numbers is 1082672. Find the other number.
- 13\. The total sale of bal I pens of a stationary store for the month of March, Apri I, May and June was ? 3,91,864. What is the sale of one day?
- 14\. A fruit seller bought 4,62,705 mangoes. If 205 mangoes were found rotten and the remaining were packed in 925 baskets, find the number of bananas in one basket.
17\*6\*1 1\*05
7 1 \*
6 8 2
3 4 1
\* \* \*
0
###### Word Problems on Four Fundamental Operations
Example:
In a stadium, there are 3,29,625 persons accomadated in 293 rows. If each row has the same number of accomodation, how many personscan be accomodated in 215 rows?
Solution: \_\_\_\_\_\_\_\_\_\_\_\_\_
- 293\) 3 2 9 6 2 5 0 125
- 2 9 3
- 3 6 6
2 9 3
7 3 2
5 8 6
14 6 5
14 6 5 0
Herethequotient is 1125
Numberof persons in 1 row = 1,125
Numberof persons in 215 rows = 1,125 x 215 = 2,41,875 Detail steps of multiplication
There are 31992 candies in 258 jars. Each jar contains the same number of candies.
How many candies are there in 125 jars?
Solution:
258\) 3 1 9 9 2 024
2 5 8
6 1 9
5 1 6
10 3 2
10 3 2
0
Here quotient = 124
Numberofcandies in 1 jar = 124
Numberofcandies in 125 jars = 124 x 125 = 15,500
Detail steps of multiplication
[1 24](#bookmark141)
[x 1 25](#bookmark142)
[6 20](#bookmark143)
[2 4 8x](#bookmark144)
[1 2 4 xx](#bookmark145)
[1 5 5 00](#bookmark146)
\--
##### \[#. EXERCISE 16“/--------------
- 1\. The total turnout of voters in three constituencies was 9,44,000. If the voter turnout was 2,64,500 and 4,32,500 in two constituencies respectively, what is the voter turnout in the third constituency?
- 2\. Hero motorcycles produced 87,54,326 bikes during a period of 5 years. If the production of bikes for the initial four years was 9,32,872 (1st year), 10,12,375 (2nd year), 12,42,256 (3rd year) and 18,30,200 (4th year) respectively; find the production of bikes in the fifty year.
- 3\. 4,32,912 lemons are packed in 348 cartons. How many lemons can be paked in 425 cartons?
- 4\. A factory makes 57,03,125 safety pins in 365 days. How many safety pins are produced in the month of November?
- 5\. How much milk there will be in 213 tank, if 652 milk tankers can hold 782400 litres of milk?
- 6\. A factory produced 8,67,151 ball pen and 2,18,574 fountain pens. A worker mixed the pens and packed them in 692 boxes. How many pens did the worker pack in one box if 669 pens left unpacked?
- 7\. A shopkeeper sold all his 523 bags of rice at? 1120 each. From his money he bought 280 bags of musterd. Find the price of each bag of musterd.
- 8\. Find thegreates 7 digit number which can be exactly divisible by 526.
###### Estimating the Product and the Quotient
You have already learnt the rounding off a number to a certain place. In this section you will learn to estimate the product of some numbers and the quotient for a division sum.
- Example 1:
Find the actual and estimated product of 3471 x 398.
Solution: Actual Product
3 4 7 1
x 3 9 8
2 7 7 6 8
3 1 2 3 9 x
1 0 4 1 3 x x
r @ 1 3 8 1 4 5 8
Estimated product
3 5 0 0
x 4 0 0
1 4 0 0 0 0 0\*
Get Set Go With Sum Up Mathematics-5
- ###### Example 2:
The cost ofabike is? 48920. Estimate the cost of9such bikes.
Solution:
Estimated cost of one bike = ? 50000
Estimated costof 9 such bikes = ? 4,50,000
- Example 3:
Estimate the quotient
(a) 16950 -310 (b) 47277 - 512
Solution:
- (a) 16950 - 310
Round the dividend and divisor to the nearest number.
Therefore,
17000 - 300 = 560 estimated
or, 570
- (b) 47277 - 52
In this sum also round the divisor and dividend to the nearest number.
Therefore,
50000 - 50
= 1000
- Example 4:
The cost of 82 7 bags of cement is ? 508605. Find the estimated cost of one bag of cement.
Solution:
To calculate the price of one bag you have to divide the total cost of bags by number of bags.
So, 508605 - 872
Now to calculate the estimated price round the dividend and divisor first of all. You will get
510000 - 800
= 637 (estimated)
Esti mated cost of one bag of cement = ? 63 7
##### B. EXERCISE 17
- 1\. Estimate the fol lowi ng product :
- (a) 7918 x 392 (b) 2125x210
(c) 6415 x 345 (d) 9892 x 410
- (e) If a train runs 689 km per day, estimate its distance in 30 days.
- (f) The costof a jeans is? 689. Estimate the cost Rahul has to spend in purchasing of 192 such jeans.
- (g) A shopkeeper sells? 792 mobiles per month. Estimate the number of mobiles he will sell in oneyear.
- 2\. Estimate the quotient
- (a) 15982 - 392 (b) 389720 - 1995
(c) 499682 - 48792 (d) 296725 - 14235
- 3\. Ifthepriceof 38 packets of apple is? 1 7,556. Estimate the cost of one packet of apple.
- 4\. Kamal purchased 2930 bags of cement, and he paid ? 57,57,450. Estimate the costof one bag of cement.
- 5\. Ramesh sells 18250 litres of milk in one month. Estimate his selling of milk per day.
Try to Solve the Following Questions-
- (a) The cost of 60 pens is? 1320. Find the cost of 115 pens.
- (b) It takes 5 minutes to polish a shoe. Calculate the time for polishing 321 shoes.
- (c) If the cost of 25 bags of rice is ? 15625 and every bags contains 625 kg of rice. Calculate the price of 1 kg of rice.
- (d) The length ofa piece of stick is 13 m 26 cm. What is the length of 324 such sticks?
you know?
An interesting fact
Observe these numbers carefully.
729,297 and 792
198,891 and 981
The digit sum of these numbers is 18.
Since 18 is divisible by 9 so these numbers are divisible by 9.
##### factors and (Multiples
You have learnt about the factors and multiples in previous class. Let us review thus again.
###### Factors
You know that 8 x 4 = 32
So, 8 and 4 are the factors of 32.
Similarly, 1 x 32 = 32
16x2= 32
So, 1,2,4,8 and 16 are also the factor of 32.
Is there any other factor of 32 ?
Ans. Yes, 32 is also a factor of 32.
So you can tel I-
- 1,2,4, 8,16 and 32 are the al I factors of 32.
Properties of Factors-
- (a) 1 dividesevery number exactly. So 1 is the smallest factor of every number.
- (b) Every number is factor of itself (other than zero) as a number divides itself exactly. The greatest factor of a number is the number itself.
- (c) A factor of a number must be less than or equal to the number.
- (d) Other than 1, every number has at least two factors.
- (e) Every non-zero number is a factor of zero.
Multiples
As you have seen i n the factors that
8 x 4 = 32
So 32 is multiple of8 and 4
- 8,16,24. .. are all the multiples of 8 because they are exactly divisible by 8.
Properties of Multiples-
(a)
(b)
(c)
(d)
Every number is a multiple of 1.
Every number is the smallest multiple of itself. And Every number is a multiple of itself.
Every multiple of a number is greater than or equal to that number.
We can find as many multiples of a number as we want.
###### Rules of Divisibility
Let us revise the rules of divisibility which you have already learnt in previous class.
- (a) A number that has 2 at its ones place will be always divisible by 2.
e.g.-2,12,22,32,42etc.
- (b) Anumberwill be always divisible by 2, ifthe digit at its ones place isdivisibleby 2. e.g. 4, 14,16,18, 24, 28 etc.
- (c) A number will be divisible by 5, if it's digit at ones place is either 0 or 5. e.g. 5,10,15,20, 25 etc.
- (d) If the sum of the digits of a number is divisible by 3, then the number will be divisible by 3.
Some example are given in the table:
Number
Sum of the digits
Whether sum is divisible by 3 or not
Whether number is divisible by 3 or not
12
1+2 = 3
Yes
Yes
13
1+3=4
No
No
15
1+5 = 6
Yes
Yes
21
2 + 1=3
Yes
Yes
965
9 + 6 + 5 = 20
No
No
123
1 + 2 + 3 = 6
Yes
Yes
249
2 + 4 + 9 = 15
Yes
Yes
- (e) If the sum of the digits of a number is divisible by 9, then the number will be divisible by 9. Some examples are given inthetable.
Number
Sum of the digits
Whether sum is divisible by 9 or not
Whether number is divisible by 9 or not
18
1+8 = 9
Yes
Yes
21
2 + 1=3
No
No
45
4 + 5 = 9
Yes
Yes
88056
8 + 8 + 0 + 5 + 6 = 27
Yes
Yes
94321
9 + 4 + 3 + 2 + 1 =19
No
No
99
9 + 9 = 18
Yes
Yes
- (f) If the last two digits at the extreme right of a number is divisible by 4, then the numberwill bedivisible by 4. Some examples are given below inthe table:
Number
Number formed by last two digits on the extreme right
Whether last two digits is divisible by 4 or not
Whether the number is divisible by 4
264
64
Yes
Yes
272
72
Yes
Yes
7928
28
Yes
Yes
2879
79
No
No
24
24
Yes
Yes
- 1\. Find all factors of:
- [(a) 32 (b) 8 (c) 19 (d) 45(e)](#bookmark160)
- 2\. Is 15 afactorof 945?
- 3\. Is 20 a factor of 3290?
- 4\. Findthefirst5 multiplesof:
- [(a) 2 (b) 9 (c) 16 (d) 15(e)](#bookmark161)
- 5\. Which of the following numbers are exactly divisible by 2?
- [(a) 15 (b) 12 (c) 17 (d) 22(e)](#bookmark162)
[(f) 108 (g) 215 (h) 412 (i) 214(j)](#bookmark163)
- 6\. Which of the following numbers are exactly divisibly by 3?
- [(a) 11 (b) 21 (c) 9 (d) 219(e)](#bookmark164)
- [(f) 12 (g) 121 (h) 294 (i) 689(j)](#bookmark165)
- 7\. Which ofthe following are exactly divisible by 4?
- [(a) 12 (b) 121 (c) 1212 (d) 476(e)](#bookmark166)
[(f) 278 (g) 19432 (h) 6954 (i) 69544(j)](#bookmark167)
- 8\. Which ofthe following are exactly divisible by 5?
- [(a) 10 (b) 125 (c) 1250 (d) 1251(e)](#bookmark168)
- [(f) 295 (g) 290 (h) 521 (i) 255(j)](#bookmark169)
95
21
98
421
129
795
674
764
1255
2550
- 9\. Which of the following numbers are exactly divisible by 9?
- (a) 295 (b) 592 (c) 595 (d) 585 (e) 855
(f) 701253 (g) 352107 (h) 2952 (i) 549 (j) 12564
- 10\. Is 14afactorof728?
- 11\. If a number is divisible by 5 and 9 both, then is itdivisible by 45 also?
- 12\. Is 7 a factor of 21 and 126? Is 7 also a factor of (21 + 126) and (126-21)?
###### Prime Numbers
You have already learnt that every number except 1, has at I east two factors i.e., 1 and number itself.
Thus, numbers greater than 1, which has only two factor are called Prime Numbers.
- (a) 2 is the smallest prime number.
- (b) 2 is only even prime number.
- (c) 2 and 5 are the only prime numbers, which end with 2 and 5.
- (d) All prime numbers, except 2, are odd.
- (e) All odd numbers are notaprime number.
###### Twin Primes
If the difference between two prime numbers is 2, then they are known as Twin Primes.
For example — 3 and 5; 5 and 7; 11 and 13; 1 7 and 19 etc.
Composite Numbers
Number which is greater than 2 and is not a prime number is called Composite Number.
For example — 4, 6,8,10,9,21 etc.
- (a) All even numbers greater than 2 are composite numbers.
- (b) All odd numbers, which are not prime, are composite numbers.
###### Prime Factors
Out of all factors of a number, the prime ones are known as Prime Factors.
For example —
Factors of 60 are
- 1,2,3,4, 5, 6,12,15,20, 30 and 60
Out of these factors, prime factors are 2, 3, 5
So prime factors of 60 = 2, 3, 5
Similarly,
Factors of 56 are :
1,2,4, 6, 7,8,14,28,56
.-. The prime factors of 56= 1,2,7
###### Prime Factorisation
All factors of 60 are
1,2, 3,4, 5, 6,12,15, 20, 30 and 60
Out of these prime factors = 1,2, 3, 5
So, Prime factorisation of 60 =2x2x3x5
Prime factors of 56 are 1,2 and 7
So, Prime factorisation of 56 = 2x2x2x7.
Example 1 :
Find the prime factorisation of 27.
Solution :
Step-1 Divide 27 by prime number.
Step-2 Divide the quotient by prime number again.
Step-3 Repeatthe processtill thequotient 1 isobtained.
3| 27
3 9
3
Prime factorisation of 27 = 3x3x3
Example 2 :
Find the prime factors of 215 and write the prime factorisation of 215.
Solution :
Factorisation of 215 = 5,43
Prime factors of 215 = 5,43
So, prime factorisation of 215 = 5 x 43
5 121 5
43
Example 3 :
Find the prime factors of 320. And write the prime factorisation of 320.
Solution :
Factorisation of 320 = 2x2x2x2x2x2x5
Prime factors of 320 = 2 and 5
Prime factorisation of 320 = 2x2x2x2x2x2x5
2
2
2
2
2
2
5
##### U^ EXERCISE 19^------------
- 1\. Which ofthe following are prime numbers? 2, 4, 6, 8, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19
- 2\. List all the prime numbers from 1 to 30.
- 3\. Find the greatest prime number among: (a) 1to20 (b) 5 to 30 (c) 30 to 50
- 4\. Write the greatest composite number among: (a) 1to23 (b) 17to55 (c) 21 to 53
- 5\. Find the least prime number which is greatest then : (a) 5 (b) 13 (c) 23 (d) 53
- 6\. Write the smallest prime number and composite number.
- 7\. Write three pairoftwin primes.
- 8\. Which ofthe following are showing prime factorisation : (a) 16 = 2x2x2x2 (b) 20 = 5 x 4
- (c) 72 = 2 x 2 x 2 x 3 x 3 (d) 72 = 2 x 4 x 9
- (e) 36 = 2 x 2 x 3 x 3
- 9\. Write the prime factorisation ofthe following numbers:
(a)
35
(b)
210
(c)
615
(d)
410
(e)
320
(f)
512
(g)
215
(h)
95
(i)
63
(j)
890
(k)
48
(I)
175
- 10\. Write the prime numbers that end with 2 and 5.
- 11\. If a number has only two factors, then what wi 11 you cal I this type of number?
- 12\. Which ofthe following are notatwin primes.
(a) 3,5 (b) 5,7 (c) 11,13 (d) 13,17
- 13\. Eliminate the odd pairfrom the following :
- (a) 3,5 (b) 5,7 (c) 7,9 (d) 23,29
###### Common Factors
Factors that are common for two or more number are called common factors.
Considertwo numbers 36 and 52
Factors of 36 = 1,2, 3,4,6,9,12,18, 36.
/ 13 /p 3, 6, 9
Factors of 52 = 1,2,4,13,26, 52. I 26 |2) 12 18
- 1 ,2 and 4 are common among the factors of both the numbers. \\ 52 W 36
Hence, the common factors of 36 and 52 = 1,2,4 x-----x ---
Highest Common Factor
The common factors 36 and 52 = 1,2 and 4 and can see that 4 is the greatest number amongthe common factors of 36 and 52
So, highest common factor or HCF of 36 and 52 = 4
Now consider anothertwo numbers:
Say 24 and 68
The factors of 24 = 1,2, 3,4, 6, 8,12, 24
The factors of 68 = 1,2,4,1 7, 34, 68
Common factors among both the factors are 1,2 and 4
- 4 is the greatest number among the common factors of 24 and 68.
So, H ighest Common factor or HCF of 24 and 68 = 4
You have leant the finding of HCF in previous class by finding the factors of given two numbers.
In this class you will learn the finding of HCF by division method for given two numbers.
HCF by Division Method
Sometimes, it becomes very difficult to find the HCF of some greater numbers. In that condition finding of HCF by the method ofdivision isapplied.
Finding HCF by the method ofdivision is based on thefollowingtwo principles-
- (a) If a number is divisible by another number, then every multiples of the first number is also divisible by the second number.
e.g. If 12 is divisible by 3 the all the multiples of 12; like, 24, 36,48, 60... and so on will bealsodivisibleby 3.
- (b) If a number divides two given numbers, then it will also divide the sum and difference of the given numbers.
e.g. if 3 divides 24 and 42 exactly then 3 will also divide the sum of 24 and 42 and the difference of 24 and 42 also.
¡.e. 24 and 42 are exactly divisible by 3 210J3 1 2(J
[Thesumof24and42 = 662 1 0](#bookmark181)
66 is also exactly divisible by 3 102) 2 1 0 (2
The difference of 42 and 24 = 18 and 18 is also ^ 0 4\_\_\_\_\_\_\_
exactly divisible by 3. 6) 1 0 2 (17
[Now calculate the HCF of 210 and 312 by the method ofdivision.1 0 2](#bookmark182)
[Solution:-](#bookmark17)
Step-1 Divide the greater number by smaller number
Step-2 Take the remainder as divisor and the divisor as dividend.
Step-3 Continue the process untill you get the remainder zero.
Step-4 The last divisor is the HCF
H.C.F.of210and312 is6.
Note : If the HCF of two numbers is 1 then the numbers are called Co-Prime.
##### EXERCISE 20
1\. Find the common factors of the following numbers and find their HCF also.
(a)
45,35
(b)
42,32
(c)
44,84
(d)
215,475
(e)
14, 74
(f)
16, 84
(g)
42,72
(h)
32,72
(i)
54, 94
Find the HCF of the following usingdivision method?
(a)
55,95
(b)
72,82
(c)
74,12
(d)
16,98
(e)
24,82
(f)
125,275
(g)
215,385
(h)
120, 542
(i)
672,132
(j)
212,436
(k)
45,78
###### Common Multiples and Least Common Multiple
Let us find the common multiples of8and 12
The multiples of8
= 8,16, 24, 32,40,48, 56, 64, 72,...
The multiples of 12
= 12,24,36,48, 60, 72,84...
Therefore the common multiples of 8 and 12 are 24,48 72,...
Least common multiple is abbreviated as LCM.
Hence Least common multipleof 8 and 12 is 24.
LCM by Prime Factorisation
To find the LCM by prime factorisation let usconsiderthe numbers 32 and 60. Prime factorisation of 32 =2x2x2x2x2
Prime factorisation of 60 = ,2 x 2, x 3x5 Common Non-common factors
Common factors =2x2
Non common factors =2x2x2x3x5 Hence product of common and non-common factors =2x2x2x2x2x3x5
= 480
###### LCM BY DIVISION METHOD
To find the LCM oftwoor more numbers division method is more convenient.
Consider 12,28, 56 and 42
###### Use the following steps
Step-1 Write all the numbers in one row and seperatethem with commas.
Step-2 Divide by the smallest prime number which divides at least two numbers exactly.
Step-3 Write the quotient and the undivided numbers as shown in the rows.
Step-4 Repeat the process and continue till co-prime numbers exists in the last row.
Step-5 Multiply all the prime number by which you have divided and the co-prime numbers left in the last row.
Step-6 The product of these numbers is the LCM of given numbers.
2
2
3
7
2
12,28, 56, 42
- 6, 14, 28, 21
- 3, 7, 14, 21
- 1, 7, 14, 7
- 1, 1, 2, 1
L 1, 1, 1
LCM = 2x2x3x7x2
= 168
###### Example 1:
Find the LCM of 120 and 45 using the method of division:
Solution:
31120,45
5 40, 15
8,3
LMC = 3x5x8x3
= 360
##### EXERCISE 21 !
1\. Find the LCM of the following by prime factorisation method :
2\.
(a)
16,20
(b)
22,24
(c)
8,20
(d)
24, 34
(e)
21,51
(f)
4,5,6
(g)
4, 5, 6, 8
(h)
44, 34
Find the LCM of the following numbers usingdivision method :
(a)
27,81
(b)
12,44,20
(c)
210,412,630
(d)
125,675,225
(e)
21,45,75,125
(f)
235,445
(g)
510,412
(h)
24, 36, 72
(i)
34,44,20
(j)
215,520
(k)
225,425
(I)
45,35,75,115
(m)
34,32,48
(n)
6,18, 34,12
###### Applications of HCF and LCM
Example 1:
Two pieces of wood are 27 metre and 21 metre long. They have to cut in small pieces. What will the maximum length of each piece?
Solution:
To find the maximum length calculate the 21^2 7 Q
HCF of the given numbers: 2 1
1 8
/. HCF = 3
6 Ô
So, the maximum length of each piece = 3 metre.
- ###### Example 2:
Find the least number of pieces of plywood, so that heaps of 20, 25 and 40 pieces can be made.
Solution:
To find the minimum number, find the LCM ofthe given numbers.
So,
2
2
5
20, 25, 40
10, 25, 20
- 5, 25, 10
1, 5, 2
Hence
LCM =2x2x5x5x2
= 200
Leastnumberof pieces of plywood = 200
##### U- EXERCISE 22 ^------------
- 1\. Find the greatest number which can divide 35 and 45 exactly.
- 2\. Students of a school are kept standing in two rows. There are 68 students in one row and 72 students in second row, but rows look odd. They decided to spread in more rows. How many maximum number of boys stand in a row if number of boy would be equal in each row?
- 3\. Two big packets of fruits contain 620 and 525 fruits. These fruits are to be packed into small packets. Which will contain the same number of fruits. How many maximum number of fruits can be packed in each small packet?
- 4\. A shopkeep sold pens for? 210 on Monday and for? 125 on Tuesday. What can be the maximum price of each pen?
- 5\. Find the least number which is exactly divisible by 27,21 and45.
- 6\. Measurement can of 9, 15 and 21 litre can be used whole to a number of times to empty a container of petrol completely. What is the minimum capacity of petrol container?
- 7\. A teacher wants to distribute chocolate among 27,35 and 45 students equally. What should be the least number of chocolates purchased so that no chocholates left with him?
Get Set Go With Sum Up Mathematics-5
- 8\. Three bells ring at the interval of 5, 20 and 30 minutes. If they all ring at 10 am together, at whattime they will ring together again?
1
2
3
4
5
6
7
8
9
10
11
12
13
A
B
C
D
E
F
G
H
I
J
K
L
M
14
15
16
17
18
19
20
21
22
23
24
25
26
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
Prime = 16 + 18 + 9 + 13 + 5 = 61 isaprimenumber
###### Try This----------------------------------------------------------------------
Add the numbers for letters in your name and see if it is a prime number or not.
In this chapter you will learn more about fractions.
###### Fraction
When a whole number is divided into or more parts, these parts are called fractions.
12 4
For example : — ,— ,— etc. are all fractions.
- 2 3 5
In a fraction, like, —
3
- 2 is called the numeratorand.
- 3 is called the denominator.
- c 2 ----►Numerator
So, —\_\_\_\_
- j \* Denominator
###### Like Fractions
Fractions having same denominators are called like fractions.
- r I 1 3 5 6 r .•
For example : —, — ,— ,— etc. are like fractions.
K 4 ' 4'4 ' 4
###### Unlike Fractions
Fractions having different denominator are called unlike fractions.
For example : etc. are unlike fractions.
4 5 8 7
###### Unit Fractors
If the numerator of a fraction is 1,then it is called the unit fractions.
1111
For example : —,—, — ,— etc. are the examples of unit fraction. 2 5 4 3
###### Equivalent Fraction
1 2 3 4 5 6
2' 4' 6' 8' 10'12
are equivalent fractions.
— ,—, -2- etc. are also the examples of equivalent fractions.
These are the equivalent fractions.
###### Proper Fraction
When numerator is less then denominator in a fraction, the fraction is called proper fraction.
For example :
1 1 A 3' 9'12
etc. are proper fractions.
###### Improper Fraction
If the numerator is equal to or greater than the denominator of a fraction, the fraction is called improper fractions.
For example :
1 Â z 3'2'4
etc. are the examples of improper functions.
Representation of an Improper Fraction
See the figures
4
5
Each of the figure is divided into 5 equal parts. In figure A all the five parts are shaded while in figure B only 4 parts are shaded.
Hence if you want to represent figure Aina fraction you can write 5 parts out of 5 are shaded. It can be represented by fraction as
#### Z1
Similarly in figure B, 4 out of 5 parts are shaded. It can be represented as.
4
5
The total shaded parts :
or it can also be written as :
Consider another, condition
###### Mixed Numbers
The fractions like
#### 4
#### 4^
#### 4^
etc are called mixed numbers.
###### Fraction as a Division
See the fraction —
4
It can also be written as 3 -^ 4
###### To Express Improper Fraction as Mixed Number
Convert — into mixed number.
In this fraction denominator is 3, which suggests that an object is divided into three
equal parts. So let us find how many 3's are contained in 7.
Now change — in mixed + number
divisor —>
<- Quotient
+- remainder
13 \_ ^
7 7
Mixed number = Quotient
Remainder Divisor
To Express A mixed Number as Improper Function
3
Convert 2y intoan improperfunction.
Here, the denominator 7 donates that each object is divided into 7 equal parts.
The number 2 tells that each of the 2 complete objects is divided and on division we get2 x 7 = 14 parts. We have 3 more parts thus we have a total of 1 7 parts.
[” 2 77](#bookmark229)
In another way
[33](#bookmark230)
Hence 2 — = 2 + —
[143](#bookmark231)
7 + 7
17
7
Example 1:
1
Express 3— as an improper function:
###### Solution:
1 1
34=3+4
4 4
3 x 4 + 1 \_ 13
4 4
##### Q. EXERCISE 23 B
- 1\. Which ofthe following are like fractions?
[1 2 I 1 1 122](#bookmark236)
[9 ' 4 ' 9'17' 8 ' 19'21](#bookmark237)
- 2\. Which ofthe following are unit fractions?
[4 12 1121](#bookmark238)
[3' 3' 3' 4' 5' 5'8](#bookmark239)
3\. Which ofthe following are proper fraction?
2 2 12 2 12
5' 8' 5' 4' 5' 2 8
4\.
Which ofthe following are equivalent fractions?
, x 2 1 ,ix36
() 4' 2 b 5' 10
M 1 1
C 2' 3
(d)
2
2
12
4
5\.
Complete the following:
(a) 4=8 (W
, x 3 ...
C 4 12
(d)
6
7
12
6\.
Rewrite as division sum :
2 . 5
(a) 4 (b)
6
(c) y
(d)
7
9
7,
Which of fol lowing are improper fractions?
, x 14 5 , x 16
(a) 5 (W 14 (C) 9
(d) 4
1 6
(e)
12
9
(f)
9
12
8\.
Express as mixed numbers :
M !0 32 , x 23
(a) 9 (b) 11 (C) 7
<d> 7
(e)
^ 3
9\.
Express the following as improper fractions:
2 1
(a) 3 (b) 2 -
(c) 1
(d)
4
j^
15
###### Comparison of Unit Fractions
You have already learnt the comparison of like fractions in previous class. In this class you will learn the comparison of unlike fractions.
Remember as you read in previous class that among the like fraction, fraction which has greater numerator is greater.
For example:
2< 1 4 4
[76](#bookmark242)
[99](#bookmark243)
Comparison of two Unit fraction:
[11](#bookmark246)
Compare — and — .
[25](#bookmark247)
and
So,
1 \_ 2 \_ 3 \_ 4
[2 4 68](#bookmark248)
1 = 2.
[510](#bookmark249)
[\_52](#bookmark250)
10> 10
5
10
1 1
2 > 5
###### Lab Activity
Compare — and —. 2 5
In mathematics lab you can also compare the fraction.
Take 5 cm long and 1 cm wide two paper.
Strip Mark them as 'A' and 'B'.
Fold one paper strip into two equal parts.
Fold another paper strip into five equal parts.
2
5
2
5
2
5
2
5
2
5
2 2
2
2
Paper strip 'A' which has been folded in five parts. Each part repesents —
Paper strip 'B' which has been folded in twoequal parts, each part represents — .
Colour one part of paper strip 'A' and one part of paper strip B. Cut the colour part from each strip of paper.
Compare them placingthem on atable.
7
5
2
You will see that — is greater than —
1 1
S°' 2 > 7
Conclusion - Between two given fraction, the fraction with smaller denominator is greater than the other provided the numerators are same.
##### EXERCISE 24
Which fraction is greater in each pair?
1 9
w 3 4
1
5
(c)
1
— /
2
2
3
(d)
2 6
1
5
Which fraction is smaller in each pair?
(a)
1
1
5' 7
(b)
1
1
9' 8
(c)
1
12
2
11
(d)
1
16
1
17
Write
or = in the box to make a correct sentence :
(a)
(d)
2 9
\_5
10
2 8
IP
20
(b)
(e)
2
7
j\_
16
1 2
9 <C) 4
J\_
15
16
1
There are some packets of chocolate in ashop. Ramesh bought —th of the packet and 5
Amit bought — of the packet. Each packet costs ? 40. Who paid less amount for the
chocolate? Z"
1
During the examination in school Amit finishes his paper earlier by — th of the total “ o
time and Rahul finishes his paper earlier by — th of the total time. Who finishes his paperearlier?
###### Fractions in their Lowest Terms
Consider a fraction || .
You know that
[1 = 2 =1 = A](#bookmark257)
[2 4 8 1632](#bookmark258)
Similarly,
[I6 = 1 = ^ = 2](#bookmark259)
[32 16 8 42](#bookmark260)
In this sequence
[16 \_ 16^2 = .8 = \_§\_Jl2. = 2 = 4:2 = 2 = 2-2\_ 2](#bookmark261)
[32 32 -2 16 16 -2 8 8-2 4 4-22](#bookmark262)
So, to make a fraction in their lower form divide numerator and denominator by equal number, until there would be no-common factor left in numerator and denominator except 1.
28
Consider another fraction — and find its lowest term.
28
Given fraction = — divide numeratorand denominator by 2.
So,
28 28 - 2 14
20 20 - 2 10
Similarly
14 \_ 14-2
10 10-2
7
5
You get the lowest term
7
5 ’
Nowthere is no common factor in numeratorand denominatorexcept 1.
Hence - A fraction is in its lowest terms if its numerator and denominator can not be divided by a common factor except 1.
- ###### Example 1 :
Which ofthe following fractions is in its lowestterm ?
[, A 167](#bookmark265)
- [(a) 30](#bookmark266)
Solution:
[, x 168x2](#bookmark267)
- [(a) 77 = 775](#bookmark268)
[3015x2](#bookmark269)
In this fraction 2 is the common factor in numerator and denominator both.
So it is not in its lowestterm.
In this fraction there is no common factor in numerator and denominator except 1.
So it is in its lowestterm.
###### To Reduce a Given Fraction in its Lowest Term
(a) Dividing by a Common Factor
Consider a fraction
24
28
[Divide the numerator and denominator by common factor, 24 24 ^-212](#bookmark273)
So, 77 = 77---7 =77 again divide the numerator and denominator by common r , 28 28 -4-2 I4
factor.
[, , 1212-26](#bookmark274)
[Hence, - 142 ](#bookmark275)
No more division by common factor is possible
is the lowestterm ofthe fraction
[728](#bookmark276)
- (b) Dividing by HCF
Consider a fraction |^
Calculate the HCF of 28 and 30
The HCF of28 and 30 is 2
- Div ide the numerator and denominator by 2.
28 = 28-2 = 14
30 30-2 15
14 - . . z , z • 28
Tjy is the lowest term of the fraction .
Consider another fraction
98
Calculate the HCF of 70 and 98
The HCF of 70 and 98 = 14
Dividethe numeratorand denominator by 14.
s 70 = 70 4- 14 = 5
[°' 98 98 -147](#bookmark277)
[570](#bookmark278)
.-. — is the lowest term of the factor—.
[798](#bookmark279)
Hence by knowing the HCF of numeratorand denominator you can reduce a fraction to its lowest term.
##### \[3 EXERCISE 25 “^-------------
- 1\. Which of the fol lowing fractions are in their lowest term :
(a) 14
29
(b) 21
Z 1 32
(C) 14
(d)
14
32
(e) 15
30
(fi 24
25
(g)
8 28
(h)
28
45
2\. Reduce the fol lowing fraction to their lowest term :
/ i 35
(a) 45
(b) 70
Z 1 44
(c) 64
(d)
45
95
/ 3 16
e 28
(fi ^
16
Z 1 32
(8) 44
(h)
IP
18
###### Addition and Subtraction of Fractions
(a) Addition and subtraction of Like Fractions:
You have already make subtraction and addition of like fractions in previous class. Let review them again by the fol lowing examples-
- ###### Example 1:
Add: — + — + —
###### Solution:
[1 3 5 1 + 3 + 5 91](#bookmark289)
\-------=------- = — = 4 —
[2 2 2 2 22](#bookmark290)
- Example 2:
[Subtract: 77](#bookmark291)
[55](#bookmark292)
Solution:
7 \_ 4 = 7-4 = \_3
[5 5 55](#bookmark293)
- (b) Addition and Subtraction of Unit Fractions
First of all convert the unitfractions into like fraction and add them.
- ###### Example 3:
Add- 4+4
5 2
Solution:
Convert the — and 5
2
to like fractions with their denominators as L.C.M of 5 and 2.
L.C.M. of 5 and 2 = 10
1 = 12Z = 2
5 5x2 10
, 1
and
1 x 5
2x5
.5
10
Now add them
2+2=2+5
10 10 10
7
10
- Example 4:
Add-
2
1
5
###### Solution:
L.C.M.of2z5and3 = 30
- • 1 = 1 x 15 = 15
2 2x15 30
1= 1 x 6 =^
5 5 x 6 30
and l = 12LJ0 = ip
3 3 x 10 30
Now add them
15 \_6+1P = 15 + 6+10 \_ 31
[30 30 30 3030](#bookmark298)
Examples:
[Subtract: 1-1 23](#bookmark299)
Solution:
- L.C.M of 2 and 3 = 6
2
2
and 4
- 1 x 3 \_ 2
[2x36](#bookmark300)
- 1 x 2 = 2
[3x26](#bookmark301)
Now subtract them
5 \_ 2 = 3-2 \_
[6 6 66](#bookmark302)
¿~t^lK
##### \[A EXERCISE 26 v
- 1\. Add the following:
- (a) 7 7 7 (b) 12 12 12
, k A A A J\_ 5. JI
- (d) 12 12 12 (e) 3 3 3
(8) il4 + l (h) 14
1
7
zh 1 1 1
(j) 77+77 + T (I) 7 + 77 + 777
J 9 8 235 61218
z . 1 1 1 z . 1 1 1 1
14 7 21 5 15 20 25
2\. Subtract the following:
/ x 12 10 3 2 z . 6 2
a — - — b — - — c — - —
15 15 4 4 5 5
z 1 1 z , 1 1 za 1 1
(d)--— (e) — —7 (f) — - —
15 20 816 1015
g 12 36 7 56 3 18
(j) (k) (I) +
J 5 25 27 81 9 72
- 3\. Rahul spent — rd parts of his pocket money on Monday, What fraction of money did he spend on these two days?
1
— th part of it on Tuesday. 6
- 4\. A shopkeeper sold — th part of cloth at 10a.m. He again sold — part of cloth at4 p.m.
1
On next day he sold — th part of cloth. Calculate the total part of cloth he sold in two b
days.
3 5
- 5\. Anuska spends th part of her pocket money on Sunday. If she had only ^ th part of money on Saturday, how much part of the money does she have now?
7 2
- 6\. Ashopkeeper has only — th part of cloth left. He sold —th part of cloth. How much part of cloth is left now?
1
- 7\. Rahul purchased some potatoes from market. — th part of potatoes he gave to his
5
friend and — rd part of potatoes he ate in the evening. How much potatoes did he 3
use?
- 8\. Ankit spends his —th partof salary on Monday and — th part of his salary on Tuesday.
6 8
How much more salary did he spend on Monday?
###### Degree of Closeness of a Fraction
Let us look at two like fractions,
2
The circles, shown above, are divided into 5 parts. For —, 2 parts are shaded and for
3
5 '
5
- 3 parts are shaded. Thedifference in number of shaded parts is 1.
Hence, it can be said that the degree of closeness for and is 1.
In conventional ways, the difference gives the degree of closeness.
- • 2 = 2zi2 = 1
” 5 5 5 5
Here, the degree of closeness = 1.
Since, denominator is same in all cases.
For fractions where denominators are different, the degree of closeness can be calculated as fol lows:
Let us take — and —
Here, denominators are 3 and 4
LCMof3 and 4 = 12
Let us convert the given fractions so that we get 12 as denominator.
1 2
3 12
2=2
4 12
(v — = 4 so, multiply 2 by 4)
12
/. Degree of closeness is 1.
Let us take another example:
LCM of 7and 11 = 77
and
And
|and^
7 11
7 77
1=L3
11 77
63 \_ 55 = A
77 77 77
Degree of closeness is 8
##### EXERCISE 27
- 1\. Find the degree of closeness for following parts of fractions:
, , 1 5 .7 ,,13.12
(a) — and — (b) — and — (c) — and —
Jo lili i□ y
(d) — and — (e) — and — (f)
2 5 5 7
22 and L5
25 24
Multiplication of Fractions by Whole Numbers
- (a) Multiplication of a Unit Fraction
Example:
Suppose Ankit purchased a chocolate bar. He divided the chocolate bar into 25 equal parts, as shown in the picture. He ate 4 pieces of chocolates from that. What part of the chocolate did he eat?
Solution:
As the whole chocolate bar has been divided in 25 equal parts, so, each parts
represents — part of chocolate. 25
1111
And Ankit ate 4 pieces that means he ate — +—+—+— part of chocolate.
25 25 25 25
Now add them, 1111
25
4
25 '
Clearly —+—+—+57 = 2b 2d 2b
4
He ate -^yth part of chocolate.
1 1
That means he ate 4x— part ofthe chocolate or4 times of the — part of chocolate.
###### Multiplication of a Proper Fraction
Consideradigit3.
3
We can write 3 as y because if we divide 3 by 1 if gives the quotient 3.
You read in the previous chapter that "When a number is divided by 1, the quotient is the number itself". So there will be no effect on a whole number if we place 1 as denominator.
Now,
Multiply
3 u n
J by 2
i.e.
— x 2
As 2 is not a fraction so place 1 as denominator to make it like a fraction.
• A x 3 1
Now multiply numerator with numeratorand denominator with denominator.
1 x 2 = 2
3x1 3
Consider another fraction
4
—and multiply it with 4.
5
#### ix4
4
5
4
1
4x4 \_ 16
5 x 1 “ 5
###### Example 1:
5
Multiply — by2
###### Solution:
A x2
A 2 = 5x2
11 X 1 - 11 x 1
. IP
11
###### Example?:
1
Ankit purchased 25 chocolates and gave — th of them to his friend. How many 5
chocolates did he gave to his friend?
Solution:
1
Ankit gave — th of 25 chocolates 5
[1 Of24 = 4x 25 55](#bookmark319)
1 25 1 x 25
[- x — =--—](#bookmark320)
[== 5](#bookmark321)
.-. Ankit gave 5 chocolates to his friend.
Example3:
1
Ifthecostofl kg of rice is? 12 then calculate the cost of 1^ kg of rice.
###### Solution:
Here you haveamixed number 1 — , convert it to an improper fraction
2
2
2
2
1x2 + 1 = 2
2 2
So you have to calculate the price of
-^ kg of rice.
Now, come to the main sum
Cost of 1 kg of rice = . 12
/. Cost of 1 x 2 = 2 kg of rice = .12x2 = .24
Similarly cost of 1 x 3 = 3 kg of rice = .12x3
= .36
Cost of — kg of rice
= . 12 x-
2
^
1
12x3 2
? 36
= .18.
##### . EXERCISE 28 J
Multiply:
(a)
1 ,
4 X3
(b)
i\*4
(c)
4 9
5 X 2
(d) -|
x 3
(e)
“8 X 3
(f)
I44
(g)
| x 5
(h) |
x 5
(i)
4x 10
(j)
10 r
15X 5
(k)
10 a
20 X 6
(1) y
x 28
(m)
1 2
5 X 3
(n)
3 2
— x —
4 5
(o)
6 7
7 X 6
<p) 4
4
X 6
Find out:
(a)
-1- th of 28
(b)
1
— th of 24 hours
(c)
1
— th of 100 years
(d)
1
y of 10 years
(e)
1
— of 12 months
(f)
1
y of 30 days
- 3\. Fill in the blanks with fraction in lowestterms:
(a)
4 hours is
of a day.
(b)
4 month is
ofayear.
(c)
6 hours is
of a day.
(d)
5 is
of 10.
(e)
10is
of 100.
(fi
1 day is
of a week.
(g)
30 seconds is
of a minute.
(h)
250 gm is
of a kilogram
(i)
300 ml is
of a litre.
(j)
200 ml is
of a litre.
- 4\. Ankit purchased 100 chocolates, but he found that — th of the total chocolates was ■ 25
not good so he threw them. How many chocolates did he kept?
- 5\. Abdul purchased 500 packets of biscuitsand he gave — th of them to his friend. How 5
many packets of biscuits did he gave to his friend?
- 6\. Ifthecostofl kg of wheat is? 40. Calculate the price of 2- kg of wheat.
3
- 7\. -th seats of a stadium were occupied by visitor while a match was playing. If the stadium has total 900 seats how many seats werevaccant?
- 8\. Ifthecostofl kg of tomato is ? 25. Find the price of 4- kg of tomato.
1
- 9\. Ankita purchased 10- metres of cloth. If the price of cloth is ? 30 per metre, how much she has to pay?
- 10\. Rakesh distributed - of the chocolates he purchased to his friend. If he purchased
100 chocolates then how many chocolates was left with him?
###### Division of a Fraction by Natural Numbers
(a) Division of a Unit Fraction
Rahul purchased a water-lemon for his family. He cut the water-lemon in equal four parts. But as the pieces were too big so he cut all the pieces in two equal parts.
As each pieces were cut into two smaller parts so there were 8 smaller pieces.
1
Rahul took are smaller pieces, i.e. Rahul took — th of the watermelon. 8
We can say that Rah u I took:
2 °f 4 “ 8 th part
- ###### (b) Division of a Proper Fraction
2
Let us consider a proper fraction say —; and divide it by 2
As we did the division fora unit fraction, this can be done similarly.
#### 4-2
means
2 5 10
or
2 2=^xA= A
5 5 2 10
Hence if we have to divide a fraction by a natural number, then we multiply the numerator by 1 and denominator by the given natural number.
- ###### Example 1:
"I
Divide — by4.
###### Solution:
- ###### Example 2:
Divide by 7. o
###### Solution:
— ¿- 7 = — x— = —
- 6 6 7 42
- ###### Example 3:
4
Divide y by 3.
###### Solution:
- 7 ’ 3 7 3 21
- Example 4:
4
Divide — by 2. 5
Solution:
A 7 = 4 x J 5 ' 5 2 5
5
Examples:
4
If the product of two number is — and one number is 2 then find another number.
###### Solution:
4 Tofind another numberdivide t by 2.
4 q 4 1 A
- .♦. — ^2 = — x — = —
6 6 2 >2^
3
3
1
So second number is y .
##### ¿a. EXERCISE29
- 1\. Divide:
15
8
(a) y - 7 (b) 5
13 1
(c) y + 3 (d) y + 9
9 4
<e) B-9 <f) HB5
3 3
(g) y \* 7 (h) y + 6
5 6
(o 4-io (j)
(k) 3 ^ 4-14
o 5
2\.
The product of two numbers is
If one of the number is 45 then find another
number.
- 3\. Rahul divided — ofthe chocolates among three children. What part of the chocolates
did each child get?
Inthischapteryou will learnt about decimal or decimal fractions.
Decimal fractions are similar to common fractions, but decimal fractions have the denominators, like 10,100,1000,10000.....
Forexample- ± -^ ^, ^ ^ ^thedecimalfractions.
One Tenth of a Unit
See the given figure.
A
1
10
Thefigure A has been divided into 10 equal parts and one part of it is shaded.
Therefore the shaded part is — .
This one tenth is also written as 0.1 and read as decimal one or point one. The dot on the left ofthe digit one iscalled decimal point.
Now considerotherfigure.
This figure has also been divided into 10 equal parts and two parts has been shaded.
2
Sothis will becalled .
2\.
1 q can be expressed as decimal points and written as 0.2.
Similarly
and soon.
#### r0-3
4= °-4
10
5
= 0-5
10
Decimal Numbers
1 2 3 4 5 6 7 8 , .
To'To'To'To'To'To'To'To' ared60™fract|onsanc\*°-i,0-2,o.3,0.4,0.5, 0.6.....are called the decimal numbers.
 Similarly
— = 0.01 100
2
Too = °-02
— = 0.03 100
and soon.
One Thousandth of a Unit
As
Tr0-1
and
= 0.01
100
Similarly,
—= 0.001 1000
2
= .002
1000
21
1000
= 0.021
211
1000
= 0.211
Similarly,
1000
= 0.003
Whole Numbersand Decimal Fractions
Considerthe figure given. All figure are considered equal
has been shaded.
This is represented as :
3 — = 3 —
10 10
4
3 — is rePresented as 3.4 and is read as three point 4 or three decimal four.
Point to be remember : O is usually written before a decimal if there is no whole past before decimal.
For example: -.2 is written as 0.2; .3 is written as 0.3 and so on.
###### Place Value of Decimals
Like whole numbers we can also show decimals on a place value chart.
CD
Ï o o
C r
T
in
C O
<U r
I—
in
C ro
CD
'u o
Q
CD
S 10
1 c WO T
1 1
g 1000
I-
3
3
2
•
5
2
4
524
It is written as 332.524 or 332 Yqqq and read as three hundred thirty two point five two four.
Lab Activity
You might have seen the ABACUS or you might have seen slate, with the continuation of beads, in the rod and slate for writing for the children.
you know?
ABACUS is considered as the first computer.
Children slate with abacus.
If you do not find it make it yourself or you can purchase it from a stationary shop.
Makingofan ABACUS.
a Take a wooden block.
- ☆ Fix five wooden sticks ABCDE as shown in the figure.
- ☆ Take 25 beads and put 5 beads in each sticks.
w Let stick A represent, tens, B represent ones, C represent Tenths, D-represent hundredth and E represent thousandth.
'<• Now put 2 beads down in stick A, 3 in stick B, 1 in stick C, 2 in stick D and 1 in stick E as shown figure.
Now the number represented on the abacus 2 tens, 3 ones, 1 -tenth, 2-hundredth and 1-thousandth.
ABCDE
ABCDE
In other words it represented 23.121.
It is read as twenty three decimal one two three.
Example 1 :
Write in decimals.
One tenth
3 tenth
(b) One and two tenth
(d) three and four hundredth
(a) 0.1 (b) 1.2 (c)
0.3
(d)
3.04
Example 2:
Write the following as decimal fractions.
(a) 0.1 (b) 0.12 (c)
1.2
(d)
1.25
Solution:
M 1 12 / x
(a . n (b) (c
12
(d)
125
10 100
10
100
Example3:
Write the following as decimal numbers.
2 4
(a) (b) . \_ \_ (c)
\_3\_
(d)
5
10 100
10
1000
Solution:
(a) 0.2 (b) 0.04 (c)
0.3
(d)
0.005
##### EXERCISE 30 ।
Write the following in decimal form :
(a)
five tenth
(b)
two tenth
(c)
Six hundredth
(d)
Five and four tenth
(e)
Sixty two and fifty two hundredth
(f)
Fourand six hundredth
(g)
Six and four hundredth
(h)
Nine and sixty four hundredth
(i)
Two and five hundred two thousandth
Write the following in decimal form :
(a) —
10
(b)
6 ÏÔ
(c)
\_2\_
100
(d)
\_8\_ 100
(e)
2Z
10
(f) ''Fo
(g)
12 —
100
(h)
A 25
6100
(i)
23-2^-
1000
(j)
27
1000
Write the foliowingas decimal fractions :
(a) 0.06
(b)
0.5
(c)
0.213
(d)
0.42
(e)
22.02
(f) 3.217
(g)
2.5
(h)
3.12
(i)
527.675
(j)
1.002
- 4\. Write the fol lowing as you read it:
- (a) 2.57 (b) 3.1 (c) 2.212 (d) 25.25 (e) 27.01
(f) 3.97 (g) 232.1 (h) 232.001
- 5\. Write in decimal fraction :
- (a) Two tenth (b) Five thousandth
- (c) Three hundredth (d) Thirty two and twenty five hundredth
- (e) One and twenty five thousandth
- 6\. Write in decimal form and decimal fraction after watching the figures.
###### Expanded Notation for Decimals
Consider a digit 725 and write its expanded form. 725 = 700 + 20 + 5
Now consider 27.29 and write its expanded form.
[29](#bookmark358)
[27.29 = 20 + 7 ++ -<](#bookmark359)
10 100
20 + 7 + 0.2 + 0.09
Consider another digit
[2 98](#bookmark360)
32 7.298 = 300 + 20 + 7 + —+ —+ —5
10 100 1000
= 300 + 20 + 7 + 0.2 + 0.09 + 0.009
In the above examples expanded form of decimal numbers 2 7.29 and 32 7.298 has been written.
###### Example 1 :
Write the expanded form of the following :
(b) 32.25 (c) 335.252
(a) 2.5
= 2 + —
10
= 2 + 0.5
(b) 32.25
2 5
= 30 + 2+10 + 100
= 30 + 2 + 0.2 + 0.05
(c) 335.252
2 5 2
= 300 + 30 + 5 +
10 100 1000
= 300 + 30 + 5 + 0.2 + 0.05 + 0.002
###### Example 2:
Write the following in short form :
(a) 20+1+0.1+0.01 (b) 300 + 40 + 5 + 0.1
Solution:
- #### (a) 21 + ^ + w = 2111
- (b) 300 + 40 + 5 + 0.1 = 345 +^ = 345.1
###### Example 3:
Write the following in the place value chart and find the place value of 2 in each number.
- (a) 2.15 (b) 32.316 (c) 112.11
Solution :
- (b) Placevalueof2 in 32.316 is2 ones
- (c) Place value of 2 in 112.17 is 2 ones.
##### . EXERCISE 31 ^-------------
- 1\. Write the following in expanded form :
- (a) 3.2 (b) 22.21 (c) 32.12 (d) 132.121
- (e) 42.25 (f) 32.45 (g) 49.291 (h) 61.215
- 2\. Fill in the blank boxes with suitable numbers.
- [(a) 0-24 =5 ](#bookmark371)
[125](#bookmark372)
- (b) °-125 = d++o+d
[26](#bookmark373)
- [(c) 1.26 = O + ^ +](#bookmark374)
- (d) 425.369 = 400 + □ + □ + g + ^ + g
- (e) 25.106 = 20 + □ + ^ + g
- 3\. Write in short forms
- (a) 5 + 0.2 + 0.005 (b) 20 + 5 + 0.1 + 0.002
- (c) 300 + 20 + 1 + 0.1 + 0.02 (d) 20 + 1 + 0.2 + 0.02
- (e) 20 + 0.1 + 0.002
Write the following numbers in a place value chart and write the pack value of 2 in each case.
(a) 4.326 (b) 2.101 (c) 9.215 (d) 210.161
###### Comparision of Decimals
Now compare 2.5 and 6.1. You know that both numbers have whole number part and decimal number part.
Whole number part in 2.5 = 2
and whole number part in 6.1 =6
As you know 6 is greater than 2
So, 6.1 is greater than 2.5
Consider another number0.72 and 0.9
0.72 has 7 tenth and 2 hundredth and 0.9 has 9 tenth.
You know that 9 tenth is greater than 7 tenth
0.9 > 0.72
Consider another number 2.55 and 2.62.
In both numberthere are whole number partsand decimal number parts.
In2.55,
Whole number part = 2 ones.
Decimal number parts = 5 tenth and 5 hundredth
In 2. 62
Whole number part = 2 Ones.
Decimal number parts = 6 tenth and 1 hundredth
You can see whole number parts are equal in both cases.
But6tenth > 5 tenth
2.61 > 2.55
Equivalent Decimals
See the figure
100
0.20
2
10
0.2
From the above figure it is clear that
20 2
or — = - or 0.20 = 0.2
100 10
Now consider another decimal fractions:
4 40 400
10' 100' 1000
On simplification we get
40 \_
100
4 , 400
4
: 10
— am
10
u ---- =
1000
Clearly
4
10
40 =
100
400
1000
or,
0.4 =
0.40 =
0.400
Similarly
0.1 =
0.10 =
0.100 =
0.1000
or
0.7 =
0.70 =
0.700 =
0.7000
0.9 =
0.90 =
0.900 =
0.9000
' A <
'^^ Point to be Remember
By adding number of zeros after the extreme right digit in the decimal number does not change its value.
###### Decimal Places in a Decimal
Considerthere numbers 3.2,16.09 and 2.369.
- 3.2 has 1 digit on the right of the decimal point thus it has one decimal place.
- 16.09 has 2 digit on the right of the decimal point thus it has two decimal places.
- 2.369 has 3 digit on the right of the decimal pointthus it has three decimal places.
###### Point to be Remember\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
Hence the number of decimal places is the number of digits on the right of the decimal point.
###### Like and Unlike Decimals
Decimal numbers can be categorised in two groups like decimals and unlike decimals.
Consider the fol lowing decimal numbers 2.1,2.12,2.5, 3.6, 3.125, 6.12, 5.136.
You can see that some decimal numbers has one decimal place while some have more decimal place.
Like Decimals — Decimals having equal number decimal places are called like decimals.
For example: 2.1,2.5, 3.6, 7.9 etc. are the examples of I ike decimals.
Unlike Decimals — Decimals having different number of decimal places are called unlikedecimals
For example: 2.1,3.75,2.791, etc. are the examples of unlikedecimals.
Some like and unlike decimals are given.
Like Decimals
5.1,6.2,0.1
2.32,1.02,3.23
4.321,1.214,4.613
Unlike Decimals
5.1,5.01
2.06,2.321,4.1
3.1,4.210, 7.9071
##### (B EXERCISE 32 ^----------
- 1\. Choose the greater decimal number from each pair: (a) 5.9; 2.6 (b) 3.2; 3.3 (c) 6.21; 6.32
- (d) 6.02; 6.12 (e) 37.21; 23.69 (f) 3.79; 324.01
- 2\. Write three more numbers equivalentto each of the given number: (a) 0.2 (b) 23.01 (c) 3.1 (d) 4.9
- (e) 7.2 (f) 0.1 (g) 0.3 (h) 0.9
- 3\. How many decimal places are in each of the following numbers: (a) 2.1 (b) 3.21 (c) 2.01 (d) 3.21 (e) 4.023
- 4\. Which ofthe following statement are true?
- (a) 2.1,3.2, 7.9,6.9are likedecimals.
- (b) 2.01,3.2, 7.9, 6.32 are like decimals.
- (c) 2.7, 2.70,2.700,2.70000 are equivalent decimals.
- (d) 3.21,2.1,6.079 are unlike decimals.
- 5\. Convert each ofthe following groups of unlike decimals to likedecimals (a) 2.1,3.21,7.31 (b) 6.21,3.32,7.916
- (c) 3.21,3.121,6.217
###### Conversion of Decimals into Common Fractions
Study thefollowing:
2
0-2 = 4
10
2
3 2 = 3 —
10
21
2.21 = 2 —
100
To convert a decimal into common fraction do the fol lowing:
- (a) Remove decimal
- (b) Put 1 as denominator
- (c) Put as many numbers of zero as equal to decimal places.
Example 1:
Convert the following into common fraction :
(a) 0.2 (b) 1.29 (c)
Solution :
3.437 (d) 5.1978
(a) 0.2 - ^ (b)
129
129 = 100
2427
(c) 3437 = iœo (d)
5.1978 = 51978
10000
###### Conversion of Common Fractions into Decimals
Study the following:
2" 2^5" TO "°-5
1 = 12125 = 21 = Q.05
4 4 x 25 100
To convert a common fraction into decimals do the following
###### Method-1
- (a) Multiply the numerator and denominator with a number so that the denominators becomes 10 or 100 or 1000 or so on if possible.
- (b) Remove the zeros
- (c) Put decimals after as many numbers as there are zeros in the denominator from unit place.
Note
This method can be applied in cases where denominator is either 5 orthose even numbers which are multiples of 2 and or 5 only.
This happens because in decimal system the numbers are written on the base of 10.
Ans. 5x2 = 10
###### Method-2
By division method
Example:
1
Convert ^ into decimals.
###### Solution:
Divide 1 by 2
2j^0.5
0
- 1 0
- 1 0 0
Step -1 Since 1 < 2 so it is not divisible by 2. Put a decimal after 0 in quotient.
Step-2 Put a zero after 1 in dividend.
Step-3 Put 5 in quotient which gives 2 x 5 = 10
Example:
1
Convert — into decimal.
4
- 4 ) 1 0 C0-25
8
- 2 0
- 2 0
0
Step -1 Since 1 < 4 so it is not divisible by 4. Put a decimal after 0 in quotient.
Step-2 Put a zero after 1 in dividend.
Step-3 2 x 4 = 8givesaremainder2.
Step-4 Since2 < 4soputazeroafter2.
Step-5 4 x 5 = 20 so put 5 in quotient.
1
4 = 0-25.
4
Note
Conversion of some fractions, like y, ^tc. for which the process of division never ends will bedealt in higherclasses.
Example 2 :
Convert 2— into decimals.
8
Solution :
21
8
= 2 +
2
8
2 x
8 + 1
17
8
8
17 x
125
2125
= 2.125
8 x
125
1000
##### (J. EXERCISE 33 ^-------------
1\.
Convert the following into common fractions :
(a)
0.5
(b) 0.2
(c) 0.3
(d)
0.31
(e)
0.12
(f) 3.15
(g) 1-2
(h)
2.16
(i)
3.567
(j) 2.612
2\.
Convertthefollowingfractions intodecimals :
(a)
1
10
(b) 100
(0
1; 1000
(d)
21
100
(e)
21
50
(f) — 25
(h)
31
4
(i)
4
. 21
(j) 250
###### Addition of Decimals
Addition of decimals isassimpleas to addition ofwhole numbers.
For example:
- (a) 0.2 + 0.5
\_2\_ 5 2 + 5
10 10 10
7
10
(b) 0.2 + 0.35
QJ
2 I 2 5 \\
10 + (io + ioo|
= + + p+ +
10 (wo 100/
2 , 35 20 , 35 55 n
— 4” — I — — U
10 100 100 100 100
The addition of decimals can be done by column method.
For example:
(a) 0.2
\+ 0.5
0.7
(b) 0.20
\+ 0.35
0.55
Example 1:
Example?:
Add 1.83 and 0.1.
Add 3.25 + 0.78
Solution:
Solution:
1 .83
\+ 0.1 0
1 .93
3.25
\+ 0.78
4.03
###### Example3:
Add 1.56, 2.1 5 and 0.51
Solution:
1 .56
2.15
\+ 0.51
4.22
###### Subtraction of Decimals
Subtraction of Decimals is as si
pie as subtraction of whole numbers.
Example 4:
Subtract 2.12 from 4.05
Solution:
4.05
-2.12
1 .93
Example 3:
Subtract 2.32 from 4.56
Solution:
4.56
-2.32
2.24
02
##### (X EXERCISE 3M %\*-------------
1\.
Add the following:
(a)
2.12 + 3.20
(b)
6.12 + 0.12
(c)
3.5 + 0.01
(d)
3.2 + 0.01
(e)
14.26 + 3.21
(f)
4.69 + 0.009
(g)
9.98 + 9.18
(h)
3.271 + 4.26
(i)
17.325 + 5.2315
(j)
6.910 + 3.911
2\.
Subtract the following:
(a)
3.21 6
(b)
7.219
(c)
6.1 90
-2.150
-5.1 20
-2.321
(d)
13.216
(e)
6.910
(f)
9.210
-5.1 69
-3.21 6
-3.1 20
(g)
6.1 71
(h)
16.616
(i)
3.915
-5.916
-7.01
-2.1 08
(j)
6.009
-2.1 1 6
- 3\. Write in the column form and subtract:
(a) 3.125-1.68 (b) 4.213-2.12 (c) 6.910-2.16 (d) 6.910-3.210
###### Multiplication of Decimal by Whole Number
Multiplication of decimal by whole number is done in the same way as multiplication of fraction by whole number.
Consider the following examples:
- [(a) 0.2 x 4 = x 4 =0.8](#bookmark408)
[10 1010](#bookmark409)
□ 124 Q 124 x 3
372
100
= 3.72
[b 1.24 x 3 = —— x 3 = ———— 100100](#bookmark410)
You can also multiply them directly usingthe followingsteps.
Step-1 Multiply them by simple method of multiplication assuming there is no decimal.
Step-2 After that, place decimal point in the product such that the number of decimal in the product is equal to the number of decimal places in the multiplicand.
- Example 1:
Multiply 24.29 x 2.
Solution:
24.29 x2
48.58
24.29 x 2 = 48.58
- Example 2:
Multiply2.12 x 12
Solution:
2.12
x 1 2
4 24
- 2 1 2 x
2 5.44
2.12 x 12 = 25.44
###### Multiplication of Decimal by Another Decimal
Example 3:
Multiply 2.34 by 1.2.
Solution:
Multiply them thinkingthere is nodecimal point.
2.34
x 1 , 2
4 6 8
2 3 4 x
2.808
Now add the decimal places in multiplicands.
There are two decimal places in 2.34 and one decimal place in 1.2.
So, total number of decimal place = 2 + 1 =3
Put the total decimal places of multiplicands countingfrom unitplace.
/. Product = 2.808 /. 2.43 x 1.2 = 2.808
Get Set Go With Sum Up Mathematics-5
#### G=--
- Example 4: Multiply 1.06 x 0.16 Solution: 1.06 x 0,1 6 6 3 6 1 0 6 x .16 9 6 /. 1.06 x 0.16 = 0.1696
Division of Decimals by Natural Numbers
Consider the following:
- (a) 0.8 = 2 (b) 0.16 = 2 (c) 0.27 = 3
Divide them using the steps given below-
Step-1 Divide them assumingthere is nodecimals.
Step - 2 Count the decimal place in dividend and put the decimal equals to decimal place in dividend countingfrom unit place in quotient.
- (a) 0.8 = 2
Solution:
2)8 0
\_8\_
- 0 Quotient = 4
Decimal place in Dividend = 1
Put the decimal equalsto 1 in quotient countingfrom unitplace.
.•. Quotient = 0.4
Hence, 0.8 = 2 = 0.4
- (b) 0.16 = 2
- 1 6
0 Quotient = 8
Put decimal after two places counting from right because dividend has two decimal places.
So, Quotient = 0.08
(c) 0.27 4- 3
- 3\) 2 7 ^
- 2 7
0 Quotient = 9
Put decimal
Quotient = 0.09
Example 4:
Divide 3.72 by 12
Solution:
12)3 7 2(^31
3\_6\_
- 1 2
- 1 2
0 Quotient = 0.31
##### (| EXERCISE 35 s
1\. Multiply:
(a) 0.2 x 2
(b)
0.26 x 3
(c)
1.26 x 4
(d) 1.92x12
(e)
2.356 x 11
(f)
3.95 x 13
(g) 6.293 x 4
(h)
12.634 x 5
(i)
2.675 x 3
2\.
Multiply:
(a) 12.26x1.1
(d) 1.32x1.2
(b)
(e)
0.2 x 0.2
2.97 x 12.1
(f)
(c) 0.32 x 0.2
3.333 x 1.2
3\.
(g) 1.271x1.2
Divide:
(a) 0.4 - 2
(h)
(b)
2.712 x 1.3
1.2-6
(c)
3.6 - 12
(d) 1.6-4
(e)
6.4-16
(f)
6.8 - 4
(g) 9.5^5
(h)
1.21 - 11
(i)
2.12 - 2
(j) 3.24 U
(k)
43.24 - 4
(I)
1.256 - 4
##### i (Poney
We will use the decimal notation to show the money value in this chapter. This is as simple as the operations in decimals.
You know that 100 paise = 1 rupee
or
1 rupee = 100 paise
1 paise =
■ 100Rupee
= 0.01 Rupee
2
Similarly, 2 paise = Tj-^Rupee
= 0.02 Rupee
3 paise = 0.03 Rupee
4 paise = 0.04 Rupee
10 paise = 0.10 Rupee
or0.1 Rupee
0.2 Rupee = 20 paise = 0.20 Rupee
Similarly, 30 paise = 0.3 Rupee
75 paise = 0.75 Rupee
125 paise = 1 Rupee and 25 paise = 1.25 Rupee
15 Rupee 28 paise = 15.28 Rupee
15 Rupee 8 paise = 15.08 Rupee
2 Rupee 5 paise = 2.05 paise
Conversion of Paise into Rupee and Rupee into Paise
Example 1:
Convert the fol lowing into Rupee
(a) 12 paise (b) 230 paise (c) 195 paise
(d) 1235 paise
Solution:
To convert paise into Rupee divide paise by 100.
12 paise
1 2 ---= 0.12 Rupee 100 H
(b)
230 paise =
230
100
= 2.30 Rupees
(c)
195 paise =
195
100
= 1.95 Rupees
(d)
1235 paise =
1235
100
= 12.35 Rupees
###### Example 2:
Convert the fol lowing into paise :
- (a) ?2.75 (b) ?3.56 (c) ? 16.25 (d) ? 275.39
Solution:
The convert a Rupee into paise multiply by 100 hence
- (a) ? 2.75 = 2.75 x 100 = 2 75 paise
- (b) ? 3.56 = 3.56 x 100 = 356 paise
- (c) ? 16.25 = 16.25 x 100 = 1625 paise
- (d) ? 275.39 = 275.39 x 100 = 27539 paise
##### U- EXERCISE 36 %•---------
(1.
Write in the form of Rupees using decimal notation :
(a) 25 paise (b) 30 paise
(e) 35 paise (f) 265 paise
(c)
20 paise
(g) 1320 p
(d) aise
95 paise
(h) 1215 paise
2\.
Convert the fol lowing into paise : (a) 0.72 (b) 0.21
(c)
1.26
(d)
21.75
(e) 16.22 (f) 156.81
(g)
272.36
(h)
0.11
###### Addition of Money
Example 1:
Express in Rupees and add :
5 Rupees 28 paise and 27 Rupees and 5 paise Solution:
5 Rupees 28 paise = ? 5.28
27 Rupees 5 paise = ? 27.05
Add them 5 28
\+ 27,05
Get Set Go With Sum Up Mathematics-5 3 2.33
#### G=--
- Example 2:
Add? 214.25 J 105.10and? 16.25
Solution:
214.25 1 05.1 0 + 1 6.25 335.60
/. Sum =? 335.60
- Example 3:
Vasco-de-Gama spent ? 675.80 on making boat, he spent ? 12.20 on his cloths and spend? 25.15 on food items. How much did he spend?
Solution:
Spentonboat = 675.80
Spent on cloths = 12.20
Spent on food = 25.15
Total = 713.15
Total expenditure = ? 713.15
- Example 4:
Chinese exported silk of ? 4315.10 and exported tea of? 70.20 more than silk. What was his total export?
Solution:
Exportsofsilk = ?4315.10
Exports of tea = ? 4315.10
\+ ? 70.20
Export of tea = ? 4385.30
.'. Total export = ? 4315.10
\+ ? 4385.30
? 8700.40
So, total export of china = ? 8700.40
Subtraction of Money
Examples:
Subtract? 27.50from? 100.00
###### Solution :
100.00
- \- 27.50
72.50
/. Difference = ? 72.50
Examples:
Ranjan Kapoor purchased a film in ? 1 725.50 and he sold it in ? 2023.20. What is his profit?
Solution:
To calculate profit subtract purchasing price from selling price.
Sellingpriceoffilm = ? 2023.20
Purchase price of film = - ? 1725.50
297.70
/. Profit = ? 297.70
##### U- EXERCISE 37 ^
- 1\. Add the following:
- [(a) 2 7.15 (b)1.20](#bookmark433)
1.20 21.1 0
[(d) 119.21 (e)26.26](#bookmark434)
[1 7.2222.22](#bookmark435)
- 2\. Add the following:
- [(a)(b)](#bookmark436)
25.1 0 21 5.1 1
\+ 215.15 +1210.12
\+ 320.1 0 + 1 20.05
\+ 41 2.1 2 + 935.1 0
(c) 12 5.75
250.25
(f) 15.20
320.1 5
1015.15
\+ 2010.12
\+ 1 000.1 2
 (d)
(e)
(f)
101.20
17.15
20.15
2111.15
120.20
31 0.35
3221.20
1 250.1 0
1 0.1 5
- 3\. Chicoo Rabbit spent? 200.00 on food. He spent? 325.20 in clothsand ? 30.12 spent on travelling. What is his total expanditure?
- 4\. Gaj Kapoor purchased a car for? 26300.20 and spent? 16120.15 on its painting. And he paid? 301.20 on transfer of paper of car. How much total cost had he to pay?
- 5\. Sevanand purchased some cloth for? 2015.20, he spent? 27215.12 on its stitching. He spent ? 20.1 5 on travelling while purchasing these items. How much did he spend total?
- 6\. Subtract:
(a)
201 25.20
(b)
15.10
(c)
27.1 2
-1 8695.1 0
-2.95
-19.19
(d) 14.20
-9.10
(e) 1 7520.1 5 (f) 10,000.00
-10.95 -1.01
- 7\. Rakes bought a pen for? 20.15 and sold it for? 9.15 less. How much money did he get for the pen?
- 8\. Anmol got? 57.20 from hisfatherand his brother got? 78.15. Howmuch moneydid Anmol's brothergot more than Anmol?
- 9\. Raman got? 20.12 from hisfatherand? 36.27from his mother. He purchased a book for? 29.16. Howmuch moneydid he save?
- 10\. Subtract:
- (a) 20 rupees 30 paise from 41 rupees 25 paise
- (b) 94 rupees 15 paise from 114 rupee 17 paise
###### Multiplication of Money
Example 1:
Multiply:
- (a) ? 20.22 by 9
Solution:
20.22
\_\_\_\_\_\_x 9 181.98
Product = ? 181.98
115.18
x 1 2
230.36
1 1518 x
1 382,1 6
Product = ? 1382.16
(b) ? 115.18 by 12
Example?:
Rakesh wants to buy 40 shirts. If the cost of one shirts is ? 395.20. How much he has to pay?
Solution:
Cost of one shirt = ? 395.20
.-. Cost of 40 shirts = ? 395.20 x 40
= ?15808
Cost of 40 shirts = ? 15 808.00
Examples:
From the price list calculate the cost of the following items.
Price List
Items \_
Price
Biscuit \_
12.15 per packet
Rice \_
42.60 per kg
Pulse \_
72.20 per kg.
Soft drink -
52.35 per bottle
(a) Costof 9 packet of biscuit
G=--
- (b) Costof 7 kg of rice
- (c) Costof 12 kg of pulse.
- (d) Cost of 21 bottles of soft drink.
Solution :
- (a) Cost of one packet of biscuit = ? 12.15
.-. Costof 9 packet of biscuit = ? 12.15x9
= ? 109.35
- (b) Costof one kg of rice = ? 42.60
/. Costof 7 kg of rice = ? 42.60 x7
= ? 298.20
- (c) Costof one kg of pulse = ? 72.20
/. Costof 12 kg of rice = ? 72.20 x 12
= ? 866.40
- (d) Cost of one bottle of soft drink = ? 52.35
.-. Costof21 bottle of soft drink = ? 52.35
= 21
52 35
1047 Ox
1099.35
/. Cost of 21 bottle of soft drink = ? 1049.35
Division of Money
Example 4 :
Divide
(a) ? 25.35 -5 (b) ? 1 70.20 - 4
Solution :
- (a) ? 25.35 -5
5j25A5^5.07
25
- (b) ? 1 70.20 - 4
4j770J0(42.55
16
10
8
22
20
20
20 0
/. ? 170.20 - 4 = 42.55
Examples:
Raju paid? 1255.75 for purchasing of 5 books. What is the cost of one book?
Solution:
To calculate the cost of one book divide the total price paid by number of books purchased.
Cost of 5 books = ? 1255.75
/. Cost of 1 book = ? 1255.75 - 5
5^125^75^251.15
10
25
25
5
5
7
5
25
25 0
.-. Costof one book = ? 251.15
##### . EXERCISE 38
- 1\. Multiply:
- (a) ? 12.20x8
(d) ?215.10x9
- (b) ? 30.95 X 7
(e) ? 19.75x12
(c) ?112.15x10
(f) ? 127.20 x6
- 2\. If the cost of one book is? 21.75. What will be the cost of 17 books?
- 3\. Ramesh purchased 30 kg potatoes. It the cost of one kg of potato is ? 11.25. How much rupees did Ramesh pay?
- 4\. A charity society gave scholarship 90 students. If charity society provides ? 215.15 scholarship per student then how much did it donate for scholarship?
- 5\. Rohit purchased 2225 packets of bread to donate them to flood victims. It the cost of one packet of bread is? 17.20 how much did Rohit spend?
- 6\. Calculate the followingas perprice list.
Price List
1 tunk
Bread
Pen Notebook Chocolate
Price
? 17.10 per packet
? 27.25 per pen
? 215.10 per book
? 115.12 per packet
- (a) Rohit bought 30 pens. How much did he pay?
- (b) Rakesh bought 25 packets of chocolate. How much did he spent?
- (c) Ankit purchased 20 packets of bread. How much did he pay?
- (d) Ankur purchased 60 notebooks. How much amount did he give to shopkeeper?
Divide :
(a) ? 19.95-5 (b) ? 205.15 - 5(c) ? 27.64 -4 (d) ? 172.71 -9
- 8\. Ifthecostof 9 books is? 279.54 then find the cost of one book.
- 9\. Amit paid? 2757.33 forthe dinner of his 30 friends. If he invites 20 more friends, then how much more rupees has he to pay?
- 10\. Raju purchased 25 books and paid ? 13525.00 to the shopkeeper. Find the cost of one book.
- 11\. The cost of 100 cows is? 2,75,5 72.00. Find the cost of one cow.
##### OTeasuRement of Length
You have learnt about the measurement of length in previous class. In this class you will learn to use decimals in the measurement of length.
Measures of Length
10 millimeters (mm)
10 centimetres (cm)
10 decimetres (dm)
1000 metres
= 1 centimetre (cm)
= 1 decimetre (dm)
= 1 metre (m)
= 1 kilometre (km)
Conversion of Smaller Units into Bigger Units-
(a)
10 mm = 1 cm
(b)
Therefore 1 mm = — cm = 0.1 cm
10
Similarly 2 mm = 0.2 cm
3 mm = 0.3 cm
4 mm = 0.4 cm
5 mm = 0.5 cm
10 cm = 1 dm
Therefore, 1 cm = —dm = 0.1 dm
' 10
Similarly 2 cm = 0.2 dm
5 cm = 0.5 dm
6 cm = 0.6 dm and so on
(c)
As you know 10 dm = 1m
Therefore 1 dm = — m = 0.1 m
Similarly 5 dm = 0.5 m
6 dm = 0.6 m and 60 cm.
(d)
As you know 100 cm = 1m
1
Therefore, 1 cm = —— m = 0.01 m
' 100
Similarly
5 cm = 0.05 m
(e)
You also know that
6 cm = 0.06 m 10cm = 0.10m 50 cm = 0.50 m 1000 m = 1 km
Therefore
Similarly
Example 1:
Convert the following:
(a) 6 mm into cm
- 1 m = km = 0.001 km
1000
- 2 m = 0.002 km
- 5 m = 0.005 km
10 m = 0.010 km or 0.01 km 100m = 0.100kmor0.1 km 500 m = 0.500 km or0.5 km 511m = 0.511 km
(b) 5 cm into dm (c)
(d)
9 m into km
(e) 215 m into km
Solution
(a) You know that
10mm = 1 cm and 1 mm = 0.1 cm
9 mm = 0.1 x 9 cm
= 0.9 cm
7dm into m
(b)
As you know
10 cm
= 1 dm
Therefore
1 cm
= 0.1 dm
•
5 cm
= 0.1 x 5 dm
= 0.5 dm
(c)
You know that
10dm
= 1 m
Therefore
1 dm
= 0.1 m
7 dm
= 0.1 x 7 m
= 0.7 m
(d)
You know that
100 m
= 1 km
•
1 m
= 0.001 km
Therefore
9 m
= 0.001 x 9 k
0.009 m
(a)
9 cm 2 mm into cm
9 cm 2 mm
=
9 + —<m
10
9x10 + 2 --------- cm
10
=
cm = 9.2 cm
10
or
9 cm 2 mm
=
n 2
9+ r
=
9 + 0.2 cm
=
9.2 cm
(b)
7m 25 cm
=
7 25
7m+ 100m
=
7m + 0.25 m
=
7.25 m
(c)
15 km 71 5 m
. 715,
—
15 km + 1000^'^
= 15 km + 0.715 km
(e) You know that
Alternate method
###### Example 2 :
Convert :
- (a) 9 cm 2 mm into cm
- (c) 15 km 71 5 m into kilometre
Solution :
1 m = 0.001 km
215m = 0.001 x 215km = 0.215km
21 5
21 $ m = 1 ooo km = 0'21 $ km
(b) 7 m 25 cm into metre
= 15.715 km
##### IB EXERCISE 39
1\.
Convert into centimetres (in decimals):
(a) 2 mm
(b)
(f)
12 mm
5 cm 3 mm
(c)
(g)
1 7 mm
13 cm 5 mm
(d)
115 mm
(e) 1 cm 2 mm
Convert into metres:
(a) 35 cm (b)
110cm
(c)
225 cm
(d)
5 m 5 cm
3\.
(e) 1 5 m 21 cm
Convert into km: (a) 5 m
(fi
(b)
12 m 25 cm
15 m
(c)
215m
(d)
1225m
(e) 11321m
(h) 17 km 975 m
(f)
(i)
5 km 215 m
121 km 579 m
(g)
1 5 km 675 m
###### Convertion of Bigger Unit into Smaller Unit
As you know
(a)
1 cm
=
10 mm
so,
2 cm
=
10x2 mm = 20 mm
3 cm
=
10x3 mm = 30 mm
10 cm
=
10 x 10 mm = 100mm
(b)
1 dm
=
10 cm
so,
2 dm
=
10 x 2 cm = 20 cm
3 dm
=
10 x 3 cm = 30 cm
7 dm
=
10 x 7cm = 70cm
(c)
1 m
=
10dm
Therefore,
2 m
=
10 x 2dm = 20dm
5 m
=
10 x 5dm = 50dm
8m
=
10 x 8 dm = 80 dm
(d)
1 m
=
100 cm
Therefore,
2 m
=
200 cm
3 m
=
300 cm
9 m
=
900 cm
- (e) 1 km = 1000 m
Therefore, 2 km = 2000 m
5 km = 5000 m
7 km = 7000 m 76 km = 76000 m
Example 1:
Convert into mm:
(a) 3.1 cm
(b)
2 cm
(c) 3.7 cm
Solution:
(a) As you know
1 cm
= 10 mm
Therefore,
3.1 cm
= 3.1x10 mm
= 31 mm.
(b) As you know
1 cm
= 10 mm
Therefore,
2 cm
= 20 mm
(c) As you know
1 cm
= 10 mm
Therefore,
3.7 cm
= 3.7 x 10 mm
= 37 mm
###### Example 2:
Convert into cm:
(a)
2.3 dm
(b) 5 m
(c) 2.3 km
Solution
•
(a)
You know that
1 dm =
10 cm
Therefore,
2.3dm =
2.3 x 10cm
=
23 cm
(b)
You know that
1 m =
100 cm
Therefore,
5 m =
5 x 100 cm
=
500 cm
(c)
1 m =
100 cm
Therefore,
2.3 m =
2.3 x 100cm
=
230cm
\[106
###### Examples:
Convert thefollowing:
(a) 2 km into metre (b) 2.5 km into m
(c) 5 km 215 m into metre
###### Solution :
(a) As you know Therefore, (b)
1km = 1000 m
2 km = 1000 x 2 = 2000 m
- 2.5 km = 25 x 1000 m
= 2500 m
(c) 5 km 215 m = 5 x 1000 m + 215 m
= 5000 m + 215 m
= 5215m
##### EXERCISE 40
Convert the fol lowing into millimetres:
2
- 3\.
- 4\.
- 5\.
- (a) 5 cm (b) 5.2 cm
Convert into centimetres:
- (a) 9.7 dm (b) 3.2 m (c)
Converts into decimetres:
- (a) 9.1 m (b) 3.20 m (c)
Convert into metres:
- (a) 2.3 km (b) 9.07 km (c)
Convert:
- (a) 5 m into dm and cm
- (c) 3.2 km into m and cm
- (e) 2.59 km in m and dm
- (g) 6975 cm into metre
(c) 5 dm
(d) 10.52 cm
(e) 7
6.9 m (d)
21.21m (e)
2.930
4.21 km (d)
40.08 km
64.4 km (d)
79.821 km (e)
5.971
- (b) 2.7 m intodm and cm
(d) 2700 m into km
(f) 2755 mm into cm
###### Addition of Length Measures
The addition of length measures having decimal point will be done in similar way as we did the addition of decimals.
- Example 1:
Add : 32.2 cm and 12.5 cm.
###### Solution :
Write it in column form and add.
- 32.2 cm
- 12.5 cm
- 44.7 cm
32.2 cm + 12.5 cm = 44.7cm.
Example 2 :
Add :31.5 m and 37.2 m.
Solution :
- 31.5 m
37.2 m
68.7 m
31.5 m + 37.2 m = 68.7 m.
Example 3 :
Add : 27 km 210 m and 12 km 15 m.
Solution :
Convert the measures into higher units before adding them
So, 27km210m= 27.210km
and 12 km 15 m = 12.015 km
Now Add them, 2 7.210 km + 12.015 km 39.225 km
Sum = 39.225 km or 39 km = 225 m
Example 4:
A car covers a distance of 132.574 km in the month of March and 213.74 km in the month of April. How much total distancedoes it cover in these two months?
Solution:
Distance covered in March Distance covered in April Total distance
132.574 km
213.74 km
346.314km
Total distance covered by car in two months = 346.314 km
##### Q. EXERCISE 41 )
1\. Add:
(a)
cm
2.159
3.216
(b)
mm
326.2
26.5
(d)
km 326.296 121.692
(e)
dm
3251.32
1 1 7.23
(g)
m
326.1 2
62.21
\+ 712.59
(h)
m
61 25.569
25.56
\+ 1 25.650
(c) m
215.74
121.47
(f) km
21 67.32
7612.23
(i) km
21.21
1 21 .2
\+ 7321.329
- 2\. Add:
- (a) 29 m 25 cm and 127 m 15 cm (b) 1 75.29 km and 27.32 km
- (c) 1 77 km 25 m and 721 km 251 m (d) 22 cm 8 mm and 1 7 cm 9mm
- (e) 275 km 1 metre and 112 km 21 5 metre
- 3\. Add 57 m 25 cm, 73 m 16 cm and 112 m 12 cm. Express the sum in metres and cm.
- 4\. Add 215 km 25 m and 1 7 km 217 m. Express the sum in km and m.
- 5\. Rahul walked 3 km 2 metre on Monday, 15 km 20 metre on Tuesday and 1 7 km 12 m on Wednesday. How many kms did he cover in these three days.
- 6\. A tailor says to Rahul that 1 m 25 cm cloth is required for stitching a trouser and 2m 25 cm cloth is required to make a shirt. How much cloth will Rahul purchase to get a shi rt and a trouser made?
- 7\. A shopkeeper sold 212 m 50 cm cloth in the morning, 125 m 10 cm cloth in the afternoon and 16 m 27 cm in the evening. How much cloth did he sell in the whole day?
- 8\. Rakes goes to school by cycle. His school is at 12 km 150 metre from his house. In one day how many kilometres did he covers while going to school and returning home?
###### Subtraction of Length Measure
Example 1:
Subtract 2.12 m from 20.12 m.
Solution:
- 20.12 m
- -2.12 m
18.00 m
.•. 20.12 m-2.12 m = 18 m.
- Example 2:
Subtract 32.21 cm from 54.12 cm.
Solution:
54.12 cm
- -32.21 cm
21.91 cm
.•. 54.12 cm - 32.21 cm = 21.91 cm.
- Example 3:
Subtract 12m 23 cm from 50 m 20 cm.
Solution:
50 m 20cm = 50.20 m.
12m23cm = -12.23m
Difference = 37.97 m
.-. 50 m 20cm-12 m 23 cm = 37.97 m.
- Example 4:
The distance of the school of Rahul is 12 km 150 m from his house. After waking for 4 km 15 m he takes bus. How much distance does Rahul cover by bus?
Solution:
Distance of school from the house of Rahul = 12.150 km
Rahul covers distance by walking = 4.015 km
Difference = 8.135 km
Rahul covers 8.135 km by bus.
##### £>. EXERCISE42 ,
Subtract :
- (a) 2 0.15cm
\- 5.75 cm
- (b) 1 75.25 km
\- 35.95 km
(c)
215.20 cm
\- 17.15cm
(d) 115.20 m
\- 95.75 m
(e) 17.25 km
\- 9.85 km
Subtract:
- (a) 12 m 20 cm from 19 m 27 cm
(c) 215 km 15 m from 21 7 km 2m
- (b) 19 km 21 5 m from 107 km 1 m
(d) 675 km 675 m from 676 km 1 m
- 3\. Amit travelled 1126.25 km by plane, 320.1 7 km by Rail and 1 7.277 km by rikshaw. If he had to cover 2000.1 7 km, how much d¡stance he has to cover now?
- 4\. Rakesh covers 5 m on foot, 928 m by cycle and 1320 km 1 7 m by train. If distance of New Delhi from his house is 1500 km 167 m then how much distance behind is he now?
###### Multiplication and division of Length Measure
Example 1:
Multiply 215.2 cm by 9.
Solution:
215.2
x 9
1 936.8
Therefore,
215.2cm x 9 = 1936.8cm
- Example 2:
Multiply 215 m 20 cm by 3
Solution:
215 m 20 cm = 215.2 m
Now multiply it by 3
21 5.2
x 3
al
645.6
So product = 645.6 m
- Example 3:
A car runs 75.325 km in an hour. How much distance will it cover in 5 hours?
Solution:
Car runs 75.325 km in 1 hour
Therefore car will cover 75.325 km x 5 hour
75.325 x 5 =
376.625 km
- Example 4:
Divide 118.25 m by 5
Solution:
5^118^25^23.65
10
18
15
32
30
25
25
.-. 118.25 m ^ 5 m = 23.65 m q
Examples:
434.75 metre thread is made by 5 workers. Calculate the length of thread made by one worker.
Solution:
Divide434.75 by 5
5J434.75(86.95
40
34
30
47
45
25
25
One worker makes 86.95 m thread.
##### M. EXERCISE M3 J
- 1\. Multiply:
- (a) 125.95 m by 3
(d) 31 7.25 m by 110
- 2\. Divide:
(a) 215.12kmby4
- (d) 17m 75 cm by 5
(b) 215.321 km by9
(e) 12 km 321 m by 3
(b) 317.2 km by 3
(e) 16m25cmby25
(c) 215.5 cm by 15
(c) 12 km 321 m by 3
(f) 27 km 264 m by 4
- 3\. Rahul collected 32 sticks. Each stick was 80.21 cm long. What isthe total length of all the sticks together?
- 4\. Rahul covers 615.25 m in 10 minutes while running. If he runs for 30 minutes how much distance will he cover?
- 5\. 2615.64 metres of cloth is to be distributed among 12 peoples. Calculate the length of cloth each people get.
- 6\. Distance of market from the house of Rahul is 17.851 km. How much distance will he cover if he has to go to market twice?
(Hint: In one trip he goes to market and return home.
So in two trip he has to cover distance x 4 )
- 7\. Rahul covers 84.056 km in four days on foot. How many km does he cover in one day?
- 8\. If the cost of cloth is 12.25 per meter how many rupees Rahul has to pay for purchasing of 20 metres of cloth?
- 9\. The length of a rope is 35.25 metre. Rani distributed the rope after making it into pieces of equal length among her 10 friends. Find the share of each girl.
i (Deowent of Weight (Ote)
You have done calculation based on measurement of weight in previous class. In this chapter you will learn the calculation of measurement of weight using decimals.
1000 gm = 1 kg
/. 1 gm = —-— kg = 0.001 kg
6 1000
2 gm = ——- kg = 0.002 kg
1000
12
12gm = woo k§ = °'012l<8
11 2
112gm = Todo kg = 0112 kg
Similarly
215
2i5gm = wkg = 0'215kg
###### Convertion of Gram into Kilogram
Example 1:
Convert into kg:
- (a) 21 7 gm
(b)
(d)
125 gm
10 gm
- (c) 40 gm
Solution:
(a)
21 7 gm =
217
1000
kg = 0.217 kg
(b)
125 gm =
125
1000
kg = 0.125 kg
(c)
40 gm =
40
1000
kg = 0.04 kg
(d)
10 gm =
10
1000
= 0.01 kg
###### Conversion of Kilogram into Gram
Example 2:
Convert into grams
- (a) 2 kg (b) 15 kg (c) 125 kg (d) 0.01kg (e) 0.005 kg
Solution:
(a)
1 kg
= 1000 gm
2 kg
= 1000 x 2 gm = 2000 gm
(b)
1 kg
= 1000 gm
•
15 kg
= 1000 x 15 kg = 15000 gm
(c)
1 kg
= 1000 gm
125 kg
= 1000 x 125 gm = 125000 gm
(d)
1 kg
= 1000 gm
0.01 kg
= 1000 x 0.01 gm
= 10gm
(e)
1 kg
= 1000 gm
0.005 kg
= 1000 x 0.005 kg
= 5gm
- Example 3:
Convert into kilogram and gm
- (a) 3420 gm (b) 2.567 kg
Solution:
- (a) 3420 gm = 3000gm + 420gm = 3 kg + 420 gm
= 3 kg 420 gm
- (b) 2.567 kg = 2.567 x 1000 gm
= 2567gm
= 2000 gm + 567 gm
= 2 kg + 567 gm
= 2 kg 567 gm
 Convert into kilogram:
(a) 6 gm (b) 10 gm (c) 600 gm (d) 4000 gm
(e) 2010 gm (f) 1695 gm (g) 59611 gm (h) 16215kg
Convert into gram:
(a) 2 kg (b) 1.6 kg (c) 0.3 kg (d) 0.002 kg
(e) 0.126kg (f) 0.12kg (g) 0.1kg (h) 0.5 kg
(i) 2.125 kg
Convert into kilogram and gram :
(a) 2516 gm (b) 6502 gm (c) 6050 gm (d) 2.625 kg
(e) 14.32 kg (f) 13.001kg (g) 17.2 kg (h) 16.005 kg
- 4\. Rahul told shopkeeper to give 1.3 kg of sugar. Shopkeeper measured 1300 gm sugar and gave to Rah u I. Was shopkeeper correct?
###### Addition and Subtraction of Weight Measure
Example 1:
Convert into decimals and add.
- (a) 2515 gm and 6316 gm (b) 2 kg 1 7 gm and 6 kg 315 gm
Solution:
- (a) 2515 gm = 2.515 kg 6316gm = 6.316kg Add- 2.515
6.316 8.831 kg
.-. Sum = 8.831 kgor8 kg831 gm
- (b) 2 kg 17gm = 2.017 kg
6 kg 31 5 gm = 6.315kg Total = 8.332 kg Sum = 8.332 kgor8 kg332 gm
- Example 2:
Subtract 14 kg 232 gm from 27 kg 115 gm
Solution :
27 kg 115 gm = 27.115 kg
14kg232gm = 14.232kg
Difference = 12.883 kg or 12 kg 883 gm
3.695 1 6.594 1 6.51 9
1 25.003
- (d) kg (e) kg
1.10 315.913
1 2.32 21 5.325
21 3.01 1 00.002
4001.325
(f) 12 kg225 gm and 25 kg 5 gm
(h) 1.259 kgand 2125 gm
(j) 1.1 kg, 2 kg 2 gm, 90 kg 900 gm
(g) 215 kg 100 gm and 2 kg 215 gm
(i) 1 7.32 kg; 5365 gm and 635 gm
Subtract :
(a) kg
320.1 50
-1 1 5.200
(b) kg 1 000.00 - 0.01
(c)
kg
(d)
kg
45.000
1 7.669
\- 7.001
-12.999
- (e) 1 gm from 2 kg.
(g) 1 7.256 kgfrom 22615 gm.
(i) 2 kg 15 gm from 18 kg 315 gm.
- (f) 999 gm from 1 kg.
(h) 14.226 kgfrom 22.121 gm.
3\.
Rajesh bought 12.250 kg potatoes, 35 kg 300 gm rice and 13 kg sugar. Calculate the total weight he bought.
4\. Rajiv purchased 372 kg 900 gm of rice. While carrying rice to his home because of an unwanted hole in the bag some rice fell in the way. At the home rice weighed only 312.2 kg. Howmuch ricedidfall intheway?
- 5\. Sonam has 12 kg 300 gm potatoes only. She gave 5 kg 120 gm of potato to her friend. How much potato is now left with her?
- 6\. From the 47.25 kg vegetable ghee shopkeeper sold 19.325 kg. How much vegetable ghee left with him?
###### Multiplication and Division of Weight Measures
Example 1:
Ifthe weight of one bag of cement is 105.2 kg, calculatethe weight of 7 such bags.
Solution:
Weight of 1 bag of cement = 105.2 kg
Therefore weight of 7 bags = 105.2 x 7 kg = 736.4 kg
- Example 2:
Ifthe cost of 1 kg of potato is 12, calcu late the cost of 125 kg potato.
Solution:
Cost of 1 kg of potato = 12.00
Therefore cost of 125 kg of potato = 12x125
= 1500.00
Examples:
Ifthecostofl kgofsugaris 16, calculatethe cost of 200 gm of sugar.
Solution:
Convert200 gm into kg and multiply
Cost of 1 kg of sugar = 16
Costof 0.2 kgof sugar = 16x0.2 Rupees
= 3.2
Example 4:
How much sugar each person get if 32.684 kg sugar will be distributed among 4 people equally?
###### Solution:
Divide the weight of sugar by number of people weight of sugar = 32.684 kg;
No. of people =4 \_\_\_\_\_\_\_
4)32.684(8.171
32
6
4
28
28
4
4
0
32.684 kg = 4 = 8.171 kg
##### {J. EXERCISE HE ^-------------
- 1\. Multiply:
- (a) 3.216kgby7 (b) 13.621 kgby3
- (c) 6.264 kg by 8 (d) 13.916 kg by 9
- 2\. Divide:
- (a) 3.264 kg by 4 (b) 13.212 kg by 9
- (c) 4.422 kg by 3 (d) 14.82 by 12 kg
- 3\. The weight of a packet of biscuit is 0.125 kg. Calculate the weight of 12 such packets.
- 4\. The cost of potato is ? 30 per kilogram. Manoj bought 21 5 gm of potato. How much he pay forthat?
- 5\. 12.72 kg of sugar was distributed among 12 person. How much sugar each person
did get?
- 6\. 2.646 gm of sugar were put equally in 21 packets. Find the weight of each packet.
- 7\. If the weigh of 10 bags of wheat is 2.120 kg. What will bethe weightof 3 bags?
#### io:
##### touRement of Capacity
As you have used decimal notation in other measure. In this chapter you shall use decimal notation in measurement of capacity. You already know that the standard unit of capacity (measuring liquids) in a litre (I), and each litre is divided into 1000 equal smaller units. This smaller unit is cal led millilitre (ml).
This means-
1000 millilitres (m/)
= 1 litre (I)
1 ml
= —I = 0.001 I 1000
5 ml
= 77777 I = 0-005 I 1000
10 ml
= l = 0.0101
1000
125ml
\- 1000 1 = 0 1251
Liquid items like milk, juice, petrol, diesel, kerosene oil etc. are measured in litres and some items like medicine, sampooare measured in millititres.
For measuring this liquid item, different types of containers are used. Some types of containers given below which is used to measuring milkand oil.
Some containers are used to measuring petrol and diesel, which is given below:
100 ml
#### G=--
Convert Millilitres into Litres
- Example 1:
Convert into litres.
- (a) 7 ml (b) 22 ml (c) 315 ml (d) 2107ml (e) 5l 120 ml
Solution:
- (a) 7 ml = —?— = 0.007 I
1000
- (b) 22 ml = I = 0.022 I
1000
- (c) 315 ml = -^- I = 0.3151
1000
- (d) 2107ml = = 21 + 0.1071 = 2.1071
1000
- (e) 5/120ml = 5 I + I = 5 I + 0.120 I = 5.120 I
1000
###### Convert Litres into millilitres
Example 2 :
Convert into millilitres :
- (a) 31 (b) 0.5681 (c) 0.0091 (d) 4515 1
Solution :
- (a) 31
11 = 1000 ml
/. 3 I = 3 x 1000 ml = 3000 ml
- (b) 0.5681
11 = 1000 ml
/. 0.568 I = 0.568 x 1000 ml = 568 ml
- (c) 0.0091
11 = 1000 ml
/. 0.009 I = 0.009 x 1000 ml = 9 ml
- (d) 4.5151
11 = 1000 ml
.-. 4.515 I = 4.515 x 1000ml = 4515ml
- ###### Example3:
Convert into litresand millilitres :
- (a) 3678 ml (b) 5.6651 (c) 14.025 1
Solution:
- (a) 3 6 78 ml = 3 000 ml + 6 78 ml
= 31 + 678 ml = 31678 ml
- (b) 5.665 I = 51 + 0.665 I
= 51 + 665 ml = 51 665 ml
- (c) 14.025 I = 141 + 0.025 ml
= 141 + 25ml = 14125ml
##### {#. EXERCISE K7 %•--------------
- 1\. Convert into litre :
- (a) 6 ml (b) 27 ml (c) 615 ml (d) 950 ml
- (e) 18605 ml (f) 8120 ml (g) 291155 ml
- 2\. Convert into millilitre : (a) 0.445 I (b) 0.0341 (c) 0.0401 (d) 5 115 ml
- (e) 2.0051 (f) 12.5051
- 3\. Convert i nto I itre and m i 11 i I itre: (a) 1.4201 (b) 0.0501 (c) 0.4701 (d) 28.0091
- 4\. Write true and false for the fol lowing statement: (a) 0.600 I = 600 ml (b) 1.350 I = 11 35 ml
- (c) 3.091 = 3 19ml (d) 4.040 I = 4140 ml
- 5\. Rohan bought 0.5 I cold drink. How many millilitre cold drink did he buy?
- 6\. Fill in the boxes to find the number of container used.
- (a) 2.500 I milk can be measured by using land 500 ml containers.
- (b) 1 I oil can be measured by using 500 ml 200 ml and 3 100 ml containers.
- (c) 4.350 I petrol can be measured by using 100 I and 50 I
containers.
- (d) 0.150 I medicine can be measured by using 100 ml and 50 ml.
###### Addition and Subtraction of Capacity Measures
Now, we shall learn to convert the measures by using decimal notation and then add or subtract like decimals.
- Example 1:
Add:
- (a) 3505 ml and 4897 ml (b) 13 I 615 ml and 271 795 ml
Solution:
- (a) 3505 ml and 4897 ml Convert into litres then add 1 1 1 3.505 I
\+ 4,897 I
8.402 I
.-. Sum = 8.402 I
- (b) 1111
13.615 I
\+ 27.795 I
41 ,410 I
/. Sum = 41.710 I
- Example 2:
Subtract 15 115 ml from 271250 ml
Solution: 1 27.250 I
-15.015 I
1 2.235 I
.-. Difference = 12.235 I
- Example 3:
A milkman has 27 litre milk in a container. He gave 5.500 I milk to Rahul and 12 1250 ml in a hotel. Now, how much mi Ik does he have?
Solution:
Add the m i I k that he gave away.
Milkgaveto Rahul = 5.5001
Milkgiven in the hotel = -12.250 ml
Total milk given = 17.7501
Now Subtract to find the remaining milk Total milk = 27.0001 milk given gave = -17.7501 09.2501
He has now 9.250 I milk.
##### EXERCISE 48
1\. Add:
(a) 14.040 I (b) 28.789 I
\+ 1 5.84 5 I + 3 7.6 78 I
(c) 66.897 I (d) 58.093 I
\+ 46.059 I + 38.809 I
(e) 7 I 653 ml and 9I 768 ml. (f) 5l 589 ml, 4 I 405 ml and 6 I 680 ml
(g) 13 1495 ml, 1 7 I 507 ml and 12 I 713 ml .
- 2\. Subtract:
(a) 9.8 78 I
-5.565 I
(b) 26.607 I
-14.016 I
(c) 44.103 I
-38.285 I
(d) 70.000 I
-67.235 I
(e) 6 I 275 ml from 9l 75 ml.
(f) 26 I 746 ml from 30 I 800 ml.
(g) 10 I 309 ml from 22l.
- 3\. Lalita bought 3.725 I of mustard oil and 2.643 I of coconut oil. How much total oil did she buy?
- 4\. Gopal brings 2.750 I milk on Monday and 4.21 5 I milk on Tuesday. How much milk Gopal brought in two days?
- 5\. Lalten Baltwala sold 18.635 I kerosene to Ramu, 16.285 I kerosene to Shyamu and 14.463 I kerosene to Mamu. How much kerosene was sold by Baltwala?
- 6\. There were 987.621 I water in Mr. Varma's tanker. His family used 427.328 I water on Sunday. How much water was left in the tanker?
- 7\. A petrol tanker contains 5000 litre petrol. 3875.385 litre petrol was transferred to one petrol pump in a container. What should be the minimum capacity of another container in which the remaining petrol can be transferred?
###### Multiplication and Division of Capacity Measures
Example:
A bottle of ketchup contains 375 ml ketchup. How much ketchup comes in 8 such bottles?
Solution:
Ketchup in 1 bottle = 375 ml
.-. Ketchup in 8 bottles = 8 x 3 75 = 3 000 ml
= ^000 = 3 litre
1000
###### Example:
9 cans of Coke contain 3 litre 375 ml Coke. What is the capacity of one can? Solution:
3 litre + 375 ml
= 3 x 1000 + 3 75 = 3 3 75 ml
9 cans contain 3375 ml Coke
3375
1 can contains = —-—= 375 ml
9
9^3375^375
27
67~”
\_63\_
45
45
0
##### EXERCISE R9 ^------------
- 1\. Multiply and express the answer in terms of I itre. (a) 3 75 ml by 16 (b) 62 5 ml by 8 (c) 75 ml by 80
(d) 11125 ml by 16 (e) 25 I 500 ml by 4 (f) 9 I 285 ml by 9
- 2\. Dividethefollowing: (a) 3.325lby5 (b) 13.2401 by4 (c) 45.81 Iby9 (d) 23.136lby6
- 3\. The petrol is selling at 58.31 per litre. Rambo buys 6.750 I petrol for his bike. How much did he pay to the pump attendant?
- 4\. The milk is selling at 39.50 per litre. Mrs. Sharma buys one and a half litre milk everyday. What is her weekly bill for milk?
- 5\. A family pack of ice cream contains 1250 ml ice cream. How much ice cream a person gets it if is shared by a 5 member family?
- 6\. A can of yogurt contains 375 ml yougurt. Monti buys 8 such cans. How much yougurt is bought by Monti?
- 7\. A big jar of oil contains 5 litre 454 ml of oil. If it is equally distributed in nine small containers, what is the minimum capacity of those containers?
##### (PedSURement of Time
In earlier classes you have read about reading a watch. You have also learnt to tell time, correctingto a minute. Check your knowledge by filling in blanks given below:
© The smaller hand of the watch is called
© © © © © ©
The larger hand of the watch is called
It takes
It takes There are There are There are
to make a complete round by the hour hand.
to make a complete round by the minute hand.
minutes in 1 hour.
seconds in 1 minute.
hours in a day.
Days of a Week
t^on^y
W/ednesd«y
###### Days in Different Months
January February
March April
31 Days W 28 or 29 Days
31 Days W 30 Days
May June
July August
31 Days W 30 Days
31 Days W 31 Days
September October
November
December
30 Days W 31 Days
###### Conversion of Higher Units into Lower Units Example:
Convert:
- (a) 6 hours 30 minutes into minutes
- (b) 18 minutes 40 seconds into seconds.
###### Solution:
- (a) 6 hours + 30 minutes
= 6 x 60 + 30 minutes
= 360 + 30 = 390 minutes
- (b) 18 minutes + 40 seconds
= 18 x 60 + 40 seconds
= 1080 + 40 seconds
= 1120 seconds
Example:
Convert:
(a) 12 years 3 months into months
- (c) 4 weeks 2 days i nto days
Solution:
- (a) 12 years + 3 months
= 12x12 + 3 months
= 144 + 3 = 147 months
- (b) 4 months + 10 days
= 4 x 30 + 10 days
= 120 + 10 days = 130 days
- (c) 4 weeks + 2 days
= 4x7 + 2 days
= 28 + 2 = 30 days
- (d) 5 years + 18 weeks
= 5 x 52 + 18 weeks
= 260 + 18 weeks = 278 weeks
Conversion of Lower Units into Higher Units
Example:
Convert:
- (a) 120 minutes into hours (b)
- (c) 7200 seconds into hours
Solution:
- (a) 120 minute into hours.
120 ,
= —— hrs = 2 hrs.
60
210 seconds into minutes
(b) 4 months 10 days into days
(d) 5 years 18 weeks i nto weeks
#### G=--
- (b) 210 seconds
210
—— minutes
3— minutes oO
60)210(3
180
30 Remainder
(c) 7200 seconds
Step-1 Convert into minutes
= 120 minutes
Step-2 Convert into hours
###### Example:
Convert:
(a) 144 months into years
(c) 560 days into weeks
(b) 320 days into months and days
(d) 150 weeks into years and weeks
###### Solution :
- (a) 144 months into years
12
24
24
/. 144 months = 12 years.
- (b) 320days into monthsand days
3 q) 32000
30
20
00
320 days = 10 months 20 days ---
- (c) 560 days into weeks. 7^560^80
56 0 0 0
.•. 560 days = 80 week
- (d) 150 weeks into years and weeks
52)l50(2
104
46 Remainder
150 weeks = 2 years 46 weeks.
##### EXERCISE 50
- 1\. Convert:
- (a) 5 minutes into seconds
- (c) 5 hours in minutes
- (e) 3 hours into seconds
- 2\. Convert:
- (a) 4 years into months
- (c) 8 years 4 months into weeks
- (e) 5 months intodays
- 3\. Convert:
- (a) 1500 minutes into hours
- (b)
(c)
(d)
(b) 7 hours 30 minutes into minutes
(d) 3 hours 30 minutes into minutes
(b) 4 years 2 months into months
(d) 5 years i nto weeks
(f) 7 months 10 days into days
390 minutes into hours and minutes
3690 seconds into hours, minutesand seconds
1320 seconds into minutes
- 4\. Vasco de Gama took 142 months to travel from Europeto India. How many years and months were taken by him to travel?
- 5\. Rajatwent back in time for 10400 weeks. How many years did he go back into time?
- 6\. Bumblebee takes 8476 seconds to travel between a flower and her beehive. Hq much time in hours, minutes and seconds is taken by Bumblebee?
- 7\. A snail takes 5 weeks and 4 days to travel from a drain to a pond. How many days is taken by the snail to finish itsjourney?
- 8\. Kandasany holds the record of staying for 786 days in space. For how many years, months and days did he stay in space?
###### Addition of Measures of Time
Example:
Add 30 minutes 48 seconds and 25 minutesand 28 seconds.
Solution:
Minutes Seconds
30
48
J 48 + 28 = 76 seconds
\+ 25
28
= 1 minute 16 seconds.
56
76
###### Example:
Add 7 hours42 minutesand 3 hours 32 minutes.
Solution:
Minutes
Hours
7
42
\+ 3
32
1 1
74
42 + 32 = 74 minutes = 1 hour 14 minutes
###### Example:
Add 7 hours 39 minutes48 second to 2 hours 47 minutes 52 seconds.
Solution:
Hours
Minutes
Seconds
1 1
7
39
48
\+ 2
47
52
1 0
87 27
00 40
Step-1 48 + 52 seconds = 100 seconds = 1 minute 40 seconds Step-2 1 + 39 + 47 minutes = 87 minutes = 1 hour 27 minutes Step - 3 1+7 + 2 hours = 10 hours.
Example:
Add 4 days 1 7 hours and 9 days 20 hours.
###### Solution :
Days Hours
- [41 7](#bookmark222)
[+ 9](#bookmark539)
[13 14 371 3](#bookmark540)
Step -1 17 + 20 hours = 37 hours = 1 day 13 hours
Step-2 1 + 4 + 9 days = 14 days.
Example:
Add 7 years 8 months and 2 years 7 months.
Solution:
Years Months
[1 78](#bookmark541)
[+ 27](#bookmark542)
[1 05^3](#bookmark543)
Step -1 8 + 7 months = 15 months = 1 year 3 months
Step - 2 1+7 + 2 = 10 years
##### {J. EXERCISE 51 ^------
Add:
- 1\. 37 minutes 39 seconds and 47 minutes 49 seconds.
- 2\. 14 minutes 1 5 seconds and 49 minutes 45 seconds.
- 3\. 8 hrs8 minutesand 14 hrs8 minutes.
- 4\. 6 hrs 7 minutes 11 second and 8 hrs 18 minutes 15 second.
- 5\. 20 hrs 18 minutes 37 seconds and 18 hrs 52 minute 42 seconds.
- 6\. 5 days 15 hrs and 6 days 9 hrs.
- 7\. 7 weeks 5 days and 2 months 2 weeks.
- 8\. 4 months 3 weeks and 2 months 2 weeks.
- 9\. 12 years 10 months and 4 years 5 months.
- 10\. 5 months 22 days and 4 months 18 days.
- 11\. 8 years 7 months 20 days and 4 years 8 months 1 7 days
- 12\. 5 months 3 weeks 2 days and 4 years 3 months 2 weeks 6 days.
###### Subtraction of Time Measures
Example:
Subtract 23 minutes 25 seconds from 38 minutes 1 7 seconds.
Solution:
Minutes Seconds
38 1 7
- \- 23\_\_\_\_\_\_\_\_\_\_25
14 52
Step-1 Since 1 7 is less than 52
So, borrow 1 minute from 38 minutes. 1 minute + 17 seconds = 60 + 17 seconds = 77 seconds
And, 77-25 seconds = 52 seconds.
Step-2 37min-23 min = 14 minutes
Example:
Subtract 24 hours 55 minutes from 36 hours 23 minutes. Solution:
Hours Minutes
36 23
- \- 24\_\_\_\_\_\_\_\_\_\_55
1 1 28
Step - 1 Since 23 is less than 55 so borrow 1 from 36 hours. 1 hr + 23 minutes = 60 + 23 minutes = 83 minutes
And, 83 - 55 minutes = 28 minutes
Step-2 35-24 hrs = 11 hours
Example:
Subtract 25 years 8 months from 42 years 4 months.
Solution:
Years Months
42 4
\- 25\_\_\_\_\_\_\_\_\_\_\_\_8\_
1 6\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_8\_
Get Set Go With Sum Up Mathematics-5
Step -1 Since 4 is less than 8 so borrow 1 from 42 years.
1 year + 4 months = 12 + 4 = 16 months and 16-8 months = 8 months.
Step-2 41 — 25 years = 16 years.
##### U- EXERCISE 52 ^------------
Subtract:
- 1\. 38 minutes 38 seconds from 52 minutes 15 seconds.
- 2\. 55 minutes 35 seconds from 70 minutes.
- 3\. 8 hours 5 minutes from 12 hours 50 minutes.
- 4\. 18 hours 22 minutes from 30 hours.
- 5\. 29 years 9 months from 40 years 3 months.
- 6\. 18 years 3 from 22 years 9 months.
- 7\. 23 months 12 days from 30 months 8 days.
- 8\. 13 months 22 days from 18 months.
- 9\. Anamika's, date of birth is 6th September 1999. What is her age on 12th March 2010?
- 10\. Gappu's date of birth is 19th April 2006. What is his age on 7th September 2011 ?
###### 24-Hour Clock Time
Mostoftheclockstell time in 12 hourformat.
Someclockstell time in 24 hourformat.
You can see such clocks at rai I way.
Railway Stations time tables are written in 24 hour format.
In 24 hour format, 1 :00 PM is called 13 hours. It is also written as 13 :00 hours.
In 24 hour format 12:00 PM is written as 24 :00 hours or 00 : 00 hours.
Time is expressed in 4-digit in 24 hr format.
Two dots (:) separate two digits on each side.
Two digits on the leftof(:) is for hours.
Two digits on the right of (:) is for minutes.
G=--
Calculation of Duration
Example:
The school starts at 8:30 AM and ends at 1:45 PM. How long does the school function?
Solution:
8:30 AM = 08:30 hours
1:45 PM = 13:45 hours
Duration = 13:45 hours-08:30 hours
Hours Minutes
1 3 45
\- 08\_\_\_\_\_\_\_\_\_30
5 1 5
= 5 hours 15 minutes
Example:
A bus starts from Haridwar at 6:45 PM and reaches Delhi at 7:30 AM the next day. How much time is taken by the bus to complete the journey?
Solution:
6:45 PM = 18:45 hours
7:30 AM = 07:30 hours
Duration upto midnight = 24:00 - 18:25 hours
24:00
-1 8:45
05:15 hours
Duration upto 07:30 hours on next day
= 07:30 + 05:15
07:30
\+ 05:1 5
12:45 hours
/. Duration = 12 hrs. 45 minutes.
Example:
The summer vacation started on 18th May and the school reopened on 12th July. What is the duration of summer vacation?
Solution :
No. of Days in May = 31 days
/. No. of holidays in May = 31-17 =14 days
No. of days in June = 30 days
/. No. of holidays in June = 30 days
And number of holidays in July = 11 days
/. Total number of holidays = 14 + 30 + 11 = 55 days
##### ^ EXERCISE 53 ^-----------
- 1\. Find the duration of time :
- (a) 7:30AMto 12:00 Noon (b) 6:15 AMto4:30PM
- (c) 8:30 PM to 11:45 PM (d) 9:15 AM to 3:30 PM
- 2\. Mr. Sharma starts for his office at 9:15 AM and comes back home at 6:30 PM. For how much time he was out from his home?
- 3\. Sampark Kranti Express leaves New Delhi at 1:30 PM and reaches Darbhanga at 11:00 AM the next day. How much time the journey takes?
- 4\. Aftab starts for a tour on cruise on 24th December and returns home on 12 February. For how long Aftab had travelled?
- 5\. Scientist Aklamandam started an experiment at 5:30 AM and finished the experiment at2:15 PM the nextday. For how long the experiment last?
- 6\. The school team entered the water park at 2:30 PM and came out at 6:45 PM. For how long did the team stay in the water park?
- 7\. The British came to India on 16th October 1638 and left India on 1 5th August 1947. For how longdid they stay in India?
###### To Find Time
Example:
Whattime will be:
- (a) 2 hours 50 minutes after 3:1 5 PM
- (b) 3 hours 35 minutes after 7:30 AM
Solution :
- (a) 3:15 pm = 15:15 hrs.
Hours Minutes
[1515](#bookmark558)
[+ 02](#bookmark559)
[18 17 6505](#bookmark560)
18:05 hours = 6:05 PM
- (b) 7:30 AM = 07:30 hours
Hours Minutes
[0730](#bookmark561)
[+ 03](#bookmark562)
[1110 6505](#bookmark563)
10:65 hours = 11:05 AM.
###### Example:
Whattime will be
- (a) 2 hours 30 minutes before 1:20 pm (b) 4 hours 40 minutes before 2:30 pm Solution:
- (a) 1:20 PM = 13:20 hours
Hours Minutes
1 3 20
-02\_\_\_\_\_\_\_\_\_30
1 0 50
10:50 hours = 10:50 AM
- (b) 2:30 pm = 14:30 hours
Hours Minutes
14 30
- \- 04\_\_\_\_\_\_\_\_\_40
9 50
09:50 hours = 9:50 AM
###### Example:
Ducky duck entered a pool on 12th February and came out after 24 days. On which date did it come out?
###### Solution :
No. of the days in February
28
No. of days in pool = Now no. of days in March = .•. It came out on 7th March.
28-11 =17
24-17 = 7
##### . EXERCISE 54 ^-------------
- 1\. Whattime will be:
- (a) 1 hour 50 minutes after 10:10 AM (b) 3 hour 15 minutes after 12:30 PM
- (c) 5 hour 40 minutes after 9:30 PM
- 2\. Whattime it was :
- (a) 3 hours 20 minutes before 2:15 PM
- (b) 8 hours 10 minutes before 4:30 PM
- (c) 2 hours 7 minutes before 2:42 PM
- (d) 9 hours 20 minutes before 10:10 PM
- 3\. Raju planted a rose sapling on 8th April. The first flower came on 15th May. How many days it took for the fi rst flower to come?
- 4\. Sachin hit a ball for six at 9:30 AM and it went out of the stadium. The ball came to ground at 12:45 PM. For how longthe ball was outside?
- 5\. Pradeep left for England on 11 th September 2012 and came back on 20th November 2012. For how many days he was out of India?
- 6\. Granny started her trip to the Kumbha Mela on 14th January she came back after 15 days. On which day did she return?
- 7\. Ankit was born on 5th March 2003. Today is 16th January 2009. How many days are left for his next birthday?
##### MGeometRy
In this lesson you will learn about rays and angles. Before that, let us recall what you learntabout line and line segment.
###### Line
A line can be extended to any length on both sides.
A line has no end points.
A line has no length.
In this figure, AB is a line.
AB and BA are the same line
A line can also be shown by a single letter.
In this figure 7 is a line.
Types of Line
Curved Lines
A B
« • » ►
Horizontal Line
Vertical Line
Slant Line
Line Segment
A part of a straight line is called line segment.
A line segment has two end points.
A line segment has length.
Note
I Part of a curved line is nota line segment. \[
B
A part of a line with one fixed end and another non-fixed end is called ray.
In this figure, AB is a ray.
The end A is fixed end or end point or initial point.
The end B can be extended.
A
B
A ray has an end point.
A ray has no length.
Example :
Write the names and types of these lines.
(a)
(c)
###### Solution :
- (a) AB; slant line
(c) MN; horizontal line
- (b) PQ; vertical line
- (d) OP; slant line.
Example:
Write names of these rays.
<>P
Q
(a)
Solution :
- (a) RayQP
- (b) Ray AB and Ray AC
- (c) Ray CA, Ray CB and Ray CD
##### \*. EXERCISE 55 ।
1\. Fill in the blanks:
(a) A line has end points, (b) A ray has end points.
(c) A ray has length. (d) A line segment has length.
(e) A has two end points.
2\. Write the names of these rays:
- 3\. Mark pairs of points A, B; C, D; E, F; and G, H and draw following:
- (a) Line AB (b) Line segmentCD
- (c) RayEF (d) RayHG
###### Angle
When two rays meet at a point, they form an angle. In this figure, ABC is an angle.
B is the vertex of angle. BA and BC are the arms of the angle.
While writing the name of an angle, the name of vertex is always written in the middle.
To denote angle, the symbol (Z) is written before the name of the angle.
So; angle ABC is written as ZABC. Sometimes, angles are also written by a single small letter, I ike a, bore.
The shaded portion shows the interiorofZABC.
Interior
The unshaded portion shows the exterior of ZABC.
Solid dots lie in the interiorofZABC.
Shaded dots lie in the exterior of ZABC.
Comparison of Angles
An angle can either be bigger or smaller than another angle. An angle can also be equal to another angle.
In thisfigure:
ZCBD lies in the interiorofZABD.
/. ZCBD < ZABD
ZABD lies at the exteriorof ZCBD.
Similarly, And,
In this figure; ZABC = ZDBE
.-. ZABC and ZDBE are called congruent angles.
Lab Activity
Trace ZABC and ZPQR on two different sheets of butter paper.
Put one sheet over another so that their vertices lie on each other. Compare these angles.
Take a sheet of paper and fold into two halves as shown here.
Unfold the paper and make two other folds as shown.
Make an outline of the shape.
Name Z1, Z2z Z3z Z4 and Z5
You can note following observations:
(a) Z1 = Z2
(b)
(c)
Z3 = Z4
Z5 < Z1
(d) Z5 isthesmallestangle
Measurement of an Angle
For an accurate measurement of an angle we need a protractor. You can find one protractor in your mathematics instruments box.
The protractor looks like a semicircle. It has scales written from 0 to 180.
Angle is measured in degrees.
A vertical line on a horizontal line makes an angleof 90°.
In this figure; ZABC = 90°
The angle measuring 90° is also called right angle.
Steps for measuring an angle.
0
Fig: Image of Protractor
Get Set Go With Sum Up Mathematics-5
- • Place the protractor above the angle so that the vertex of the
angle coincides with the centre of the protractor. ^
- • One arm of the angle should be in line with the base of the protractor.
- • The reading which coincides with another arm of the angle gives the value of the angle. g
ao 90 100
In this figure; ZABC = 60°
Types of Angles
Acute Angle: An angle which is more than 0° and less than 90° is called acute angle.
In this figure;
ZABC = 30°
0° < 30° < 90°
.-. ZABC is an acute angle.
Obtuse Angle : An angle which is more than 90° and u less than 180° is called an obtuse angle. a\\
In this figure,
ZABC = 120°
90° < 120° < 180°
120°
.-. ZABC is an obtuse angle.
Straight Angle: An angle which measures 180° is called a straight angle. In this figure;
ZABC = 180°
.-. ZABC is a straight angle.
180°
Example:
Look at these figures and write the type of angle shown by them.
###### Solution:
- ( a) Acute angle (b) Obtuse angle (c) Obtuse angle
- ( d) Right angle (e) Acute angle (f) Straight angle.
Drawing an Angle
Draw an angle which measures 60°.
© Draw a ray BC.
- © Place the protractor over BC so that the base I i ne of protractor is over BC.
- © Ensure that centre of the protractor is over B.
- © Mark a point A where the reading shows 60°.
© JoinAtoB.
© ZABC = 60°
###### Lab Activity
Things Required: Thick cardboard sheet, split pin, Process: Cut two equal strips of the cardboard sheet. Keep one strip over another and insertthesplitpin nearoneend.
##### EXERCISE 56 ^------------
1\. In this figures of pairs of angles which angle is smaller?
2\. Find the measurement of these angles.
3\. Identify acute angles, right angles and obtuse angles from these angle:
4\.
5\.
6\.
With the help of protractor, draw these angles:
(a) 30° (b) 55° (c) 75° (d) 80° (e) 105
What is the measure of each angle of an equilateral triangle?
What is the measure of each angle of a square?
What is the measure of each angle of a regular hexagon?
7\.
###### Parallel Lines
Have you seen a pairof railway line?
Even if you go from Kashmir to Kanyakumari, the two lines never meet.
When two lines are drawn; there are two and only two possibilities: The two lines interest each otheror
The two I i nes never i ntersect.
When two lines do not intersect each other even if extended to infinite length to any end, they are cal led parallel lines. Examples of parallel lines:
Opposite edges of the top of a rectangular table, or a book, or a ruler, or railway lines, etc.
Railway line
Edges of ruler
Electric wires on poles
© The distance between two parallel lines always remains the same.
Drawing A Parallel Line
\[1S2
©
©
©
©
©
©
Take a set square and a ruler.
Draw a line AB as shown in figure.
Position the set square on AB, as shown
Draw a line along the slanting edge of the set square.
Slide the set square along AB.
Draw another line along the slanting edge of the set square.
© Line CD and EFare parallel. © It is also written as CD | | EF
###### Perpendicular Lines
Which type of angle is made by a vertical flagpole with the horizontal ground?
The answer is— right angle.
When two lines are at right angles to each other, they are called perpendicular lines. Examples of perpendicular lines.
In this figure; AB and CD intersect each other at O.
We have;
ZAOC = ZCOB = ZBOD = ZAOD = 90°
Hence AB and CD are perpendicular to each other. ^^-------^\_
Here; OC is perpendicularto AB.
It is also written as OC ± AB
Similarly,OD±AB;AO±CDand BOZCD. v
D
- ###### (a) Drawing a perpendicular line at a point on it.
® DrawalineAB.
- © MarkapointCon line AB.
- © Place the set square so that one of its straight edges isalongthe line AB.
- ® The vertex of the set square should be one point C.
- ® Draw a I ine along another edge of set square to get a I ine segment CD.
® CD.LAB
- ###### (b) Drawing a perpendicular line from a point which is not on the line.
® DrawalineAB.
- ® Mark a point D which is noton the line.
- ® Position the set square so that one of its straight edges is along the line AB.
- ® Position the set square so that its another edge is touching the point D.
- ® Draw a line segment joining D with line AB.
® CD-LAB
### a
Lab Activity
Paper folding can be used for drawing parallel linesand perpendicular lines.
- (c) Drawing parallel lines
© Take a sheet of paper.
© Fold along one of the edges in straight line.
® Fold once again alongthe crease ofthefirstfold.
© Unfold the paper and you would get two parallel lines; as shown by dotted lines,
(b)
- (d) Drawing perpendicular lines
© Take a sheet of paper.
© Fold it into two halves.
® Fold again at right angles to the first fold.
® Unfold the paperand you would gettwo perpendicular lines.
(b)
(d)
(d)
##### J. EXERCISE 57 ^------------
- 1\. Tick (/) the pairof parallel lines in these figures:
(b)
- 2\. Tick(/) perpendicular lines in these figures:
3\. Which of these objects usually are perpendicularto the ground?
4\. Write (T) fortrue and (F) for false :
- (a) Two lines in a plane are either parallel or intersect each other.
- (b) If two lines are perpenducularthen they make acute angles.
- (c) Iftwo lines make right angles then they are perpendicular.
- (d) The distance between two parallel lines are always same.
- (e) Railway lines are examples of perpendicular lines.
###### Symmetry
If a figure can be folded along a line in two equal halves, then it is a symmetrical figure.
The line is called the line of symmetry or the mirror line.
Symmetry in 2-D Shapes
Following figures are symmetrical along the dotted lines.
FAC 1 1
(a) (b) <S (
(e) (f)
Many letters in the Alphabets are symmetrical.
Find those letters and write their names.
Symmetry in 3-D Shapes
Let us take the example of an apple.
-X—i—X- i
\\ / \\ / \\
No Symmetry^^^ \\\_\_\_\_
Get Set Go With Sum Up Mathematics-5
1 X I Z
1 X\_\_\_\_\_\_\_\_\_\_\_1\_\_\_\_\_\_\_\_\_\_\_z
1 x 1 z
1 X 1 z
! / --------Az------
1 / z ’ X
/ Z ' X
c) (d)
(g)
z A <—A
/ \\ /
Symmetry \\ \\ /
G=--
Let us take the example of a cone.
No Symmetry Symmetry
Let us take the example of a cylinder.
No Symmetry
Symmetry
##### EXERCISE 581
1\. Which of these figures are symmetrical? (a)
\[158
(c)
(e)
(g)
(b)
(d)
(f)
(h)
2\. Which of these letters are symmetrical?
(d)
# W M J
Which of these figuresshowthecorrect mirror line?
4\. Which of these numbers are symmetrical?
Mirror Image
A mirror image is similar but opposite. Let us take example of your hand as seen in mirror. Your right hand looks like the left hand ofyour mirror image.
Look at some other examples of mirror images.
###### Lab Activity
Take a square sheet of paper and fold it to make four quadrants.
##### M. EXERCISE 59 f
Drawthe mirror lines (if possible) forthesefigure.
##### Rxea and Volume
We often need to measure area, volume and perimeter of various things, for various
purposes.
Perimeter: The length of a boundary of a figure is called perimeter.
Area: The surface covered by a figure is called area.
Volume: The space occupied by something is called volume.
Look at these figures:
In other words, perimeter is the sum of the lengths of the sides of a polygon.
Perimeter of a Rectangle
ABCD is a rectangle; in a rectangle opposite sides are equal.
Hence, AB = DC and; BC = AD
•
Perimeter of rectangle ABCD
A
B
= AB + DC + BC + AD
= AB + AB + BC + BC
= 2AB + 2BC
c
D
= 2 (AB + BC)
If AB = DC = Length and BC = AD = Breadth.
Then, perimeter of Rectangle = 2 (length + Breadth) A
Perimeter of a Square
ABCD is a square
Hence, AB = BC = DC = AD
Perimeterof square ABCD R
D r
AB + BC + DC + AD
AB
BC = DC = AD = Side of square
Perimeterof square = 4 x side
###### Example:
The length and breadth of a rectangle are 25 cm and 20 cm respectely. Find its perimeter.
###### Solution :
Length = 25 cm
Breadth = 20 cm
Perimeter = 2 (Length + Breadth) = 2(25 + 20) = 2 x 45 = 90 cm
25 cm
E
B
D
Example:
The side of a square is 4 cm. Find its perimeter.
Solution :
A
4 cm
R
Side = 4 cm Perimeterofsquare = 4 x side
E
u
E u
= 4x4
"T
= 16 cm
c
4 cm
D
###### Example:
The perimeterof a square shaped carrom board is 320 cm. How long is one side of the carrom board?
Solution:
Perimeter = 320 cm
.•. 4 x side = 320 cm
or. side = —— =80cm
4
Example:
Ramlal wants to fence his rectangular garden by a rope. The garden is 200 m long and 175 m wide. What is the length of the rope needed to fence the garden?
Solution:
Length = 200 m
Breadth = 1 75 m
1 75 cm
Perimeter of garden = 2 (length + breadth) = 2 (200 + 1 75) = 2 x 375 = 750 m
E u o o CM
Example:
C
A cushion cover is in the shape of a square, with each side measuring 22 cm. What will be the cost of putting fan along the boundary of cushion cover, iffan sells at? 2.50 per cm?
Solution:
Side = 22 cm Perimeter = 4 x side = 4 x 22 = 88 cm
Now, Cost = Rate x Perimeter
= 2.50 x 22 = ?55
A,-------------, B
D 22 cm
##### EXERCISE 60
1\. Find the perimeteroffollowingfigures :
Find the perimeter of these rectangles :
- (a) Length = 12 cm and Breath = 8 cm
- (b) Length = 55 cm and breath = 45 cm
- (c) Length = 7 cm and breath = 4 cm
Find the perimeter of squares whose sides are given below:
- (a) 6 m (b) 7 cm (c) 1.5 cm
(d) 2.5 cm
- 4\. Perimeters of squares are given below. Find their sides:
(a) 280 m
(b) 764 m
(c) 884 cm
(d) 120 cm
- 5\. A gardener needs to buy 1440 m long wire for fencing his garden. What is the length of each side of this square-shaped garden?
- 6\. A room is 72 inches longand 60 inches wide. Find the perimeter of the room.
- 7\. A box of a gift is 15 cm longand 12 cm wide. Find the length of the ribbon which is to be wrapped around it.
- 8\. A race track is made around a rectangular park. The park is 300 m long and 150 m wide. What is the length of the race track?
- 9\. Raju wants to put adhesive tape on the edge of a photo frame. The photo frame is 32 cm longand 24 cm wide. Find the required length of tape?
- 10\. The series of diwali bulbs sell is at ? 25 per metre. Mohan wants to decorate his roof top with these bulbs. The rooftop is 18 m long and 10 m wide. How much series bulbs Mohan needs to buy for decoration?
- 11\. A cyclist makes 4 rounds of a square shaped playground. Each side of the playground is240m. What isthedistance covered by the cyclist?
###### Area
(a) Comparison of sizes :
Look atthis figure :
(ii)
(iii)
Figure (i) shows a square.
Figure (ii) shows a big square which is made by four squares which are of the same sizeas in fig (i)
Fig (iii) shows a rectangle which is made of four squares which are of the same size as in fig (i).
it isclearthat;
Area in fig (i) < Area in fig (iii)
Area in Fig (ii) = Area in fig (iii)
Area in Fig (ii) = Area in Fig (iii) = 4 x Area in fig (i)
Let us take example of one surface of a Rubik's cube.
The whole surface shows a square.
This square is composed of 16 small squares.
Standard unit of Area: If the sides of a square are 1 unit. Then area is a 1 square units.
In case of the surface of the Rubik's cube, let us assume that the side of smal ler square is 1 cm.
Then area of smaller square = 1 square cm.
As, there are 16 small squares on the surface, hence area of the whole surface of Rubik's cube = 16 square cm.
Find the Area Using Square Paper
Square paper can be easily used for finding approximate area of a given figure. For this, you need to fol low these steps:
Stepl: Countthe number of complete squares.
Step 2: Countthe number of squares which are covered more than half by the figure.
Count them as 1 complete square.
Step 3: Countthe half filled squares and count them as half.
Step 4: Don't count less than half filled squares.
Step 5 : Sum of squares in steps 1,2 and 3 gives the area of the given figure.
Example:
Find the area offol lowing figures: (Note: Area of each square-1 sq cm)
###### Solution:
- [(a) Number of fully filled squares=5](#bookmark625)
.•. Area = 5 square cm
- [(b) Number of fully filled squares=6](#bookmark626)
[Numberofhalffilled squares=4](#bookmark627)
4
Area = 6 + — = 6 + 2 = 8 sq cm
- (c) Numberoffully filled squares = 2
Numberof more than half filled squares = 3
Numberofhalffilled squares =2
2
.-. Area =2+3+y=2+3+1 = 6 sq units
- (d) Numberoffully filled squares = 10
[Numberof halffilled squares=5](#bookmark628)
- [.-. Area = 10 + — = 10 + 2.5 = 12.5 sq cm 2](#bookmark629)
- [(e) Numberoffully filled squares=4](#bookmark630)
Numberof more than half killed squares = 6
Numberofhalffilled squares = 2
2
.-. Area = 4 + 6 + y = 10 + 1 =11sqcm
(J. EXERCISE 61 ^---
- 1\. Findtheareaoffollowingfigure:
(Area of 1-square = 1 sq cm)
(a)
(b)
(c)
###### Conversion of the Units of Area
Suppose area of a field is given in square metre and you need to convert in square centimetre, then how would you do it?
We know,
1 m = 100 cm
1 sq m = 1 x 1 m = 100 x 100 sq cm = 10000 sq cm
###### Units of Area
1 sq cm
1 sq m
1 sq km
100 sq mm
10000 sq cm
1000000 sq m
###### Example:
Convert4 sq m into sq cm.
Solution:
- 4 square metre
= 4 x 1 sq m
1m = 100 cm
.-. 4 sq m = 4 x 100 x 100 sq cm
= 40000sqcm.
Example:
Convert 3600 sq m in sq decametre.
Solution:
3600 sq m
\- 3600 x w^w
\[168
= 36 sq decameter
###### Lab Activity
1
2
3
4
5
10
9
8
7
6
11
12
13
14
15
20
19
18
17
16
Draw a rectangle ABCD with length 5 cm and breadth 4 cm.
Divide length AB into 5 partsand width BC into4 parts.
Each part of AB and BC should be 1 cm long make a grid as show in this figure. Countthe numberof small squares.
Number of small squares = 20
Side of small square = 1cm
Areaof small square = 1 x 1 = 1 sq cm
Numberof squares = 20
AreaofRectangle = Length x Breadth
= 5 x 4 = 20sq cm
Thus, area of rectangle is equal to the number of small squares.
In these figures count the number of small squares and verify the formula of area of rectangle.
##### St. EXERCISE 62
Convert :
- (a) 5sqm intosqcm
(b) 3 sq cm intosq mm
(d) 10000 sq cm i nto sq m
(c) 400sq mm intosqcm
(3.
Calculate area of rectangle whose lengths and breadths are given :
- (a) Length = 7cm; Breadth = 6 cm (b) Length = 18 cm; Breadth = 12 cm
(c) Length = 75 cm; Breadth 50 cm (d) Length = 120 cm; Breadth = 100 cm
Find the area of square whose sides are given below :
(a) 12 cm (b) 6 m
(c) 14 cm
(d) 15m
4\.
5\.
6\.
The length of a carpet is 4 m 75 cm and its width is 60 cm. Find the area of carpet.
A square board of ludo has a side measuring 35 cm. What is its area?
A squares side is 12 cm long; while a rectangle's sides are is 15 cm long and 9 cm wide. Which of these is bigger in area?
- 7\. A square field is 80 m long. What is its perimeter and area?
- 8\. The perimeter of a garden is 90 m. If the garden is 20 m wide; find the area of the garden.
- 9\. The perimeter of a square is 60 cm. Find the area of the square.
- 10\. A wall is 10 m high and 50 m long. A brick is 10 cm long and 5 cm wide. How many bricks are there in the wall if the thickness of the wall is same as that of a brick?
Let us take a small cube with each side = 1 cm
Then volume of cube = 1x1x1 cubic cm
- = 1 cubic cm
Now let us use the small cube to make bigger cubes and cuboids.
Lab Activity
Two cubes of sides 1 cm each are kept to make a cuboid. Here, volume of cuboid = 2 x Volume of cube
= 2x1 cubiccm
= 2 cubic cm
Similarly, use 5 cubes to make cuboid.
1 cm 1 cm
1 cm 1 cm
5 cm
Volume of 1 cuboid
= 5 x volumeofcube
5 x 1 cubiccm
- 5 cubiccm
a)
Now, use 20 cubes to make cuboid
Volume of cuboids in one row = 5 cubic cm
.-. Volume of cuboid in 4 rows =4x5cubiccm
= 20 cubic cm
Let use small cubes to make a bigger cube as shown here. Take 3 rows of 3 cubes each.
Make 3 layers of such rows
Volume of one row of cubes.
= 3 cubic cm
Volume of 1 layer of 3 rows of cubes
3x3 cubiccm
9 cubic cm
Volumeof 3 layersof 3 rowsofcubes = 3x9cubiccm = 27cubiccm
Based on above activities we can drive following formulae.
Volume of cube = side x side x side
Volume of cuboid = length x width x height
###### Conversion Table for Units of Volume
1000 cubic mm = 1cucm
1000 cubic cm WOOcubicdm
1 cu dm
1 cm m
Example:
Convert:
- (a) 2 cu cm intocu mm
(b) 5 cm m intocu cm
Solution:
- (a) 2 cu cm
= 2x 10x 10x 10cumm = 2000 cu mm
(b) 5 cu m
= 5 x 100 x 100 x WOcucm
= 5000000 cu cm
Example:
A brick is 16 cm long, 5 cm wide and 3 cm thick. What is the volume of the brick?
Solution:
Length = 16cm
Breadth = 5 cm
Height = 3 cm
Volumeofcuboid =lxbxh
= 16x5x3 cubiccm
= 240 cubic cm
Example:
A book is 18 cm long, 11 cm wide and 4 cm thick. What is the volume of the book?
Solution:
length = 18 cm
Breadth = 11 cm
Height = 4 cm
Volumeofcuboid = I x b x h
= 18x11 x 4 cubic cm
= 792 cubiccm
Example:
Sideofacube is 6 cm. Find the volumeof cube.
Solution:
Side = 6 cm
Volume of cube = side x side x side
= 6x6x6 cubiccm
= 216cubiccm
Example:
Side of a cube is 4 cm. It is melted so form a smaller cube of side 2 cm. How many smal ler cubes are formed?
###### Solution :
Side of bigger cube
4 cm
Volume of bigger cube = 4x4x4cucm = 64 cu cm
Side of smaller cube = 2 cm
Vol ume of smal ler cube = 2x2x2cucm = 8 cu cm
. Volume of bigger cube
No. of smal ler cubes = ------------—------- Volume of smaller cube
= = 8 cubes.
8
##### K EXERCISE 63 ^------------
- 1\. How many cubic centimetres are there in one cubic meter?
- 2\. How many cubic millimeters are there in one cubic centimeter?
- 3\. Convert:
- (a) 0.5cu m intocucm (b) 15000cumm intocucm
- (c) 180000 cu cm into cu m
- 4\. Calculate the volumes of cuboids whose dimensions are give below:
- (a) Length = 8 cm, breadth = 4 cm and height = 2 cm
- (b) Length = 12 cm, breadth = 10 cm and height = 5 cm
- 5\. A cuboidal tank is 15 m long, 8 m wide and 4 m deep. How much water can the tank hold?
- 6\. Find the volumes of cubes whose sides are as follows:
- (a) 2 m (b) 4 cm (c) 15 cm
- 7\. The volume of a cubical box is 512 cubic cm. Find the measurement of its sides.
- 8\. A swimming pool is 3 0 m long and 10 m wide. If there is 30,00,000 litre water in pool, what is the depth of water in the pool?
###### Perspective View
While looking a picture how do you know what is nearer and what is farther?
Look at the pictures given above. A thing which is nearer looks bigger than a thing which is farther.
This happens because things appear smaller when they move away for from us. We know that the sun is much bigger than our earth, yet the sun looks very small because it is too for from us.
Vanishing Point
Have you seen a railway line? We know that the two railway lines never meet but they appear as if they are meeting at the horizon. The point at which the lines appear to meet is called the vanishing point.
In fact, painters use the knowledge of vanishing points to create an illusion of depth in their paintings. Look at fol lowing pictures to understand vanishing point.
Perspective and View Point
Perspective of on object changes with change in the view point. To understand this let us take the example of the fol lowing figure of a simple skyscraper.
Viewed from ground
Different views of a Car
Perspective of a Cube
Took a cube and look at it from different angles to understand the change in
Different Perspectives of a glass
Different perspectives of a bus
Floor Maps
When architects make a plan for a house, they make floor maps. A floor map gives aercal view of the house if roofs are removed. You can collect floor maps from internet to see different examples. One example is given here.
Stairs
This floor map shows the following:
- • 2 Bedrooms
- • 2 Balconies
- • 1 Lobby
- • 1 Kitchen
- • 1 Studyroom
- • 1 Stair
Deep Drawing
While a floor map gives the idea of number of rooms and some other facilities, a deep drawing shows how will the house look in reality, following is the example of deep drawing.
In this drawing, you can see balconies, doors and windows.
##### Bi EXERCISE EM ^
Find the vanishing point in following pictures :
Which of these drawings has perspective?
4\.
5\.
- 6\. Draw a railway line with perspective.
- 7\. Draw a floor map of your house.
###### Nets of Solids
Net of a cube
® Take an empty carton of tooth paste.
® Open from the top and bottom
® Open from the side.
® Spread the net.
(5)
Trace the following net and makeacube.
###### Making a Cylinder from the Given
® Cut a rectangular piece of paper of any size.
® Fold the sheet to make a hoi low cyl inder.
Fold along the shorter side
fold along the longer side
###### Make a cylinder with top and bottom.
® Make a rectangle of 10 cm x 11 cm
® Make two circles near each side of 11 cm. The diameter of the circle should be 3.5
cm.
® Cut the shape out. Ensure that the circle does not come off.
® Roll italongthe side measuring 11 cm.
® You will getacylinderwithtopand bottom.
###### Making a Cone
- ® Make a triangle, with the base measuring 11 cm. Remaining two sides of the triangle should be of equal length.
- ® Draw a circle of diameter 3.5 cm.
- ® Cut outthe shape.
- ® Fold alongthe slant height
- ® You will get a cone with a base.
##### EXERCISE 65
- 1\. Match the object with the correct net:
Trace the following net on a paper. Cutout windows from the shaded area. Make the
cuboid.
- 3\. Trace the following net on a paper. Cut out windows from the shaded area. Make the
##### rapotteKiw
Patterns in Square Numbers
® 1x1=1
1+3=4
® o oo
2x2=4
4 + 5= 9 or, 1 + 3 + 5 = 9
® O ® oo# ® ® ®
® o ® o oo® o ® ® ® o oooo
3x3 = 9
9 + 7= 16 or, 1+3 + 5 + 7=16
4x4 = 16
16 + 9= 25 or, 1+3 + 5 + 7 + 9 = 25
® O ® O ® oo® o®
®®®O® 5x5 = 25 oooo®
® ® • • •
1 square is equal to 1.
###### Try This : ------------------------------
1 + 3 + 5 + 7 + 9+11 = ?
1+3 + 5 + 7 + 9+11+13 = ?
1+3 + 5 + 7 + 9+11+13 + 15 = ?
- 2 square is equal to sum of first two odd numbers.
- 3 square isequal to sum offirst three odd numbers.
- 4 square isequal to sum of first four odd numbers.
- 5 square isequal to sum of first five odd numbers.
n square isequal to sum offirst n odd numbers.
2 x 2 - 1 x 1 = 3
- • • \_ n = • •
- • O U •
3x3-2x2 = 5
- • •• nn •••
- • OO - = •
- • OO •
4 x 4 - 3 x
3 = 7
• •
• O
• o
• o
• • oo oo oo
• • • •
Let us analyse these numbers: 1x1=1 and 9x9 = 81 2x2=4 and 8 x 8 = 64 3x3 = 9 and 7 x 7 = 49 4x4 = 16 and 6x6 = 36 5x5 = 25
10 x 10 = 100
(Number at units place is 1)
(Number at units place is4)
(Number at units place is 9)
(Number at units place is 6)
(Numberat units place is 5)
(Numberat units place is 0)
All square numbers have any of these numbers at units place.
1,4, 9, 6, 5 and 0
This means that following number, can never be at unit's place of a square number:
- 2, 3, 7 and 8
But it is not necessary that a number ending with 1,4, 5, 6, 9 and 0 is a square number.
Example:
Express following square numbers as the sum of consecutive odd numbers.
- (a) 36 (b) 16
Solution:
- (a) 36 = 6 x 6
/. 36 is the sum of first 6 odd numbers
/. 36 = 1+ 3 + 5 + 7 + 9 + 11
- (b) 16 = 4x4
/. 16 is the sum offirst4odd numbers.
/. 16 = 1+ 3 + 5 + 7
Example:
Without actual addition, find the sum:
1+3 + 5 + 7 + 9 + 11+13 + 15
Solution:
This shows the sum of first 8 odd numbers.
/. 1+3 + 5 + 7 + 9+11+13 + 15 = 8x8 = 64
Example:
By looking at the pattern, complete:
[25 - 16 =9](#bookmark665)
[36 - 25 =11](#bookmark666)
[49 - 36 =1 3](#bookmark667)
###### Solution :
25-16 = 5 x 5-4 x 4 = (5 + 4)(5-4)
= 9x1=9
36-25 = 6x6 = 5x5 = (6 + 5)(6-5) = 11x1=11 49-36 = 7 x 7-6 x 6 = (7 + 6)(7-6) = 13 x 1 = 13
/. Next two patterns 8 x 8-7 x 7 = 15
9x9-8x8 = 17
Example:
Which smallest number should be subtracted from these numbers to make it a perfect square?
- (a) 40 (b) 70
Solution:
(a)
and
6x6 =36
7x7 =49
Here, And
36 < 40 < 49
40-36= 4
or,
40-4 = 36
4 subtracted from 40, makes it a perfect squares.
(b)
And
8x8 =64 and 9x9 = 81
64 < 70 < 81
70-64 = 6
/. 6 subtracted from 70, makes it a perfect square.
##### J. EXERCISE 66 ^----
- 1\. Find the next square number.
- (a) 144 (b) 196
- 2\. Find the previous square number.
- (a) 81 (b) 196
- 3\. Find a square number between 40 and 50.
- 4\. Express these square numbers as the sum of odd numbers.
- (a) 49 (b) 169 (c) 121
Get Set Go With Sum Up Mathematics-5
a
Without actually adding, find the sum :
- (a) 1+3 + 5 + 7+11 + 13
- (b) 1+3 + 5 + 7 + 9+11+13 + 15 + 17+19
Find values :
(a) 11x11-10x10
- (c) 25 x 25-24 x 24
(b) 15x15-14x14
- (d) 36 x 36-35 x 35
- 7\. Complete thefollowing :
- [(a) 64 - 49 = 15](#bookmark672)
[49 - 36 = 13](#bookmark673)
[36 - 25 = 11](#bookmark674)
- (b) 8x8 = 1+ 2 + 3 + 4 + 5 + 6 + 7 + 8 + 7 + 6 + 5 + 4 + 3 + 2 + 1 7x7=1+2+3+4+5+6+7+6+5+4+3+2+1
- 8\. Which ofthe follow can never be a square number?
- (a) 625 (b) 225 (c) 522 (d) 123 (e) 197
- 9\. Find all square numbers between :
- 1 and 50.
- 10\. What is the smallest number needed to be added to 200 to make it a perfect square?
###### Triangular Numbers
Lookatthefollowing numbers :
1+2 = 3 1+2 + 3 = 6 1+2 + 3 + 4 = 10 1+2 + 3 + 4 + 5 = 15
So, triangular numbers can give us the following pattern.
1( + 2), 3( + 3), 6( + 4), 10( + 5), 15( + 6), 21(+7), 28( + 8), 36
More Interesting Properties of Triangular numbers
1x2
IstTriangular number = —-—= 1
2x3
2nd triangular number = —-—= 3
3x4
3rd triangular number = —-—=6
4x5 n
4the triangular number = —-—= 10
5x6
5th triangular number = —-—= 15
###### Look at the following property of triangular numbers
Sum of any two consecutive triangular numbers isasquare number. Let us illustrate with following figures.
10 + 15 25
Let us observe following patterns:
1 sttriangular number is 1 and 1 x9 + 1 = 10 is atriangular number.
2nd triangular number is 3 and 3 x 9 + 1 = 28 isatriangularnumber.
3rd triangular number is 6 and 6x9 + 1 =55 isatriangularnumber.
###### Pascal's Triangle
Blaise Pascal, who invented the early calculators, gave the interesting pattern of numbers. It iscalled Pascal's triangle.
Let us observe the fol lowing pattern :
Some interesting observations in Pascal's Triangle.
1
Counting numbers
Triangular numbers
The second diagonal of Pascal's triangle has counting numbers.
The third diagonal of Pascal's triangle has triangular number. Sum of numbers in a row is double the sum of numbers in previous row.
###### Example:
Find the next triangular number:
45, 55, ....
Solution :
55-45 = 10
.•. Nexttriangular numbercan be calculated as follow:
55 + 11 =66
Example:
You have 15 candies. Arrange them in two patterns of triangular number.
Solution : \#
- • •
Arrangement 1 :
Arrangement 2:
###### Example:
Which isthe6th triangular number:
Solution:
6x7
6th triangular number = —-— = 21
##### U- EXERCISE 67 ^—
- 1\. Write the nexttriangularnumber: 210,231...
- 2\. Make two triangular patterns, by using 28 marbles.
- 3\. Write the 250th triangular number.
- 4\. Write the 25 the triangular number.
- 5\. Write next row in the Pascal's Triangle.
1 6 15 28 15 6 1
6\. Write (T) fortrue and (F) for false
(a) Sum of two consecutive triangular number gives a square number.
(b) Third diagonal in Pascal's triangle shows counting number.
(c) Second diagonal in Pascal's triangle shows triangular number.
(d) 10th triangular number + 11 = 11th triangular number
###### Border Strips
We can use reflection and rotations of geometrical patterns to create borders. Borders give interesting touch to floors, walls carpets, saris, etc.
- 1\. Use of Reflection
(c)
(b)
PSPSPSPSPSPSPSPSPS
(d)
2\.
3\.
e a
e a
e a
e a
e a
e a
e a
e a
e a
###### Tiling Patterns
Look at fol lowing tessellations.
##### K EXERCISE 68 ^-----------
Use following patterns to make tiles and borders.
(a) W
(b) D
(c) 9
Calculate and drawing informations from data is called data handling. You have already learnt about graph and pictograph in previous class.
###### Data
Data is the information in the form of numerical figures.
If one tells- "There are 11 players in a cricket team". It is a numerical information and is a data.
But if someone says "Ankit is dwarf"; as it is is not giving a numerical information hence it is not a data.
Collection and Recording of Data
Collection and recording of data can be done in several ways. Recording of data in different types of tablular form are given here.
Let consider a company. The management wants to know the age of its employees. It calls every employee and records their age. Age recorded on a sheet in years are recorded
From the above table you cannot give the answer of some question easily, like
- (a) How many employees are 22 years old?
- (b) How many employees are 42 years old?
- (c) What is the minimum age of an employee?
- (d) What is the maximum age of an employee?
Now arrange the data in ascending order.
Table-2
20 21 21 21
27 27 27 29
35 35 42 42
55 55 56 56
bZ ®
27 27
29 32
42 55
59 59
Get Set Go With Sum Up Mathematics-5
as fol lows :
Table-1
27
27
42
35
21
55
35
27
21
32
59
27
56
55
20
29
42
42
21
56
59
27
29
55
Arrangement of data in this style, has done in Table-2 is better. But writing in this way requires lot of time and concentration. Some data may be missed while the information is collectingfora large number of people.
After looking data in this type of table it is easy to answer the question about the maximum and minimum age of person as asked in question number 'e' and'd'. But to answer the questions like 'a' and 'b' again requires a more time as the data is about a large number of people.
Therefore, data are put in the another type of tabular form.
In th is table three columns are drawn. 1st column contains Age (in years), 2nd column contains tally and 3rd column has numberofemployees.
Table-3
Age (in years)
No. of employee
20
21
27
29
32
35
42
55
56
59
1
3
5
2
1
2
3
3
2
2
###### Table-4
In tally column ' |' stands for 1 and P^jJ stands for 5. This tabular form of data is more convenient.
Now seethe pictograph ic representation of data.
20 21 27 29 32 35 42 55 56 59
^ represents 1 employee
Get Set Go With Sum Up Mathematics-5
Age (in years) of employee—»
###### Two Dimentional Data
So far we 'were' discussing about the data, which has only one d i mention I, in other words, it had one type of data only like age.
But some data has more than one type of information. Such type of data are recorded in two dimentional way.
Observe the tabular form of data as given here-
###### Table—4
One Direction
Days Mon Tue Wed Thur Fri Sat
Sun
Eggs sold 100 150 120 240 100 150
(in dozen)
300
This is the example of one-dimentional data. This gives information regarding only one item that is eggs (sold) in week.
Now see the example of two dimentional data.
###### Table—5
c o
w
□
“O c o w o c/i
—> One Direction
Days
Item sold
Mon
Tue
Wed
Thur
Fri
Sat
Sun
Shirts
20
50
70
30
20
50
50
Trousers
40
40
70
50
50
100
40
Socks (in pair)
50
30
70
100
30
50
50
Shoes (in pair)
40
30
40
50
30
40
50
Table 5 gives information about the sell of more than one items in a week.
Now try to answer the fol lowing questions.
(a) How many shirts were sold on Sunday?
Ans. 50
(b) How many trousers were sold on Monday?
Ans. 40
(c) On which day maximum numbers of trousers sold?
Ans. Saturday
Now see the examples-
Example 1:
In the study room of Ankit, there were different items. He orgranised then in his room as given below:
Book
Pen
Pencil
Colours
Book
Pencil
Color
Pen
Book
Colours
Pen
Book
Colours
Colours
Book
Book
Pen
Colours
Book
Pencil
Pencil
Colours
Pencil
Pen
Pencil
Colours
Book
Pen
Colors
Colours
Pencil
Pencil
Pencil
Pencil
Pen
Pencil
Pen
Book
Pen
Book
Make a tabular form for these items and the fol lowing questions. Draw a pictograph also.
- (a) How many books does Ankit have?
- (b) How many pencil does he have?
- (c) How many items are equal in number?
- (d) What is the difference between pencils & colours?
- (e) How many total items he have?
Solution:
Ankit's study room
Name of items
Tally
Number of items
Book
10
Pen
rw mi
9
Pencil
rw rw i
11
Colours
rw rw
10
- (a) 10.
- (b) 11.
- (c) Booksand colours.
- (d) 11-10 = 1.
(e) 10 + 9 + 11 + 10 = 40.
Book
Pen
Colours
Here 1 ^. represents 1 item.
###### Example 2:
The following table shows the number students studying different subject in different schools.
Subject/School
English
Math
Science
Hindi
SST
Red Roses School
700
400
500
200
600
St. Marry School
500
400
600
300
200
City Academy
800
400
300
400
100
Gyan Bharti
500
900
600
700
200
- (a) How many students of science are in Gyan Bharti?
- (b) In which subject Red Roses School has maximum number of students?
- (c) What isthe total number of students in City Academy?
- (d) In which subject St. Marry School has minimum numbers of students?
Solution:
- (a)
Subject/School
English
Math
Science
Hindi
SST
Red Roses School
St. Marry School
City Academy |
Gyan Bharti -----------------------------► 600
- (b) English - 700 students
(c) 800 + 400 + 300 + 400 + 100 = 2000
- (d) SST — 200 students on ly
##### EXERCISE 69 ^-------------
- 1\. The fol lowing data shows numberof pens with various students in a class:
4,5,2,3,1,5,2,2,3,3,2,4,5,43,1,1,1,1,2,2,3,4,4,5,2,2,2,2
Tally these data and then make a pictograph.
- 2\. The fol lowing data shows pocket money of students of class 5.
- 50, 30, 30, 75, 50, 30, 30, 50, 50, 75, 30, 30 10,10,10, 20, 20, 30, 30, 50, 75, 20, 20, 50,50
Tally thesedata and then make a pictograph.
- 3\. The following table shows the quantity of different items at Ram lai's shop.
Items
Potato
Onion
Bringal
Cabbage
Carrot
Chilli
No. of items
80
60
50
40
20
10
Make a pictograph using this data and answer these questions:
- (a) Which vegetable is in the least quantity?
- (b) Which vegetable is in the highest quantity?
- (c) How much carrot is in stock?
- (d) Which item is in least demand?
- 4\. Raju Stationary Stores has following items in the shop:
Items
Pen
Pencil
Sharpner
Craysons
Glue
Tape
Quantity 2000 3500 1200 4800 900 600
Make a pictograph using this data and answer fol lowing questions:
- (a) Which item is least in stock?
- (b) Which item has the highest stock?
- (c) How many pensand pencils are there?
- (d) How many glues are in stock?
- 5\. Ferns & Petals is a store which sells flowers. The following table shows the stock of different flowers.
Flower
Rose
Marigold
Jasmine
Tulip
Dahlia
Number
250
150
500
120
70
- 6\. The fol lowing table shows the number of goals scored by different players.
Make a pictograph from this data and answer following questions :
- (a) Who is the highest scorer?
- (b) Who scored the least number of goals?
- (c) What is difference in goals scored by Pele and Mardona?
Players
Maradona
Messi
Ronaldo
Rivoldo
Pele
Goals
18
20
16
14
12
(d) What is the total number of goals?
###### Bar Graph
While pictographs look quite interesting, it is not suitable for representing many types of data. Moreover, a nice pictograph needs the help of a highly skilled artist.
Bar graphs are easy to makeand sometimes, more convenientto interpret.
Drawing a Bar Graph
(a)
(b)
(c)
(d)
(e)
(f)
Draw two axes which are mutually perpendicular to each other.
Divide both axes in different parts, based on the type of date.
Mention one variable on the x-axis and another variable on the y-axis.
Write the heading of the bar graph.
Write units (if any).
Bars can made vertical and horizontal, but vertical bars are usually preferred.
Example:
Study the following bar graph and answer the questions.
- (a) Which day sees the maximum children in park?
Ans. Saturday.
- (b) What is the possible reason of good crowd on Saturdays?
Ans. Halfday or school closed.
- (c) Which day sees the least number of children in park?
Ans. Wednesday.
- (d) On which two days, there are equal numberof children inthepark?
Ans. Monday and Thursday.
Example:
The following table shows the number of birds in the birdhouse coming on different days. Make a bar chart from th is data.
Birds
55
60
45
35
75
20
30
Day
Mon
Tue
Wed
Thu
Fri
Sat
Sun
Solution :
##### |\]k EXERCISE 70 ^-------------
- 1\. Read the following graph and answerthe questions based on them.
- (a) Which is the costliest item?
- (b) Rohit buys one cake and 10 pastries. How much money he has to pay? (c) What is the price of a box which contains 5 cookies?
- 2\. Read the fol lowi ng graph and answer the question based on then :
No. of People born
- (a) Which month sees the least number of birthdays?
- (b) Payal sends birthday greetings to all these people. In which month does she sends the maximum numberof birthday greetings?
- (c) If this data shows the birthday of students of Bal Vidayalaya, then how many students are born in these six months?
3\. Make a bar graph using following table:
(a)
Weight
35
30
40
25
20
No. of Boys
12
15
18
20
22
^^ Sports
Football
Cricket
Hockey
Kabaddi
Badminton
Participants
40
100
30
20
50
Cars
Maruti
Honda
Fiat
Tata
Hyundai
Number
5000
2000
2500
4500
3000
(d)
Plant
Banyan
Peepal
Rose
Dahlia
Maize
Qunatity
100
80
10
10
20
Pie Chart
In a pie-chart data is shown as different parts of a circle. Since it looks like a pie so the name pie-chart is given to it. Followingexample shows a pie-chart.
Observations from this pie chart.
© Rice is consumed the most.
© Dal and vegetables are eaten equally.
Continuous Growth Chart: When a particular data increase at every fixed interval of time, it is shown by continuous growth chart. Let us take example of following chart.
Following observations can be made from this growth chart.
There is continuous growth in population.
The population was 20 lakh in 2000.
The population was double to 40 lakh in 2004.
. EXERCISE 71
This pie-chart shows the items in breakfast of Motu. Answerthe following questions :
- (a) Which is the most favourite item Motu.
- (b) How many sweet items Motu eats?
- (c) What is the total number of items in his plate?
- (d) Which items are in equal numbers?
2\.
Look at fol lowing chart and answerthe questions which follows:
Growth of a baby panda
Months ^ 1 2 3 4 5 6
- (a) How much a baby panda weighs after one month of its birth?
- (b) Between which two months the weight remains the same?
- (c) What is the weight of a 6 month old Panda?
Answer the fol lowing question :
- 1\. Write the number names.
- (a) 25412 (b) 30215 (c) 265721 (d) 282910
- 2\. Write the following numbers in figures.
- (a) Two lakh three thousand forty one
- (b) Sixty nine thousand twenty five.
- (c) Sixteen lakh forty one thousand three hundred ninty six.
- (d) Eleven thousand two.
- 3\. Write the following in Hindu-Arabic numerals.
- (a) XXXVIII (b) CCXXVI (c) MCVI (d) CMXI (e) XCV
- 4\. Write the following in Roman-numberals.
- (a) 68 (b) 98 (c) 105 (d) 47
- 5\. Write the following numbers in expanded form.
- (a) 639059 (b) 8020034
- 6\. Find the difference of place value of 5.
- (a) 5216051 (b) 7352015
- 7\. Counting by hundred write the numbers between.
- (a) 68715 and 69015 (b) 759610 and 76010
- 8\. Write the greatest numberof 5 digit.
- 9\. Write the smallest number of 8 digit.
- 10\. Write the successor of:
- (a) 597609 (b) 7755215
- 11\. Write the predecessor of:
- (a) 125010 (b) 252001
- 12\. Write following numbers in ascending order:
200305, 200201, 555011, 201301, 19511
- 13\. Write the following numbers in descending order:
55007, 21512, 69543, 43215, 65432
- 14\. In each of the following replace \* by >, < or = to make the sentence true.
- (a) 55605 \* 55759 (b) 22215 \* 19613
(c) (2 7515 + 3 01)\*2 7816 (d) (16211 - 15) \* 1610 7
- 15\. Using the test of divisibility, state which of the following numbers are divisible by 4 by 9:
- (a) 7251116 (b) 7254306
- 16\. Write a 5-digit number which is divisible by 2 butnotby4.
- 17\. (a) Find the smallest numberthat rounds to 600
- (b) Find the greatest numberthat round to 600.
- 18\. If the cost of a table is ? 6755. Estimate the cost of 9 such tables.
- 19\. Estimate the cost of one shirt if the cost of 8 shirt ¡5^782.00.
- 20\. Frame a word problem for the number sentence.
210 + 515 = ?
- 21\. Find the HCF ofthe following:
- (a) 75,90 (b) 112,510 (c) 84,24
- 22\. Find the smallest numberwhich isexactlydivisibleby25, 35and 70.
- 23\. Find the least length which can be cut into whole number of pieces of lengths 40m, 25m and 20 m.
- 24\. Find the difference between 970051 and 769895.
- 25\. Total votes polled in a election was 270593. If Jatmal Hawani defeated his nearest rival Moha Ambran by 67230 votes. How many vote were polled in favour of Jatmal Hawani?
- 26\. Which ofthefollowingare prime numbers?
- 3, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20
- 27\. Reduce the following to lowest tens :
28\. Express 4— asan improper fraction.
5 6
- 29\. Find the degree of closeness of — toy.
15 ' 19
31\.
32\.
Which is smaller?
2 2
19 ' 19
Multiply:
(a) x 2
(b) y x 14
#### <a) 26
(b) y- 5
Amit gave account?
2
— th rupees to his wife. If he has ^16598.00. How much is left in his
- 35\. Express as decimal fraction :
- (a) 0.4 (b) 0.005
- 36\. Express in expanded form :
- (a) 3.5 (b) 20.19
- 37\. Choose decimals from bracket equivalent to the given number:
- (a) 6.9 (6.92,6.90,6.09) (b) 20.09 (2.009,200.9,20.090)
- 38\. Add 20.30 and 19.03.
- 39\. Subtract 20.30 from 21.01.
- 40\. Multiply 35.12 by 7.
- 41\. Divide21.2 by4.
- 42\. A bottle contain 20 litre of milk. How much milk is there in 20 such bottles?
- 43\. A pen contain 85 ml of milk. How much milkthere in such 10 pans?
- 44\. How many— litre bottle can be filled from a can containing 20.5 litres of petrol?
- 45\. Divide 190.75 I itre of mi Ik among 7 persons equally.
- 46\. A shopkeeper has 264.325 kg of sugar. If he sell 1 32.300 kg to a person, how much sugar is left with him?
- 47\. Ashok starts for the college at 9.45 a.m. and returns home at 3.00 p.m. It took 60 minutes in goingand returning. How much longdid he stay at col lege?
- 48\. Ankit purchased 4 pens at ^3 6.2 0 per pen. He sold them at?37.00 per pen. What was his earning?
- 49\. Rahul purchased 2 shirts for ?2715.25 and a pair of shoes for ^1210.20. How much did he spend?
- 50\. A person clear?6715.20 per month. What is his yearly income?
- 51\. If the yearly income of a person isd 5303.00, calculate his monthly income.
- 52\. The cost of 14 pens is ^284.90. Calculate the cost of such 8 pens.
- 53\. Which is greater: the difference of 6950 and 5850 orthe sum of 1275 and 8690?
- 54\. Which is smaller: the sum of 3290 and 4810 or difference of 8930 and 831 ?
- 55\. What should be added to the difference of 8930 and 830 to get 9000?
- 56\. Give two prime numbers whose sum is also a prime number.
- 57\. Can a sum of two odd prime number be also a prime number?
- 58\. Write 10 prime numbers.
- 59\. Ifthecostof 1 kg of rice isd 2.75, what will bethecostof 500 kgof rice?
- 60\. Which is the even prime number?
- 61\. Ifthecostof5 litre of milk is?75.00, whatwill bethecostof 1.2 litreofmilk?
- 62\. Convert into metres and add 7 m 20 cm, 15 m 25 cm and 1 7.5 m.
- 63\. Rahul bought 0.6 metre of cloth at the rateof?20.50 per metre. How much money did he spent?
- 64\. Convert into kilogram: 2595 gm.
- 65\. Convert into kilogram and add : 27 kg 250 gm, 20 kg 30 gm and 1 7.5 kg. Z"
- 66\. A shopkeeper sold 25.750 kg of potatos. If he had total 100 kg of potato, how much potatoes is leftwith him?
- 67\. Convert into litres :
- (a) 207 ml (b) 43 75 ml
- 68\. A bottle of medicine can hold 75 ml syrup. How much litres of syrup is there in 100 such bottles?
- 69\. Four jars have 6.8 I of milk. What is the capacity of each jar?
- 70\. Convert:
- (a) 1200 minutes into hours.
- (b) 1 700 minutes into hours and minutes.
- (c) 24 days into seconds.
- (d) 365 days into hours.
- 71\. Add:
- (a) 20 hours 17 minutes and 30 hours 50 minutes.
- (b) 10 hours27minutesand 5 hours 52 minutes.
- 72\. Subtract:
- (a) 35 minutes 30 seconds from 40 minutes 20 second.
- (b) 1 hours 35 minute 20 second from 3 hours.
- 73\. Name the rays, segments or line in the following.
- 75\. Measure each angle.
- 76\. Which of the fol lowing angles are acute or obtuse :
73°, 59°, 40°, 30°, 180°, 35°, 70°, 120°
- 77\. Construct angle 60°, 30°, 75°, 90°, 180°
- 78\. Which of the following pairs of line are parallel to each other:
- 79\. Which of the fol lowing segments are perpendicular to each other:
- 80\. Drawthe mirror line:
- 82\. Convert:
- (a) 0.5 sq m into sq cm (b) 7500cucmincu
- 83\. The length and breadth of a rectangularfield are 25m and 20 m respectively. Find its
- (a) Perimeter (b) Area
- 84\. The side of a square field is 65 m. Find the cost of its cultivation at the rate of ?20 per square metre.
- 85\. Find the area of a room which is 4 m long and 3 m wide. Calculate the cost of carpeting at the rate ofMO.OO per square m.
- 86\. How much cubic metre water can be kept in a 10 m long, 5 metre wide and 2 metre deep water tank?
- 87\. How many rectangular pieces of 30 cm x 20 cm x 15 cm can be made from a cube if the side of cube is 9m?
- 88\. Find the vanishing point offollowingfigure:
«•J:
89\.
90\.
Rail track
Find:
- (a) 8th square number Complete the pattern:
(b) 13th triangular number
1x9+1 = 10
12x9 + 2 = 110
123 x 9 + 3 = 1110 1234 x 9 + 4 = 11110
12345 x 9 + 5 =
123456 x 9 + 6 =
1234567 x 9 + 7 =
- 91\. Draw a bo rd er pattern using letter C.
- 92\. The following table shows the price of different models of mobile phone. Make a bar chart from this data.
Brand
A
B
c
D
E
Price (»)
2200
2800
3900
5200
6400
- 93\. Following table shows the price of sugar for a five year period. Plot a continuous growth chart for th is.
Year
2001
2002
2003
2004
2005
Price (a/kg)
16
18
20
25
35
- 94\. Following pictograph shows the number of fruits consumed in a hotel. Represent this data in a table.
ooooo
oooooooooooo
ooooo
> ooooooooooo
oooo
here 1 shows 100 fruits.
1\.
2\.
7
##### Put on yew Thinking Cup
5
### 8
Four bells toll at intervals of 3, 4, 5 and 6 minutes. They begin tolling at 5:00 AM. At whattime will they toll together again?
Find the hidden pattern and fill in the blanks.
- 3\. The digit 5 comes how many times when we count from Oto 100?
- 4\. Name these angles and showthe relation amongthem.
###### 5.
Convert these fractions into simple forms :
12
(a) 24
9
(b)
(0 25
30
(d)
20
25
How many square numbers are there between 0 to 100?
7\. The gap between two electric poles is 10 metre. How many poles are there on a stretch of 1 km?
- 8\. Look at the shapes in the left column. The smaller shape shows the part to be cut out. In the right colum, select the correct shape which is obtained after removing the cut out.
(iv)
Get Set Go With Sum Up Mathematics-5
FORMATIVE ASSESSMENT-1 (Chapter 1 to 4)
Time: 1 hr.F.M. 20
- 1\. Simplify:
- (a) 3526198-2167892 (b) 67215 + 3216985
- 2\. If the cost of 7 shirts is ? 880.25, what will be the cost of one shirt?
- 3\. Find the least number which is exactly divisible by 3,9, and 12.
- 4\. Find the value of 12 + 4 + 3.6 + 9.
- 5\. Form a greatest number of 7 digits using each of the digits 3,0,6,7,8,9,2
- 6\. Write in Roman Numerals:
- (a) 205 (b) 110 (c) 98
- 7\. Fill in the blank:
- (a) Placevalueof2 in 329608 is
- (b) Hindu-Arabic numeral for CXII is
- 3 12
C 5
- (d) The value of 647 estimated to nearest tens is
- 8\. Rahul packed 143190 mangoes in 258 bags. How many mangoes are needed to pack in 410 such bags?
- 9\. Write in figures:
- (a) Twenty four lakh six thousand five hundred four.
- (b) Nine lakh ninty nine thousand nine hundred ninty nine.
- 10\. Fill in the blank:
- (a) The predecessor of 1000 is
- (b) Hindu Arabic number of XXXIII is
(c)0.75l= ml
- (d) 2 gm = kg
FORMATIVE ASSESSMENT-2 (Chapter 5 to 7)
Time: 1 hr.F.M. 20
- 1\. A shopkeeper has 2520.20 kg of rice in his godown. He sold 525.10 kg. How much rice is left in his godown?
- 2\. Simplify:2.69 + 17.695-3.303
- 3\. How many shirts can be purchased for ?173940.95 if the cost of one shirt is ?1512.53?
- 4\. What will be cost of one kg of wheat if 35 kg of wheat cost ^603.75 ?
- 5\. Rakesh purchased 32.325 kg of wheat, 17.53 kg of rice and 12.395 kg of vegetable. He hired a rikshaw to carry them to his house. If rikshaw puller charges ?3.00 per kg, how much did Rakesh pay to rikshaw puller?
- 6\. Add:32.32,6.50and27.35
- 7\. Subtract:
- (a) 80.39 kg from 116.295 kg (b) 320.295 I from 420.1 5 9 I
- (c) 5.32 m from 1500 cm
- 8\. Which fraction is greater in each pair?
- (a) y and y (b) -|and y
Simplify:
1\_1
10 8
- 10\. Ankit purchased 100 chocolates, but he found that ^ th of the total chocolates was not good so he threw them. How many chocolates did he kept?
FORMATIVE ASSESSMENT-3 (Chapter 8 to 10)
Time: 1 hr.F.M. 20
- 1\. Convert into metres:
- (a) 30000 mm (b) 500 cm (c) 5 cm
- 2\. Find the cost of carpeting a rectangular room of size 6m x 3m at the rate of ?7.00 per square metre.
- 3\. The weight of scooter is 125 kg 500 gm. What will be the weight of 9 such scooters?
- 4\. Convert the following:
- (a) 27 kg 315 gm into gm (b) 13 kg 312 gm into kg
- 5\. Convert the following into kg:
- (a) 2 gm (b) 2 kg 300 gm
- 6\. Raju covered 2.12 km by cycle, 5.21 km on his foot and 2750.375 km by aeroplane. How much total distance did he cover?
- 7\. The length of 12 ropes is 146.16 m. Find the length of one rope.
- 8\. Convert:
- (a) 1 3220 ml in I and ml. (b) ^3220.25 into paise.
- 9\. Convert the following into millimetres:
- (a) 5 cm (b) 5.2 cm (c) 5 dm (d) 10.52 cm (e) 7dm
- 10\. Convert into centimetres:
- (a) 9.7dm (b) 3.2m (c) 6.9m (d) 21.21m (e) 2.930m
FORMATIVE ASSESSMENT-4 (Chapter 11 to 13)
Time: 1 hr.
EM. 20
- 1\. Find the space occupied by 200 bricks, if the dimension of bricks are 20 cm, 5 cm and 2 cm.
- 2\. What is the difference between 9 a.m. and 11 p.m?
- 3\. How much cubic metre water can be kept in 3 m wide, 6 m long and 2 metre deep tank?
- 4\. Construct an angle of 135°.
- 5\. Find the cost of fencing of a field of 35m x 17m at the rate of »5 per metre
- 6\. Rahul reached school at 9.10 am and left for home after 6 hour 20 minutes. At what time did he leave the school?
- 7\. Construct a 90 0 angle.
- 8\. Construct an angle of 120 0
- 9\. How much cubic metre water can a 12 m long, 10m wide and 2 m deep tank hold?
- 10\. Convert:
- (a) 525 months into years and month
- (b) 25 days into weeksand days
FORMATIVE ASSESSMENT-5 (Chapter 14 to 16)
Time: 1 hr.
EM. 20
Draw a graph based on following information: Rahul's snaks corner
Pizza
Chips
Kurkure
Biscuit
Cake
- 2\. Following data shows number of students who prefer certain leisure activity. Make
a bar chart from this data.
Activity
Internet
Hiking
Cricket
Chess
Magic
No. of Student
50
65
85
40
30
- 3\. The following table shows the salary of Mr. Khanna in different years. Plot a continuous growth chart with this data.
Activity
2001
2002
2003
2004
2005
No. of Student
15000
16000
18000
20000
25000
4\. Draw a graph based on following information: Rahul's snaks corner
Days
Mon
Tues
Wed
Thurs
Fri
Sat
Sat
Milk sold
30
20
45
50
100
20
10
Draw a railway line with perspective.
Draw a floor map of your house.
- 7\. Find the next square number.
- (a) 144 (b) 196
- 8\. Find the previous square number.
- (a) 81 (b) 196
- 9\. Find a square number between 40 and 50.
- 10\. Express these square numbers as the sum of odd numbers.
- (a) 49 (b) 169 (c) 121
Exercise-1\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. (a) 815068, (b) 708920, (c) 300000. 2. (a) 81 5905, (b) 2999999, (c) 2651968.
- 3\. 213506,213516,213526,213536 4. 30521 7, 30531 7, 30541 7
- 5\. 2 76819,3 76819,4 76819
- 6\. (a) 708605, 708606, 708607, 708608, 708609. (b) 22311 6, 22311 7, 223118, 22311 9, 223120
- 7\. 100000. 8. 9999999.9. 56430
Exercise-2---------------------------------------------------------
- 1\. (a) 5,21,016, Five lakh twenty one thousand sixteen.
- (b) 48,33,736, Forty eight lakh thirty three thousand seven hundred thirty six.
- 2\. (a) 2,65,201, Two lakh sixty five thousand two hundred one.
- (b) 87,62,789, Eighty seven lakh sixty two thousand seven hundred eighty nine.
- 3\. (a) 5,21,310, Five lakh twenty one thousand three hundred ten.
- (b) 2,06,301, Two lakh six thousand three hundred one.
- (c) 32,80,371, Thirty two lakh eighty thousand three hundred seventy one.
- (d) 39,01,014, Thirty nine lakh one thousand fourteen.
- 4\. (a) 7,18,612, (b) 8,73,457, (c) 26,60,019, (d) 39,54,268.
- 5\. (a) 5,72,453, (b) 42,23,362, (c) 72,54,284.
- 6\. Five lakh thirty eight thousand seventeen potatoes.
- 7\. (a) 12,62,425, (b) 5,34,673. 8. (a) 655419, 665419, 675419, (b) 355679, 365679, 375679.
- 9\. (a) Greatest 5 digits number = 99999
Greatest4 digit number = 9999
Numberof 5 digit numbers = 90000
- (b) Greatest 7-digits number = 9999999
Greatest 6-digit number = 999999
Numberof 7-digits number = 9000000
Exercise-3\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. (a) Place value of 6 is 600000, (b) Place value of 6 is 6000000, (c) Place value of 6 is 60000, (d) Place valueof 6 is 600000.
- 2\. Placevalueof 5 is 5 lakhs or 500000.
- 3\. (a) 700000 + 60000 + 300 + 50 + 4. (b) 300000 + 4000 + 800.
- (c) 8000000 + 700000 + 20000 + 70 + 6. (d) 500000 + 5000 + 900 + 60 + 5.
- 4\. (a) 700000 + 20000 + 600 + 50 + 1, Place value of 7 is 700000
- (b) 7000000 + 50000 + 5000 + 300 + 20, Placevalueof 7 is 7000000
- (c) 400000 + 70000 + 5000 + 400 + 6, Place value of 7 is 70000 v
- (d) 7000000 + 30000 + 500 + 20, Place value of 7 is 7000000
- 5\. (c) Place value of 3 is 3000, (b) Place value of 2 is20000, (c) Place value of 8 is800000.
- 6\. (a) 8 is in ten lakhs place, (b) 5 is in lakhs place. 7. (a) 6,86,486, (b) 74,73,692, (c) 92,16,426.
Exercise-H---------------------------------------------------------
- 1\. (a) >,(b) <,(c) >,(d) <,(e) <,(f) <.
- 2\. (a) Greatest number = 800201, Smallest number = 52315
- (b) Greatest number = 9121512, Smallest number = 99999
- 3\. (a) 300902, 534198, 799651,852002, (b) 20401 9, 229725, 307578, 540020,
- (c) 2095738,2195738, 2345958,2459958.
- 4\. (a) 7985923, 7885923, 7785923, 7685923, (b) 562365, 532365, 521365, 512365,
(c) 2459958, 2345958, 2195738, 2095738
- 5\. (a) Greatest number = 854320, Smallest number = 203458
- (b) Greatest number = 976410, Smallest number = 146790
- 6\. Greatest number = 997530, Smallest number = 300579.
- 7\. Greatest number = 9997510, Smallest number = 1000579.
Exercise-5\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. (a) 3,025,708; There million twenty five thousand seven hundred eight.
- (b) 8,805,610; Eight million eight hundred five thousand six hundred ten.
- (c) 513,507; Five hundred thirteen thousand five hundred seven.
- (d) 800,700; Eight hundred thousand seven hundred.
- (e) 2,030,790; Two million thirty thousand seven hundred ninety.
- (f) 5,040,203; Five million forty thousand two hundred three.
- 2\. (a) 3,530,256, (b) 675,400, (c) 8,000,362, (d) 1,45,242, (e) 7,005,024, (f) 9,724,009.
Exercise-6\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. (a) XLI, (b) Lil, (c) LIX, (d) XLIX, (e) XXXVII, (f) LXI, (g) XCV, (h) LXXXI, (i) LXXIX, (j) XCI.
- 2\. (a) 39, (b) 44, (c) 96, (d) 550, (e) 565, (f) 56, (g) 65, (h) 145, (i) 79.
- 3\. (a) <,(b) <,(c) <,(d) >,(e) <. 4. (a) 990, (b) 110, (c) 30, (d) 100, (e) 110.
Exercise-7\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. (a) 927115, (b) 19515945, (c) 17547556, (d) 12783454, (e) 13645462, (f) 15144524, (g) 9932099, (h) 10570009, (i) 18899888, (j) 1 6422765.
- 2\. (a) 5977929; Fifty nine lakhs seventy seven thousand nine hundred twenty nine.
- (b) 122202 7; Twelve lakhs twenty two thousand twenty seven.
- (c) 13162645; One crore th irty one lakhs sixty two thousand six hundred forty five.
- (d) 11190678; One crore eleven lakhs ninety thousand six hundred seventy eight.
- (e) 6467809; Sixty four lakhs sixty seven thousand eight hundred nine.
#### G=--
Exercise-8------------------------------
- 1\. Total numberofanimals = 1178588.
- 2\. Total numberoftrees in Ashok Vatika = 2129208.
- 3\. Total persons were visited the Ramilila Maidan = 3362983
- 4\. Total pages in both books = 34619
- 5\. Total soldiers in both army = 2114410
- 6\. Total numberoffruits ate = 16592535.
Exercise-9---------------------------------------------------------
- 1\. (a) 3078513, (b) 214764, (c) 2787937, (d) 4866994, (e) 3087276, (f) 280825, (g) 1538299, (h) 5145821.
- 2\. (a) 8910838, (b) 8281098, (c) 1154801, (d) 95459. 3. 1953696
4\. (a) 1023,1027,1031,1035,1039 (b) 520, 51 7, 514, 511,508.
Exercise-10----------------------------------------------------------
- 1\. 5820706. 2. 151685. 3. 4100228. 4. 94382. 5. 8660572.
6\. 3999811. 7. 1982412. 8. 1058537 9. 1228060. 10.7205361
Exercise-U-----------------------------------------------------
- 2\. 10540541 3. smallest number-5,50,001, Greater number-6,49,999.
Exercise-12--------------------------------------------------------
- 1\. (a) 56470, (b) 2400, (c) 421500, (d) 79000, (e) 795000, (f) 8521000.
- 2\. (a) 136728, (b) 729225, (c) 43741352, (d) 32484710, (e) 6465104, (f) 2123410, (g) 1115246, (h) 1492445, (i) 6761 72, (j) 22475012, (k) 16249400, (I) 1877045, (m) 29931 300, (n) 14400000.
- 3\. (a) 0, (b) 345565, (c) 452250, (d) 0, (e) 12635, (f) 25343200, (g) 0, (h) 0.
Exercise-13\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. 935465. 2. 1227692. 3. 438000.
4\. 193232. 5. 649230.
9\. 2165890.
(b) 730198 x 117 = 85433166
- 6\. 27191625. 7. 7031192. 8. 448705
- 10\. (a) 17476560, (b) 10700235, (c) 0, (d) 3751, (e) 0.
11.136875 12.(a)831018 x 25 = 20775450.
Exercise-14----------------------------------------------------------
1\. (a) Quotient =110196; Remainder = 17, (c) Quotient = 34778; Remainder = 68,
(b) Quotient = 7079; Remainder = 72,
(d) Quotient = 25431; Remainder = 331,
(e) Quotient = 13 3 79 7; Remainder = 484,
(f) Quotient = 2804; Remainder = 4,
(g) Quotient = 843 7; Remainder = 42 7,
(i) Quotient = 85683; Remainder = 71 7
2\. (a) Quotient = 41 75; Remainder = 44,
(d) Quotient = 10010; Remainder = 9,
(h) Quotient = 1 1655; Remainder = 2500,
(b) Quotient = 1 742; Remainder = 53, (c) 2780263,
(e) Quotient = 101010; Remainder = 10.
1\. ?512.
2\. 125.
3\. ? 1120.
4\. ? 76348.
5\. 3000 litre.
6\. 554.
7\. 21225.
8\. 320.
9\. 2100.
10.2100.
11.2100.
12.1724.
13.? 3212.
14.500.
15\. Quotient = 521 ; Dividend = 1 77661.
Exercise-16---------------------------------------
1\. 247000. 2. 3736623. 3. 528700. 4. 468750.
- 5\. 255600 6. 1568. 7. 2092. 8. 9999786.
Exerc¡se-17----------------------------------------------------------
- 1\. (a) 3200000, (b) 400000, (c) 1800000, (d) 4000000, (e) 21000 km, (f) ? 140000, (g) 9600.
- 2\. (a)40,(b)200,(c) 10,(d)20. 3. 2000. 4. 2000. 5. 600 litre.
Exercise-18----------------------------------------------------------
- 1\. (a)1,2,4,8,16,32,(b)1,2,4,8,(c)1,19,(d)1,3,5,9,15,45,(e)1,5,19,95. 2. Yes. 3. No
- 4\. (a) 2, 4, 6, 8, 10, (b) 9, 18, 27, 36, 45, (c) 16, 32, 48, 64, 80, (d) 15, 30, 45, 60, 75, (e) 21,42, 63, 84, 105.
- 5\. (b), (d), (e), (f), (h) and (i) are divisible by 2. 6. (b), (c), (d), (e), (f), (h) and (j) are divisible by 3.
- 7\. (a), (c), (d), (g), (i) and (j) are divisible by 4. 8. (a), (b), (c), (e), (f), (g), (i) and (j) are divisible by 5.
- 9\. (d), (e), (f), (g), (h), (i) and (j) are divisible by 9. 10. Yes. 11. Yes. 12. Yes.
Exerc¡se-19----------------------------------------------------------
- 1\. 2,11,13,17and 19. 2. 2, 3, 5, 7,11,13,1 7,19,23,29.
- 3\. (a) 19, (b) 29, (c) 47. 4. (a) 22, (b) 55, (c) 52. 5. (a) 3, (b) 11, (c) 19, (d) 47.
6\. 2,4. 7. 3, 5; 5, 7; 11,13. 8. a, c, e.
- 9\. (a) 5 X 7, (b) 2 X 3 X 5 X 7, (c) 3 X 5 X 41, (d) 2 X 5 X 41, (e) 2 X 2 X 2 X 2 X 2 X 2 X 5, (f) 2 X 2 X
2 X 2 X 2 X 2 X 2 X 2 X 2, (g) 5 X 43, (h) 5 X 19, (i) 3 X 3 X 7, (j) 2 X 5 X 89, (k) 2 X 2 X 2 X 2 X 3,
(l)5 X 5 X 7.
10.2and5. 12. Prime number. 13.d. 14.c.
Exercise-20--------------------------------------------------------
- 1\. (a) 5, 5, (b) 2, 6, (c) 2,4, (d) 5, 5, (e) 2,2, (f) 2,4, (g) 2, 6, (h) 2, 8, (i) 2, 2.
- 2\. (a)5,(b)2,(c)2,(d)2,(e)2,(f)25,(g)5, (h)2, (i)12, (j)6, (k)3.
Exercise-21--------------------------------------------------------
- 1\. (a) 80, (b) 264, (c) 40, (d) 408, (e) 357, (f) 60, (g) 120, (h) 748.
- 2\. (a) 81, (b) 660, (c) 129780, (d) 3375, (e) 7875, (f) 20915, (g) 105060, (h) 72, (i) 3740, (j) 22360, (k) 3825, (I) 1575, (m) 1632, (n) 612.
Exercise-22\_\_\_\_\_\_\_
1\. 5. 2. 4.
6\. 315 litre. 7. 945.
3\. 5. 4. 5.
8\. At 11.00 a.m.
5\. 945.
Exercise-23\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. 4p-|- 2. ^^-and^- 3. -|,4-,j,yand4- 4. (a)and(b)
- 5\. (a)4,(b) 14,(c)9,(d) 14. 6. (a) 2 - 4, (b) 5 - 6, (c) 6 - 7, (d) 7 - 9. 7. (a),(c),(e).
- 8\. (a)1-^/(b)24rz(c)3^,(d)1^,(e)1^-. 9. (a) (b) (c) (d)
y / 4 J I 3 O I Z I 3
Exercised\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. (a) ^,(b) ^-,(c) ^,(d) 2. (a) , (b)-1-, (c), (d).
- 3\. (a) <, (b) >, (c) =, (d) =, (e) <. 4. Ramesh. 5. Rahul.
Exercise-25\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
1\. (a),(b),(f),(h). 2. (a)^,(b)4-,(c)44'(d)57r'(e)4,fô4r,(g)^,(h)4^
Exercise-26\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
1\. (a)^-,(b) (c) -|-,(d) 44,(e)5,(Û5,(g) 44^) ^,(0 44^) 44'(k) 44^ 44'^44'
[7 4 5 6 30 12 42 72 30 3642](#bookmark721)
in)3ÔÔ' 2‘ (a) h,(b) T,(c) T,(d) 6Ô,(e) T'^ 3Ô'(g) Ts/(h) T'^ 78'
[rï 4 2 7 , 1 ♦ 4 13 c1](#bookmark722)
[25 ' k 81 ' 72 3" 2 P^d- ^’16 5.](#bookmark723)
- [6- ~ 7- 7524](#bookmark724)
Exercise-27\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. (a) 7, (b) 2, (c) 21, (d) 1, (e) 4, (f) 203.
Exercise-28\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. (a) 4r7b) 4-'(c) 4r ' <d) 44 7e) 44 7 0 #,(g) ^r,(h) ^, (i) 4, (J) 30, (k) 3, (I) 24, (m)
- (n ) , (o) 1, (p) 44 • 2. (a) 4, (b) 6 hours, (c) 25 years, (d) 5 years, (e) 3 months, (f) 10 days.
- 3\. (a) -¡-,(b) -^(c) ^-,(d) ^(e) ^,(f) ^,(g)4-,(h) 4\_,(i) ^,0)^-.
- 4\. 96. 5. 100 packets. 6. 100. 7. 225 seats.
- 8\. ?105. 9. ?315. 10.50 chocolates.
Exercise-29\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. (a) 4r7b)^,(c) 4|,(d) T^Je) -^(0 ^(g) (h) 4-00^7)4-0^4-01) -L
zl zU Z/ Z/ l3 Z3 4y O I4 3 z IU
Exercise-30
- 1\. (a) 0.5, (b) 0.2, (c) 0.06, (d) 5.4, (e) 62.52, (f) 4.06, (g) 6.04, (h) 9.64, (i) 2.502.
- 2\. (a) 0.2, (b) 0.6, (c) 0.07, (d) 0.08, (e) 2.7, (f) 11.2, (g) 12.05, (h) 6.25, (i) 23.027, (j) 0.027.
„ / 5 , . 213 ... 42 , . no 2 ,217 , . , 5 ,,. , 12 ... 675
- 3\. (a) 100, (b) w , (c) 10Q0, (d) wo, (e) 22 10Q, (f) 3 100Q, (g) 2 w, (h) 3 wo , (i) 3271Q00,
1 1000 •
- 4\. (a) Two point five seven, (b) Three point one. (c) Two point two one two. (d) Twenty five point two five, (e) Twenty seven point zero one. (f) Three point nine seven, (g) Two hundred thirty two point one. (h) Two hundred thirty two point zero zero one.
5\.
253 25 25
- (a) ^ ,(b) Yqqq /(c) yæ,(d)32 jæ,(e) 1 yqqq .
- 6\. j|j ;0.08
1 34 K134:34ÏÔ0Ô'
Exercise-31----------------------------------------------------------
- 1\. (a) 3 + 0.2, (b) 20 + 2 + 0.2 + 0.01, (c) 30 + 2 + 0.1 + 0.02, (d) 100 + 30 + 2 + 0.1 + 0.02 + 0.001, (e) 40 + 2 + 0.2 + 0.05, (f) 30 + 2 + 0.4 + 0.05, (g) 40 + 9 + 0.2 + 0.09 + 0.001, (h) 60 + 1 + 0.2 + 0.01 + 0.005.
- 2\. (a) 10,100, (b) 10,1000, (c) 1,100, (d) 20, 5,10,1000, (e) 5,1000.
- 3\. (a) 5.205, (b) 25.102, (c) 321.12, (d) 21.22, (e) 20.102.
- 4\. (a) 2 hundredth, (b) 2 ones, (c) 2 tenth, (d) 2 hundreds.
Exercise-32
- 1\. (a) 5.9, (b) 3.3, (c) 6.32, (d) 6.12, (e) 37.21, (f) 324.01.
- 2\. (a) 0.20; 0.200; 0.2000, (b) 23.010; 23.01000; 23.0100, (c) 3.10; 3.100; 3.1000, (d) 4.90; 4.900; 4.9000, (e) 7.20, 7.200, 7.2000, (f) 0.10; 0.100; 0.1000, (g) 0.30; 0.300; 0.3000, (h) 0.90; 0.900; 0.900.
- 3\. (a) one, (b) two, (c) two, (d) two, (e) three. 4. (a) T, (b) F, (c) T, (d) T.
- 5\. (a) 2.10, 3.21,7.31, (b) 6.21,3.320, 7.916, (c) 3.210,3.121,6.21 7.
Exercise-33\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
. , . 5 2 / \\ 3 , 31 , . 12 3 15 / x 2 „ 16 , 567 „ 612
- 1\. (a) 1Q , (b) w , (c) w, (d) 10Q , (e) wo, (f) 3 10Q, (g) 1 1Q , (h) 2 1QQ , (i) 3 1000, (j) 2 100Q .
- 2\. (a) 0.1, (b) 0.02, (c) 0.007, (d) 0.21, (e) 0.7, (f) 0.16, (g) 0.003, (h) 3.25, (i) 5.5, (j) 0.084.
Exercise-34--------------------------------------------------------
- 1\. (a) 5.32, (b) 6.24, (c) 3.51, (d) 3.21, (e) 1 7.47, (f) 4.699, (g) 1 9.16, (h) 7.531, (i) 22.5565, (j) 10.821.
- 2\. (a) 1.066, (b) 1.099, (c) 3.869, (d) 8.047, (e) 3.694, (f) 6.090, (g) 0.255, (h) 9.606, (i) 1.807, (j) 3.893.
- 3\. (a) 1.445, (b) 2.093, (c) 4.750, (d) 3.700.
Exercise-35-----------------------------------------------
- 1\. (a) 0.4, (b) 0.78, (c) 5.04, (d) 23.04, (e) 25.916, (f) 51.35, (g) 25.1 72, (h) 63.1 70, (i) 8.025.
- 2\. (a) 1 3.486, (b) 0.04, (c) 0.064, (d) 1.584, (e) 39.937, (f) 3.9996, (g) 1.5252, (h) 3.5256.
- 3\. (a) 0.2, (b) 0.2, (c) 0.3, (d) 0.4, (f) 1.7, (g) 1.9, (h) 1.1, (i) 1.06, (j) 0.81, (k) 10.81, (I) 3.014.
Exercise-36--------------------------------------------------------
- 1\. (a) ? 0.25, (b) ? 0.3, (c) ? 0.2, (d) ? 0.95, (e) ? 0.35, (f)? 2.65, (g) ? 1 3.20, (h) ? 12.1 5.
- 2\. (a) 72 paise, (b) 21 paise, (c) 126 paise, (d) 21 75 paise, (e) 1622 paise, (f) 15681 paise, (g) 27236 paise, (h) 11 paise.
Exercise-37--------------------------------------------------------
- 1\. (a) ? 28.35, (b) ? 22.30, (c) ? 376.00, (d) ? 1 36.43, (e) ? 48.48, (f) ? 335.35.
- 2\. (a) ? 972.47, (b) ? 2480.38, (c) ? 4025.39, (d) ? 5433.55, (e) ? 1387.45, (f) ? 340.65.
- 3\. ? 555.32. 4. ? 42721.55. 5. ? 29250.47
- 6\. (a) ? 1430.10, (b) ? 12.15, (c) ? 7.93, (d) ? 5.10, (e) ? 1 7509.20, (f) ? 9998.99.
- 7\. ? 11.00. 8. ? 20.95. 9. ? 27.23. 10. (a) ? 20.95, (b) ? 20.02.
Exercise-38--------------------------------------------------------
- 1\. (a)? 97.60, (b)? 216.65, (c)? 1121.50, (d)? 1935.90, (e)? 237.00, (f)? 763.20.
- 2\. ? 369.75. 3. ? 337.50. 4. ? 19363.50. 5. ? 38270.00.
- 6\. (a) ? 81 7.50, (b) ? 2878.00, (c) ? 342.00, (d) ? 12906.00.
- 7\. (a)? 3.99, (b)? 41.03, (c)? 6.91, (d)? 19.19.
- 8\. ?31.06. 9. ? 1838.22. 10/541.00. 11.i2755.72.
Exercise-39--------------------------------------------------------
- 1\. (a) 0.2 cm, (b) 1.2 cm, (c) 1.7 cm, (d) 11.5 cm, (e) 1.2 cm, (f) 5.3 cm, (g) 13.5 cm.
- 2\. (a) 0.35 cm, (b) 1.10 cm, (c) 2.25 cm, (d) 5.05 cm, (e) 15.21 cm, (f) 12.25 cm.
- 3\. (a) 0.005 km, (b) 0.015 km, (c) 0.215 km, (d) 1.225 km, (e) 11.321 km, (f) 5.215 km, (g) 15.675 km, (h) 17.975 km, (i) 121.579 km.
Exercise-HO--------------------------------------------------------
- 1\. (a) 50 mm, (b) 52 mm, (c) 500 mm, (d) 165.2 mm, (e) 700 mm.
- 2\. (a) 97 cm, (b) 320 cm, (c) 690 cm, (d) 2121 cm, (e) 293 cm.
- 3\. (a) 91 dm, (b) 32 dm, (c) 42100 dm, (d) 400800 dm.
- 4\. (a) 2300 m, (b) 9070 m, (c) 64400 m, (d) 79821 m, (e) 5971 m.
- 5\. (a) 50 dm, 500 cm, (b) 27 dm, 270 cm, (c) 3200 cm, 320000 cm, (d) 2.7 km, (e) 2590 cm, 25900 dm, (f) 275.5 cm, (g) 69.75 metre.
Exerc¡se-41--------------------------------------------------------
- 1\. (a) 5.375 cm, (b) 352.7 mm, (c) 337.21 m, (d) 447.988 km, (e) 3368.55 dm, (f) 9779.55 km, (g) 1100.92 m, (h) 6276.779 km, (i) 7463.739 km.
- 2\. (a) 156.40 m or 156 m 40 cm, (b) 202.61 km, (c) 898.275 km, (d) 40.7cm, (e) 387.216 km.
- 3\. 242 m 53 cm. 4. 232 km 242 cm. 5. 35.034 km. 6. 3.5 m.
- 7\. 353.87cm. 8. 24.3km.
Exercise-HZ
- 1\. (a) 14.40 cm, (b) 139.30 km, (c) 198.05 cm, (d) 19.45 cm, (e) 7.40 km.
- 2\. (a) 7 m 7 cm, (b) 87 km 786 m, (c) 1 km 987 m, (d) 326 m. 3. 536.473 km. 4. 179.217 km.
Exercise-H3\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. (a) 377.85 m, (b) 1937.889 km, (c) 3232.5 cm, (d) 34897.5 m, (e) 36.963 m.
- 2\. (a) 53.78 km, (b) 63.44 km, (c) 4.107 km, (d) 3.55 m, (e) 0.65 m, (f) 6.818 km.
- 3\. 2566.72 cm. 4. 1845.75 cm. 5. 217.97 m. 6. 71.404 km.
- 7\. 21.014 km. 8. ? 245.00. 9. 3.525 m.
Exercise-MM\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. (a) 0.006 kg, (b) 0.01 kg, (c) 0.6 kg, (d) 4 kg, (e) 2.01 kg, (f) 1.695 kg, (g) 59.611 kg, (h) 16.215 kg.
- 2\. (a) 2000 gm, (b) 1600 gm, (c) 300 gm, (d) 2 gm, (e) 126 gm, (f) 120 gm, (g) 100 gm, (h) 500 gm, (i) 2125 gm.
- 3\. (a) 2 kg 516 gm, (b) 6 kg 502 gm, (c) 6 kg 50 gm, (d) 2 kg 625 gm, (e) 14 kg 320 gm, (f) 13 kg 1 gm, (g) 17 kg 200 gm, (h) 16 kg 5 gm. 4. Yes.
Exercise-^S\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. (a) 10.587 kg, (b) 19.800 kg, (c) 216.738 kg, (d) 226.52 kg, (e) 4632.565 kg, (f) 37.23 kg, (g) 21 7.315 kg, (h) 3.3 84 kg, (i) 2 3.3 2 kg, (j) 94.002 kg.
- 2\. (a) 204.950 kg, (b) 999.99 kg, (c) 37.999 kg, (d) 4.670 kg, (e) 1.999 kg, (f) 0.001 kg, (g) 5.359 kg, (h) 7.895 kg, (i) 16.3 kg. 3. 60.55 kg. 4. 60.7 kg. 5. 7.18 kg. 6. 27.925 kg.
Exercise-46\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. (a) 22.512 kg, (b) 40.863 kg, (c) 50.112 kg, (d) 125.244 kg.
- 2\. (a) 0.816 kg, (b) 1.468 kg, (c) 1.474 kg, (d) 1.235 kg.
- 3\. 1.5 kg. 4. ?6.45. 5. 1.06 kg. 6. 0.126 kg. 7. 0.636 kg.
Exercise-HZ\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. (a) 0.006 I, (b) 0.027 I, (c) 0.615 I, (d) 0.950 I, (e) 18.605 I, (f) 8.020 I, (g) 29.155 I.
- 2\. (a) 445 ml, (b) 34 ml, (c) 40 ml, (d) 5015 ml, (e) 2005 ml, (f) 12505 ml.
- 3\. (a) 1 1420 ml, (b) 50 ml, (c) 420 ml, (d) 28 I 9 ml.
- 4\. (a) True, (b) False, (c) False, (d) True. 5. 12505 ml.
- 6\. (a) two, one, (b) one, one, 3, (c) four, three, one, (d) one, one.
Exercise-M8\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. (a) 29.885 I, (b) 66.4671, (c) 112.956 I, (d) 96.902 I, (e) 1 71421 ml, (f) 16 I 674 ml, (g) 43 1715 ml.
- 2\. (a) 4.313 I, (b) 22.591 I, (c) 5.818 I, (d) 2.765 I, (e) 2 I 800 ml, (f) 4 I 54 ml, (g) 3 I 691 ml.
- 3\. 6.368. 4. 6.9651. 5. 49.3831. 6. 560.2931. 7. 1124.6151.
Exercise-H9\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. (a) 6 I, (b) 5 I, (c) 6 I, (d) 18 I, (e) 102 I, (f) 83.565 I. 2. (a) 665 ml, (b) 3.310 ml, (c) 507 ml, (d) 3.856 ml.
3\. ? 393.59 4. ?414.75. 5. 250ml. 6. 3 litre. 7. 606ml.
Exercise-50
- 1\. (a) 300 seconds, (b)450 minutes, (c) 300 minutes, (d) 210 minutes, (e) 10800 seconds.
- 2\. (a) 48 months, (b) 50 months, (c) 100 months, (d) 260 weeks, (e) 150 days, (f) 220 days.
- 3\. (a) 25 hours, (b) 6 hours 30 minutes, (c) 1 hour, 1 minute and 30 seconds, (d) 22 minutes.
- 4\. 2years38 months. 5. 200years 6. 2 hours, 21 minutesand 16seconds.
- 7\. 39 days. 8. 2 years, 2 months and 26 days.
Exercise-51--------------------------------------------------------
1\. 85 minutes 28 seconds.
4\. 14 hours 25 minutes 26 seconds.
7\. 10 week 1 day.
10.10 months 10 days.
12.9 months 2 weeks 1 day.
2\. 69 minutes.
3\. 22 hours 16 minutes.
- 5\. 39 hours 11 minutes 19 seconds. 6. 12 days
8\. 7 months 1 week. 9. 1 7 years 3 months.
- 11.13 years 4 months 7 days.
Exercise-52--------------------------------------------------------
1\.
13 minutes 37 seconds.
2\. 14 minutes 25 seconds.
4\.
11 hours 38 minutes.
5\. 10 years 6 months.
7\.
6 months 26 days.
8\. 4 months 8 days.
9\.
10 years 6 months 6 days
10.5 years 4 months 18 days.
3\. 4 hours45 minutes.
6\. 14 years 6 months.
Exercise-53---------------------------------------------------------
- 1\. (a) 4 hours 30 minutes, (b) 10 hours 15 minutes, (c) 15 hours 15 minutes, (d) 6 hours 15 minutes.
- 2\. 9 hours 15 minutes. 3. 21 hours 30 minutes. 4. 51 days.
- 5\. 32 hours45 minutes. 6. 4 hours 15 minutes. 7. 308 years 9 months 29 days.
Exercise-54--------------------------------------------------------
- 1\. (a) 12 : 00 noon, (b) 3 : 45 PM, (c) 3 :10 AM.
- 2\. (a) 9 : 55 AM, (b) 8 :20 AM, (c) 2:23 PM, (d) 12 :40 PM. 3. 39days. 4. 3 hours 15 minutes.
- 5\. 71 days. 6. 29thJanuary 7. 48 days.
Exercise-55--------------------------------------------------------
- 1\. (a) no, (b) one, (c) on, (d) fixed, (e) line segment.
- 2\. (a) Ray AB, (b) Ray PQ and Ray PR, (c) Ray PQ, Ray PR and Ray PS, (d) Ray OM, Ray OP and Ray ON.
- 3\. (a) ^a----B^ (b) c------D\* (c) e------^ (d) ^g------H
Exercise-56
- 1\. (a)ZPQR < ZBAC,(b)ZABC < ZPQR,(c)ZCBD < ZABD,(d)ZABD < ZABC.
- 2\. (a) 30°, (b) 45°, (c) 90°, (d) 150°, (e) 135°, (f) 75°.
- 3\. (a) Right Angle, (b) Acute Angle, (c) Obtuse Angle, (d) Obtuse Angle. 4. Do it yourself.
- 5\. 60°. 6. 90°. 7. 120°. 8. Do ityourself. 9. Do ityourself.
Exercise-57\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_\_
- 1\. (a)/,(b)X,(c)/,(d)X.
- 3\. (a) Yes, (b) No, (c) Yes, (d) No, (e) Yes, (f) No.
2\. (a)X,(b)/,(c)X,(d)/.
- 4\. (a)T,(b)F,(c)T,(d)T,(e)F.
Exercise-60--------------------------------------------------------
- 1\. (a) 42 cm, (b) 76 cm, (c) 34 m, (d) 35 cm.
- 3\. (a) 24 m, (b) 28 cm, (c) 6 m, (d) 10cm.
- 5\. 365 m. 6.264 inches.
- 9\. 112cm. 10.1400.
- 2\. (a) 40, (b) 200, (c) 22.
- 4\. (a) 70 m, (b) 191 m, (c) 221 cm, (d) 30 cm.
- 7\. 54 cm. 8. 900 m.
- 11\. 3840m.
Exercise-61----------------------------------------------------------
- 1\. (a) 6 sq. cm, (b) 8 sq. cm, (c) 12 sq. cm, (d) 13 sq. cm, (e) 14 sq. cm.
Exercise-62--------------------------------------------------------
- 1\. (a) 5000 sq. cm, (b) 300 sq. mm, (c) 4 sq. cm, (d) 1 sq. m.
- 2\. (a) 42 sq. cm, (b) 216sq. mm, (c) 3 750 sq. cm, (d) 12000sq. m.
- 3\. (a) 144sq.cm, (b) 36sq. mm, (c) 196sq.cm, (d)225sq. m. 4. 28500sq.cm. 5. 1225sq.cm.
- 6\. Square > Rectangle (.•. square = 144 sq.cm and rectangle = 135 sq.cm)
- 7\. Perimeter = 320m; Area = 6400sq.cm. 8. 500sq.m 9. 225 sq.cm. 10.1000sq.m.
Exercise-63--------------------------------------------------------
- 1\. 1000000 euern. 2. 1000 eu mm. 3. (a) 500000 eu cm, (b) 15 eu cm, (c) 0.18 eu m.
- 4\. (a) 64cucm, (b) 600cu cm. 5. 480euern.
- 6\. (a) 8 cu cm, (b) 64 cu cm, (c) 3375 cu m. 7. 8 cm. 8. 10 m.
Exercise-66--------------------------------------------------------
- 1\. (a) 169, (b) 225. 2. (a) 64, (b) 169. 3. 49.
- 4\. (a)1 + 3 + 5 + 7 + 9+11 + 13,(b) 1 + 3 + 5 + 7 + 9+11 +13 + 15 + 17+19 + 21 + 23 + 25,
- (c) 1+3 + 5 + 7 + 9 + 11 + 13 + 15 + 17+19 +21
- 5\. (a) 49, (b) 100. 6. (a) 21, (b) 29, (c) 49, (d) 71.
- 7\. (a) 25-16 = 9,16-9 = 7, 9-4 = 5, (b) 6x6 = 1 + 3 + 5 + 7 + 9 + 11,5x5 = 1 + 3 + 5 + 7 + 9,4 x 4 = 1 + 3 + 5 + 7
- 8\. c,dande 9. 4,9,16,25,36,41. 10.25.
Exercise-67---------------------------------------------------------
- 1\. 253. 2. Doityourself. 3. 31375. 4. 325.
- 5\. RWWW^ 6. (a)T,(b)F,(c)F,(d)F.
Get Ready for Examination
1\.
- (a) Twenty five thousand four hundred twelve, (b) Thirty thousand two hundred twelve, (c) Two lakh sixty five thousand seven hundred twenty one. (d) Two lakh eighty two thousand nine hundred ten.
2\.
4\.
7\.
10\.
12\.
(a) 20341, (b) 69025, (c) 641396, (d) 11002.
- (a) LXVIII, (b) XCVIII, (c) CV, (d) XLVII.
- (b) 8000000 + 20000 + 30 + 4.
(a) 68815, 68915, (b) 759710, 759810, 759910.
(a) 597610, (b) 7755216.
19511,200201,200305,201301,555011.
3\.
5\.
6\.
8\.
14\.
17\.
21\.
(a) <, (b) >, (c) =, (d)
(a) 550, (b)599.
(a) 15, (b) 2, (c) 12.
18\. ? 63000.
22\. 350.
25\.
203363\.
11
28\.
i
29\. -y.
33\.
36\.
(a)^-, (b) 1.
(a) 3 +^, (b) 20 +
39\.
0.80.
40\.
44\. 41.
49\. ? 3925.45.
(a) 38, (b) 226, (c) 1106, (d) 909, (e) 95.
(a) 600000 + 39000 + 50 + 9,
(a) 4999950, (b) 49995.
99999\.
9\. 10000000.
11\. (a) 125009, (b) 252000.
13\. 69573, 65432, 55007,4321 5, 21 512.
15\. (a) By 4, (b) By 9.
19\. ? 100.00.
23\. 180 m.
16.55002
20\. 725.
24.210156.
26\. 3, 5, 9, 11, 13, 17 and 19.
2
30 —
19 •
31\.
34\. ? 8299.00.
19
100‘
245.84.
45\. 27.25 paise.
50\. ? 80582.40.
- 53\. The sum of 12 75 and 8690.
- 56\. 2 and 5. 57. No
- 59\. ? 63 75.00. 60. 2
- 64\. 2.595 kg. 65. 64.78 kg.
- 68\. 7.5 I. 69.1.7 1.
35\.
37\.
\_2\_
9 '
(a) -j^-, (b)
27\. (a)^-, (b)^, (c) -|-.
32\. (a)-y, (b) 24.
5 1000'
(a) 6.90, (b) 20.090.
41\. 5.3.
46\. 132.025.
51\. ? 1275.25.
42\. 400 litre.
38\. 39.33.
43\. 850 ml.
47\. 4 hours 15 minutes. 48. ? 3.20
52\. ? 162.80.
- 54\. Sum of 3290 and 4810. 55. 900.
- 58\. 2, 3, 5, 7, 11, 13, 17, 19, 23, 29.
- 61\. ? 18.00. 62. ? 39.95 m. 63. ? 12.30.
- 66\. 74.250 kg. 67. (a) 0.207 litre, (b) 4.375 litre.
70\. (a) 20 hours, (b) 28 hours 20 minutes,
(c) 2073600 seconds, (d) 8760 house.
71\. (a) 51 hours 7 minutes, (b) 16 hours 19 minutes.
72\. (a) 4 minutes 50 seconds, (b) 1 hour 24 minutes 48 seconds. 73. Do it yourself.
- 74\. Doityourself. 75. Doityourself.
- 77\. Do ityourself. 78. a, b, e.
- 81\. Doityourself. 82. Doityourself.
- 84\. (a) 90 m, (b) 500sq. m.
87\. 100 cubic m. 88. 90.
91\. 111110,1111110,11111110.
- 76\. Acute - 73°, 59°, 40°, 30°, 35°, 70°. Obtuse - 180°, 120°.
- 79\. a, b, e, f. 80. Do ityourself.
- 83\. (a) 5000 sq. cm, (b) 0.0075 cu m.
- 85\. ? 84500.00. 86. 12 sq. m; ? 480.00.
- 89\. Do ityourself. 90. (a)64, (b)91.
- 92\. Doityourself.
Put on your Thinking cap---
1\. 6:00am. 2. (a)12,(b)2.
3\. 20times.
4\. Do ityourself.
6\. 9. 7. 10/.
Get Set Go With Sum Up Mathematics-5