Shubharambha Math Book 5 for CTP 2077

Addition and Subtraction of like Fractions.

Class Discussion

Let's take few examples of like fractions.

Example 1

Add: 3 + 2
7 7
Solution:
3 2 3+2 5 To add like fractions
7 + 7 = 7 = 7
Add the numerators and keep
Example 2 the denominator common.

Add: 1 + 4 + 6
15 15 15
Solution:
1 4 6
15 + 15 + 15

= 1 +4+ 6
15

= 11
15

Example 3

Subtract: 7 – 2
8 8
Solution:
7 2
8 – 8 To subtract like fraction subtract
the numerators and keep the
= 7 – 2 = 5 denominator common.
8 8

Example 4

Simplify : 8 + 2 – 7
11 11 11
Solution:
8 +2– 7 10 – 7 3
181 + 2 – 7 = 11 = 11 = 11
11 11

Maths Zone -Grade 5 151

Addition and Subtraction of Mixed Number/Fraction

Class Discussion

Let's take few examples of mixed fractions.

Example 1

Add: 2 3 + 4 2
7 7
First Method Whole number is added to

Solution: whole number and fraction is

2 3 + 4 2 added to fraction.
7 7
3 2 3 + 2 5 5
= ( 2 + 4 ) + 7 + 7 = 6 + 7 = 6 + 7 = 6 7

Second Method

Solution: 3 2 2 + 3 = 2 3
7 7 7 7
2 + 4

= 2 × 7 + 3 + 4 × 7 + 3 [ Convert mixed number in Improper Fraction.]
7 7

= 177 + 31 = 17 + 31 = 48 = 6 6
7 7 7 7

[ Convert Improper Fraction into mixed number]

Example 2

Subtract: 3 4 from 6 5
9 9

First Method Second Method

Solution: Solution:

6 5 - 3 4 6 5 – 3 4
9 9 9 9
= 6 × 9 + 5 3×9+4
= (6 – 3) + 5 - 4 9 – 9
9 9
5 – 4 59 – 31
= 3 + 9 = 9

= 3 + 1 = 3 1 = 28 = 3 1
9 9 9 9

152 Maths Zone -Grade 5

Example 3

Simplify : 3 3 + 5 5 – 6 1
8 8 8

First Method Second Method

Solution: Solution:

3 3 + 5 5 – 6 1 3 3 + 5 5 – 6 1
8 8 8 8 8 8

= (3 + 5 – 6) + 3 + 5 – 1 = 3 × 8 + 3 + 5 × 8 + 5 – 6 × 8 + 1
8 8 8 8 8 8

= (8 – 6) + 3+5–1 = 27 + 45 – 49
8 8 8 8

= 2 + 7 = 2 7 = 27 + 45 – 49
8 8 8

= 72 – 49
8

= 23
8

= 2 7
8

Exercise 7.2

1. Find the sum of the following like fractions.

a. 3 + 1 b. 12 + 5 c. 15 + 7 d. 2 + 7
5 5 17 17 19 19 27 27

e. 2 1 + 1 f. 4 3 + 2 g. 8 5 + 3 122 h. 5 3 + 2 147
2 2 7 7 12 17

i. 3+ 7 j. 5 + 4 k. 20 + 15 l. 6 + 5 3
9 13 17 4

2. Find the difference of the following fractions.

a. 7 – 2 b. 14 – 12 c. 18 – 12 d. 15 – 8
9 9 19 19 23 23 21 21

Maths Zone -Grade 5 153

e. 3 2 – 1 f. 4 3 – 2 g. 6 5 – 3 122 h. 7 8 – 2 139
3 3 7 7 12 19

i. 2– 2 j. 7 – 3 k. 5 – 1 l. 6 – 4
7 9 12 15

3. Simplify:

a. 3 + 4 + 122 b. 7 + 8 + 250
12 12 20 20

c. 3 + 6 – 120 d. 8 – 4 + 165
10 10 15 15

e. 1 1 +2 2 +3 3 f. 5 3 + 1 1 + 2 5
7 7 7 8 8 8
7 3 120 8
g. 4 10 + 1 10 – 3 f. 6 9 –1 2 –3 4
9 9

4. Solve the following problems.

a. Sarita actaeke37 of cake and Rita ate 2 of the same cake. How
much did they eat together? 7

b. In an examination 2 of the questions were objectives. What
5
fraction of the questions were subjectives?

c. Amosrhnoipnkgeaenpder3h41aldin2t2h43e l of kerosene. If he sold 12 1 l in the
afternoon then find, 4

(i) How much kerosene did he sell all together?

(ii) How much kerosene was left with him?

154 Maths Zone -Grade 5

Addition and Subtraction of Unlike Fractions

Class Discussion

Let's take few examples of unlike fractions.

Example 1

Add : 1 and 1
2 4
Solution:

First Method: Second Method:

1 and 1 1 + 1 LCM of 2 and 4 is 4
2 4 2 4
4 ÷ 2 = 2 2 × 1 (1st Nr)
= 21 × 2 + 1 = 1×2+1×1 4 ÷ 4 = 1 1 × 1 (2nd Nr)
× 2 4 4

= 24 + 1 = 2+1
4 4

= 43 = 3
4

Example 2

Add : 3 2 and 2 1
Solution : 3 9

First Method Second Method Third Method

3 2 +2 1 3 2 + 2 1 3 2 + 2 1
3 9 3 9 3 9

= (3 + 2) + 2 + 1 = 11 + 19 = 11 + 19
3 9 3 9 3 9

= 5+ 2 × 3 + 1 = 11 × 3 + 19 = 11 × 3 + 19 × 1
3 × 3 9 3×3 9 9

= 5+ 6 + 1 = 33 + 19 = 52
9 9 9 9 9

= 5+ 6+1 = 33 + 19 = 5 7
9 9 9

= 5 + 7 = 52 Choose your best
9 9
method to solve
7
= 5 7 = 5 9 the problems.
9
Maths Zone -Grade 5 155

Example 3

Subtract : 4 from 3
10 5
Solution:

First Method Second Method

3 – 4 3 – 4 LCM of 5 and
5 10 5 10 10 is 10.

= 3×2 – 4 = 3×2–4×1
5×2 10 10

= 6 – 4 = 6-4 = 6–4
10 10 10 10
1
1 2 1
2 10 5
= 10 5 = 5=

= 1
5

Example 4

Subtract : 3 2 – 2 1
3 4
Solution:

First Method Second Method

3 2 – 2 1 3 2 – 2 1
3 4 3 4

= (3 – 2) + 2 – 1 = 11 – 9
3 4 3 4

= 1+ 2 × 4 – 1 × 3 = 11 × 4 – 9 × 3 M3 = 3, 6, 9, 12, 15 .....
3 × 4 4 × 3 12 M4 = 4, 8, 12, 16, ...
44 – 27 LCM = 3 and 4 = 12
= 1+ 8 – 3 = 12
12 12
17
= 1 + 5 = 12
12
5
= 1 5 = 1 12
12

156 Maths Zone -Grade 5

Example 5

Simplify : 3 1 + 1 3 + 2 4
4 8 12
Solution:
M4 = 4, 8, 12, 16, 20, 24, ...
3 1 + 1 3 + 2 4 M8 = 8, 16, 24, ...
4 8 12 M12= 12, 24 ...
LCM = 24
= (3 + 1 + 2) + 1 + 3 + 4
4 8 12 F4 = 2 × 2
F8 = 2 × 2 × 2
= 6+ 1×6+3×3+4×2 F12 = 2 × 2 × 3
24 LCM = 2 × 2 × 2 × 3
= 24
= 6+ 6+9+8
24

= 6 + 23 = 6 23
24 24

Example 6

Pabitra bought 5 2 m of ribbon. She gave 2 1 m to her sister and
3 4
1
1 4 m to her best friend Priya. How long ribbon is left with

Pabitra?

Solution: Ribbon left with Pabitra.

5 2 – 2 1 – 1 1
3 4 4

= (5 – 2 – 1) + 2 – 1 – 1
3 4 4

= 2+ 2×4 – 1×3 – 1×3 [LCM of 3, 4 and 4 is 12]
3×4 4×3 4×3

= 2 + 8 – 3 – 3
12 12 12

= 2+ 8–3–3 =2+ 8–6
12 12

= 2 + 21 = 2 + 1 = 2 1
\ 12 6 6 6
1
The ribbon left with Pabitra = 2 6 m.

Maths Zone -Grade 5 157

Exercise 7.3

1. Add :

a. 2 + 1 b. 3 + 3 c. 4 + 13 d. 2 1 + 1 1
3 6 5 10 7 21 2 4

e. 3 1 + 5 1 f. 3 2 +2 1 g. 1 3 + 2 5 h. 4 5 + 3 1
4 3 3 5 10 8 6 9

i. 2 7 + 5130
15

2. Subtract:

a. 2 – 1 b. 4 – 3 c. 5 – 11 d. 3 4 – 2 1
3 6 5 10 7 21 5 15

e. 6 2 –4 1 f. 5 9 – 2 3 g. 3 7 – 2 5 h. 8 3 – 316
3 4 11 4 8 12 4

i. 7 11 – 4 3
15 10

3. Simplify:

a. 1 + 2 – 3 b. 5 – 3 + 145 c. 3 2 + 1 3 + 2 5
2 3 5 12 10 3 4 6
5 1 4 3 1 5 1 2 3
d. 4 6 – 2 2 + 5 10 e. 7 4 – 3 8 – 2 16 f. 7 2 – 4 3 + 5 4

4. Solve the following problems.

a. Nima spent 1 of her monthly income in food, 1 in rent and 1 in
education 5 3 4

(i) How much income did she spend?

(ii) If the whole icome is assumed 1, what fraction of income is
left?

b. Hari did 4 of a work and Krishna did 3 of a work. Ram did 5
15 10 12
of the same work. How much work did they complete? What is

the remaining work if the whole work is assumed 1.

158 Maths Zone -Grade 5

Multiplication of a Fraction by a whole number

Class Discussion

Let's discuss about the multiplication of fraction and a whole number.

+=


1 + 1 = 2
2 2 2

2 × 1 ⇒ 2 × 1 = 2 ⇐ 1
2 2 2

+ =+
+

1 + 1 + 1 =1 1
2 2 2 2

3 × 1 ⇒ 3 × 1 = 3 ⇐ 1 1
2 2 2 2

+++ =+

1 + 1 + 1 + 1 1 + 1
3 3 3 3 3

4 × 1 ⇒ 4 × 1 = 4 ⇐ 1 1
3 3 3 3

To multiply a fraction by a whole number we multiply the
numerator of the fraction by the given whole number.

Maths Zone -Grade 5 159

Multiplication of a Fraction by another Fraction

Class Discussion

×= Double

shaded part

1 × 1 = 1×1 = 1 should be
2 3 2×3 6
1 × 1 = consider
2 3

×=

2 × 3 = 2 × 3 = 2×3 = 6 = 1
3 4 3 4 3 × 4 12 2

To multiply a fraction by another fraction we multiply the
numerator by numerator and denominator by the denominator.

Value of the given Fraction of a whole number of quantity.

Class Discussion

There are 8 chocolates. 1 of these chocolates are red in colour. So, 2
4
chocolates are red.

Mathematically,

160 Maths Zone -Grade 5

1 of 8 = 1 × 2 2
4 4
8=

\ 2 chocolates are red.

Example 1

There are 42 students in a class. If 2 of them are absent,
7

(i) Find the number of absent students

(ii) Find the fraction of present students

(iii) Find the number of present students.

Solution:

(i) The number of absent students = 2 of 42
7
6
= 2
7 × 42

= 2 × 6 = 12

(ii) The fraction of present students= 1 – 2
7

= 7–2 = 5
7 7

(iii) The number of present students = 5 of 42
7
6
= 5
7 × 42

= 5 × 6 = 30

OR,

The number of present students = Total students – absent students

= 42 – 12

= 30

Maths Zone -Grade 5 161

Example 2

Simplify: 3 1 × 3 3 × 3112
3 5

Solution:

3 1 ×3 3 ×2 1
3 5 12

= 130 × 18 × 25 Converting Mixed Fraction
5 12 into Improper Fraction

5 18 6 25 5
5 12
= 130 × ×

1 1 21

= 5 × 5 10 × 18 × 25
3 × 5 × 12
= 25
2×5×2×3×3×5×5
= 3×5×2×2×3

= 5 × 5 = 25

Prime Factorization Method

Exercise 7.4

1. Multiply

a. 4× 1 b. 5× 3 c. 4 × 5 d. 4 × 3
5 7 5 4 7 5

e. 1 1 × 1 1 f. 3 1 × 3 1 g. 2 2 × 10 h. 5 2 × 3
8 15 5 8 5 7

i. 1 of 8 j. 3 of 60 k. 2 of 4 l. 4 of 4 4
2 4 5 6 8 8

2. Simplify :

a. 3 × 7 × 2 b. 5 × 7 × 2 c. 3 × 1 × 7
4 9 3 7 5 5 2 5 8

d. 7 × 6 × 3 e. 2 5 ×3 4 × 4 4 f. 3 4 ×2 2 × 1 3
9 21 4 8 7 5 5 19 8

162 Maths Zone -Grade 5

3. Solve the following problems.

a. There are 50 students in a class. Among them 3 are girls.
5

(i) How many girls are there?

(ii) How many boys are there?

b. Distance between Pokhara and Kathmandu is 200 km. Snith

travelled 1 parts of the distance by a car and remaining
distance b4y a bus.

(i) How many kilometers did he travel by car?

(ii) How many kilometers did he travel by bus?

c. Divide Rs. 1575 into two parts, so mthoant eByi.bHekowgemtsu25chofdothees
total and Rajesh gets the remaining

each get?

Maths Zone -Grade 5 163

Division of Fraction

Class Discussion

Let's observe few examples:

5 × 1 = 1 2 × 3 =1 Reciprocal
5 5 1 3 2
5 2 3 Product of two
and 3 and 2 numbers is 1
'0' has no reciprocal
Reciprocal are each other. Reciprocal are each other.

To get reciprocal of a number, Divide 1 by the given number.

Reciprocal of 7 = 1 and reciprocal 3 = 1 = 4 [Reciprocal of a = 1 ]
7 4 3 3 a

4

Division of Fraction by a whole number

Let's take an example: 3 ÷ 2
4

⇒ +++++++++++++++++++++ +++++++++++++++++++++ +++++++++++++++++++++ +++++++++++++++++++++

3 3 ÷2= 3 × 1 = 3×1 = 3
4 4 4 2 4×2 8

How many groups of 2 are there in 3 ?
4
3
⇒ 8

There are 3 groups of 2 and total parts are 8.

Dividing a fraction by a whole number means multiplying by the reciprocal.

164 Maths Zone -Grade 5

Division of whole number by a Fraction

Class Discussion

Let's investigate the idea.

There are 6 apples, each person gets 2 apples.

How many people will get apples?

6÷2=3

How many groups of 2 are in 6.

There are 3 groups of 2 in 6.

Look at the same problem differently. 6 ÷ 1
2
There are 6 apples. Each person gets 1 of an apple.
2 2
How many people are there? = 6 × 1

How many 1 are in 6 whole? = 12
2

12 34 56 78 9 10 11 12
89


There are 12 groups of 1 of 6 whole.
2

Example 1

Divide: 6 ÷ 2
3

Solution:

6÷ 2 = 3 3 =3×3=9
3 2
6×

Let's observe it in number line.

1 234 56 7

0 123 45 6

Maths Zone -Grade 5 165

Division of Fraction by a Fraction.

Let's observe an example : 3 ÷ 1 23
4 4 1
1 3
How many groups of 4 we can make from 4 ? Flip

It takes 3 groups of 1 to make 3 .
4 4

3 ÷ 1 = 3 × 4 = 3
4 4 4 1


Change

Keep

First fraction '÷' Sign into Divisor
or whole multiplication into

number as it '×' reciprocal
is

Example 1

Divide: (a) 10 ÷ 2 (b) 4 ÷ 8 (c) 4 ÷ 8
3 5 7 21
Solution :

(a) 10 ÷ 2 (a) 4 ÷8 (c) 4 ÷ 8
3 = 5 7 21
5 3 4 1 4 21 3
= 2 5 × = 7 × 82
10 × 1 × 8
5 1
= 5 × 3 2 3
2
= 2 =

= 15 = 1 = 1 1
10 2

166 Maths Zone -Grade 5

Example 2

A rope of 8 2 m long has been made 6 equal pieces. Find the
5

length of each piece of the rope?

Solution:

We divide 8 2 m by 6 equal parts.
5 piece of rope
2
Length of each = 8 5 ÷ 6 7

= 42 ÷6= 42 × 1 = 7 = 1 2 m
5 5 6 5 5

∴ The length of each piece of rope = 1 2 m
5

Example 3

Divide : 4 ÷ 12 ÷ 24 Maths Songs
8 16 32

Solution:

4 ÷ 12 ÷ 24 Keep change Flip
8 16 32 Necessary Cancel
Multiply Nr. Nr, Dr. Dr.
= 84 × 112623× 32 4 That is our answer.
24 3
by SBS
= 23 × 4 = 8
× 3 9

Exercise 7.5

1. What is the reciprocal of each of the following.

a. 4 b. 7 c. 3 d. a
f. 0 5

e. p g. 1 h. 1
q 5 15

Maths Zone -Grade 5 167

2. Divide:

a. 3 ÷ 1 b. 7 ÷ 1 c. 8 ÷ 1
2 3 4

d. 1 ÷ 3 e. 2 ÷ 4 f. 6 ÷ 3
3 5 7

g. 3 ÷ 15 h. 8 ÷ 3272 i. 6 4 ÷ 4 3
4 16 9 7 5

j. 6 3 ÷ 17
8 32
3. Simplify :

a. 6 ÷ 12 ÷ 3 b. 8 ÷ 1 ÷ 1 c. 7 × 6 ÷ 5
7 14 2 5 3 4 12 7 8

d. 4÷ 1 3 × 2 1
5 3

4. Solve the following problems.

a. Keshav has a piece of wood that is 3 of a foot in length. He
1 a foot long. How many
needs to cut that into pieces of 16 4
pieces can he cut? of

b. Deepak has 5 feet long rope. If he cuts the rope into pieces of
1
4 foot long, find the number of pieces.

c. Kamal has 1 l of oil. He wants to split it between himself and
2
his three friends equally. How much liter of oil will each of

then get?

d. The cost of 2 1 kg of apple is Rs. 122 1 . Find the cost of 1 kg
of apple. 2 2

168 Maths Zone -Grade 5

Lesson

2 Decimal Number

Class Discussion Fraction Decimal Number name
1 0.1 One tenths
Figure 10
0.01 One
1 Hundredths
100

1 0.001 One
1000 Thousandths

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5

Place value Table of Decimal Number

Hundreds Tens Ones Tenths Hundredths Thousandths
2 4 3
56 9

243.569

∴ Two hundred forty three point five six nine.

Maths Zone -Grade 5 169

Expanded form : 200 + 40 + 3 + 5 + 6 + 9
10 100 1000

Comparison of Decimal Numbers

Example 1

Comapare : 75.257 and 75.273

Solution: 75.273 First compare whole
numbers then
75.257
decimal numbers
= starting from tenths
place, hundredths
=
place and so on.
<

\ 75.257 < 75.273

Exercise 7.6

1. Express into decimal number.

a. 3 = ......... b. 7 = ......... c. 55 = ......... d. 235 =.........
10 100 10 10

e. 73 = ......... f. 215 = ......... g. 5 = ......... h. 27 =.........
100 100 100 1000

i. 376 = ......... j. 41205060 = ......... k. 3576 = ....... l. 1 =.........
1000 1000 1000

2. Express into fraction.

a. 0.6 = ......... b. 0.08 = ......... c. 4.5 = ......... d. 0.75 =.........

e. 45.7 = ......... f. 0.084 = ......... g. 15.3 = ......... h. 36.24 =.........

i. 32.037 = ...... j. 0.0973 = ......

3. Write the place name and place value of underlined digit?
a. 5.2 = ......... b. 43.35 = ......... c. 0.008 = ......... d. 7.243 =.........

170 Maths Zone -Grade 5

4. Express the given number in place value chart and write their
number name.

a. 3.6 = ........ b. 43.27 = ....... c. 513.28 = ...... d. 174.267 =.......

5. Write in expanded form.

a. 3.7 b. 27.45 c. 512.83 d. 417.368

6. Write in short form.

a. 5 + 6 b. 20 + 5 + 6 + 3 c. 400 + 80 + 5 + 1 + 2
10 10 100 10 100

d. 600 + 30 + 4 + 2 + 3 + 4
10 100 1000

7. Write in short form

a. 50 + 5 + 0.2 + 0.06 + 0.06 = .........................

b. 100 + 40 + 3 + 0.4 + 0.02 = .........................

c. 60 + 3 + 0.5 + 0.02 + 0.005 = .........................

d. 5000 + 900 + 90 + 2 + 0.8 = .........................
8. Compare the given decimals and put <, > or = sign.

a. 2.5 ........ 3.7 b. 4.6 ........ 4.2 c. 5.42 ........ 5.47

d. 0.1 ........ 0.01 e. 0.01 ........ 0.001 f. 85.678 ........ 85.768

Conversion of Decimal into Fraction

Class Discussion

To convert decimal into a fraction follow these steps:

Step 1 Write down the decimal divided by 1 like this : decimal
1
Step 2 Multiply both top and bottom by 10 or multiple of 10 for

every number. (For eg if there are two digits after the decimal

point, then multiply by 100, if there are three digits after the

decimal (point) then multiply by 1000 and so on.)

Step 3 Simplify (or reduce) the fraction.

Maths Zone -Grade 5 171

Example 1

Convert 0.75 into a fraction

Solution: Write down 0.75 divided by 1. ⇒ 0.75
Step I 1
Step II Multiply both top and bottom by 100 (because there are

2 digits after the decimal point that is 10 × 10 = 100)

× 100 Top number turns
into a whole number
0.75 = 75
1 100

× 100

Step III Simplify (or reduce) the fraction.

75 = 75 3 = 3 [or by any other process]
100 1004 4

∴ 0.75 = 3
4

Example 2

Convert 0.625 into a fraction

Solution: 625 25 5
1000
0.625 = 0.625 = 0.625 × 1000 = = 5
1 1 × 1000 8

40 8

∴ 0.625 = 5
8

Conversion of Fraction into Decimal

Class Discussion

To convert a fraction into a decimal follow these steps.
Step 1 : Find a number you can multiply by the bottom of the fraction

172 Maths Zone -Grade 5

to make it 10 or 100 or 1000 or any 1 followed by 0s.

Step 2 : Multiply both top and bottom number by that number.

Step 3: Then write down just the top number, putting the decimal
point in the correct spot.

(One space from the right hand side for every zero in the
bottom number).

Example 1

Convert 3 to a decimal.
4
Solution:

Step 1 : We can multiply 4 by 25 to make it 100.

Step 2 : Multiply top and bottom by 25.

× 25

3 75
4 = 100

× 25

Step 3 : Write down 75 with the decimal point 2 spaces from the

right (because 100 has 2 zeros)

∴ 3 = 0.75
4

Example 2

Convert 3 into a decimal.
16
Solution:

3 = 3 × 625 = 1875 = 0.1875 It will be difficult to
16 16 × 625 10000 the students, so prefer
long division method
∴ 3 = 0.1875 in such problems.
16


Maths Zone -Grade 5 173

Conversion of fraction into decimal using long division

Example 1

Convert 5 into decimal.
6

Solution: Here, 6 can't be made the multiple of 10 So, we need to

apply long division method.

6 5 0.833 ... When we put decimal, 0 (zero) comes
–0 automatically with the remainder.
50

–48
20 Again put another zero.

– 18

20 This problem never ends as remainder
– 18 comes 2 in every steps.
2

∴ 5 = 0.833 (up to three decimal places)
6

Example 1

Convert 7 into decimal using long division.
8

Solution:

Here, 7 = 87 0.875 It can be done by
8 –0 previous method
also.
70

–64

60

–56

40

–40

×

∴ 7 = 0.875
8

174 Maths Zone -Grade 5

Addition and Subtraction of Decimal Numbers

Addition and subtraction of decimal numbers is similar to the addition
and subtraction of whole numbers. To add or subtract decimals we align
the numbers according to their place in decimals.

Example 1

Add the following decimals.

(a) 0.3 + 0.8 (b) 0.75 + 2.32 (c) 0.5 + 0.57 + 0.234

Solution :

(a) Align the numbers according to their place
in decimals.
1
0.5 and
0.3

+ 0.8

1.1

Solution : (c) Solution: 0.500 are
similar
(b) Solution : 11
You can add
1 0.500 zeros after
decimal number
0.75 + 0.570 as you required
+ 2.32 1.1070

3.07 + 0.234

1.304

Example 2

Subtract the following decimals.

(a) 0.12 – 0.09 (b) 3.75 – 1.05

(a) Solution : (b) Solution:
3.75
0
– 1.05
0.12
2.70
– 0.09

0.03

Maths Zone -Grade 5 175

Example 3

Simplify : 13.8 – 6.4 + 12.50

Solution:

13.8

–6.4

7.4 First, add first and last and
then subtract second.
Now,

7.40

+ 12.50

19.90

∴ 13.8 – 6.4 + 12.50 = 19.90


Exercise 7.7

1. Convert the following decimals into fractions and reduce the
functions into their lowest terms wherever necessary.

a. 0.5 b. 1.5 c. 2.6 d. 0.02

e. 0.25 f. 0.075 g. 2.50 h. 4.005

2. Express the following fractions into decimals by making
denominators tens, hundreds and thousands.

a. 5 b. 2 c. 1 d. 3 2
10 5 2 5

e. 5 1 f. 270 g. 11 h. 2570
2 25

i. 12 3 j. 16 3
4 8

3. Express the following fractions into decimals using long division

method. (up to three decimal places).

a. 1 b. 7 c. 2 d. 5
5 9 3 6

e. 176 f. 3 47 g. 4 5 h. 1251
9

176 Maths Zone -Grade 5

i. 1265 j. 175
17

4. Add the following decimals.

a. 0.235 + 0.273 b. 0.069 + 0.74 c. 0.057 + 0.4

d. 0.58 + 0.013 e. 1.4 + 2.7 f. 6.45 + 7.98

g. 2.357 + 8.14 h. 125.6 + 2.375 i. 452.44 +23.456

5. Subtract the following decimals.

a. 0.7 – 0.4 b. 0.8 – 0.55 c. 0.95 – 0.325

d. 7.98 – 4.44 e. 45.9 – 17.246 f. 420.37 –101.295

g. 10 – 0.08 h. 11.05 – 7.22 i. 600.007–400.06
6. Simplify: b. 3.7 – 1.55 + 0.08

a. 0.9 + 0.7 – 0.8

c. 12.65 –5.78 +0.88 d. 45.234 + 7.48 – 9.76

e. 2.75 – 3.8 + 5.67 – 1.45 f. 4.87 – 5.67 + 9.22 – 3.66

7. Solve the following problems.
a. Indu went to a toy store and purchased a doll for Rs. 35.75. She
gave the sales person Rs. 50 for her purchase. How much change
did she receive?

b. Kamala bought fruits for Rs. 375.50 and vegetables for Rs. 215.75.
How much did she pay altogether?

c. What is the combined thickness of five shims 0.008 cm, 0.125 cm,
0.15cm, 0.185cm and 0.005 cm?

d. Ram, Basanta and Hari have combined height of 7 meter. If Ram
is 2.31 meter tall and Hari is 2.6 meter tall, How much tall is
Basanta?




Maths Zone -Grade 5 177

Multiplication of Decimals by 10,100 and 1000

While multiplying decimal numbers by numbers such as 10,100, and 1000,
move the decimal (point) to the right as many places as there are zeros in
the factor.

Example 1

Multiply : 0.54 by 10. 0.54 × 10
Solution:
0.54 × 10 = 5.4 = 54 × 10 = 54 = 5.4
100 10

[Move the decimal (point) one step to the right (10 has one zero)]

Example 2

Multiply : 2.75 by 100. 2.75 × 100
Solution:
2.75 × 100 = 275. = 275 = 275 × 100 = 275
100

[Move the decimal point two steps to the right (100 has two zero]

Example 3 0.47 × 1000

Multiply : 0.47 by 1000. = 47 × 1000 = 470
Solution: 100
0.470 × 1000 = 470. = 470

[1000 means we move the point three steps to the right. Keep one zero at
the end of 0.47, so that the decimal point can "jump over to" that place.]

Interesting Fact:

When 0.01 (a hundredth) is multiplied by ten we get ten hundredths,

which is equal to one tenth.

0.01 × 10 = 1 × 10 = 11000 = 1 = 0.1
100 10

178 Maths Zone -Grade 5

Multiplication of Decimal numbers by whole numbers

Follow these steps:
1. Multiply normally ignoring decimals.
2. Put the decimal (point) in the answer. It will have as many
decimal digits as the decimal number has.

Example 1

Multiply : 22.6 by 12.

Solution:

Multiply these numbers as whole numbers ignoring the decimal
(point).

Compensate by placing the decimal (point) in the
product

22.6 ⇒ 22.6 1 decimal digit
× 12 × 12 1 decimal digit
452 452
226 226
2712 271.2

Alternative Method :

22.6 × 12 ⇒ 226 × 12 = 2712 = 271.2
10 10

Multiplication of a decimal number and a whole number can be solved

by repeated addition.

4 × 0.3 = 0.3 + 0.3 + 0.3 + 0.3 = 1.2
5 × 0.15 = 0.15 + 0.15 + 0.15 + 0.15 + 0.15 = 0.75
and
3 × 0.007 = 0.007 + 0.007 + 0.007 = 0.021.

Maths Zone -Grade 5 179

Multiplication of Decimals by other decimal numbers

Follow these steps:
a. Multiply normally ignoring the decimal points.
b. Put the decimal (point) in the answer it will have as many decimal
digits as the two original numbers combined.

Example 2

Multiply : 3.05 by 2.7

Solution:

Multiply normally ignoring the decimal points.
Compensate by placing the decimal (point) in the
product

3.05 ⇒ 3.05 2 decimal digits 3 decimal
× 2.7 × 2.7 1 decimal digit digits
2135 2135
3 decimal digits
610 610
8235 8.235

Alternative Method :

3.05 × 2.7 ⇒ 305 × 27 = 8235 = 8.235
100 10 1000

Exercise 7.8

1. Find the product of :
a. 4.49 × 10 = ....... b. 70.5 × 10 = ....... c. 0.05 × 10 = .......

d. 5.52 × 100 = ....... e. 35.6 × 100 = ....... f. 0.007 × 100 = .......

g. 0.96 × 100 = ....... h. 0.7 × 10 = ....... i. 7.77 × 1000 = .......

j. 27.3 × 1000 = ....... k. 0.009 × 1000 = ....... l. 5.373 × 1000 = .......

2. Find the product of :

a. 8 × 0.5 b. 9 × 0.7 c. 12 × 0.34

180 Maths Zone -Grade 5

d. 15 × 0.27 e. 3.7 × 9 f. 4.23 × 15

g. 2.169 × 17 h. 2.34 × 43

3. Find the product of :

a. 0.7 × 0.3 b. 0.25 × 0.7 c. 0.523 × 0.9

d. 1.5 × 1.3 e. 3.72 × 0.8 f. 5.397×0.6

g. 15.75 × 1.7 h. 9.235 × 4.5 i. 4.005 × 3.6

j. 41.23 × 5.62 k. 7.05 × 3.06 l. 3.009 × 0.54

4. Solve the following problems.
a. The cost of 1 kg sugar is Rs. 78.50. Find the cost of 12 kg sugar.

b. If the average speed of a car is 85.75 km/hr what distance will it
cover in 4.5 hours?

5. Convert the following:
a. Rs. 7.25 into paisa (100 paisa = Rs. 1)

b. 25.65 liters into ml ( 1 l = 1000 ml)

Maths Zone -Grade 5 181

Division of Decimals by 10, 100 and 1000.

While dividing decimal numbers by numbers such as 10, 100 and 1000.
Move the decimal point to the left as many places as there are zeros in the
divisor.

Example 1

Divide : 3.6 by 10 3.6 ÷ 10 ⇒31.06⇒ 36 × 1
Solution: 10 10

3.6 ÷ 10 = 0.36 ⇒13060 ⇒ 0.36

[Move the decimal point one step to the left (10 has one zero.)]

Example 2 356.5 ÷ 1000 ⇒ 356.5
10
Divide : 365.5 by 100 3565
Solution: ⇒ 3565 × 1 ⇒ 1000 ⇒ 3.565
10 100
356.5 ÷ 100 = 3.565

[Move the decimal point two step to the left (100 has two zero.)]

Example 3 725.35 ÷ 100 ⇒712050.305

Divide : 725.35 by 1000 ⇒ 72535 × 1 ⇒ 72535 ⇒0.72535
Solution: 1000 100 100000

725.35 ÷ 100 = 0.72535

[Move the decimal point three step of the left (1000 has three zero)]

182 Maths Zone -Grade 5

Division of decimal by whole numbers.

Follow these steps.
a. Divide normally, ignoring decimals point.
b. Put the decimal point in the answer very precisely.

Example 1

Divide the following decimals.

(a) 2.7 ÷ 9 (b) 25.875 ÷ 15 (c) 0.2975 ÷ 7

Solution:

(a) 2.7 ÷ 9

= 29.7 By long division method.
= 27
3 9 2.7 0.3 2 cannot be divided by 9 place 0 in the
–0 quotient.
10×9 27
3 –27 Divide 2.7 = 27 tenths by 9 we get 3
= 10 × tenths in the quotient.

= 0.3 ∴ 2.7 ÷ 9 = 0.3

Solution:
b) 25.875 ÷ 15

= 251.85751 725 By long division method.
25875
= 1000 × 15 15 25.875 1.725
–15
= 1725 108
1000 –105
37
= 1.725 – 30
75
–75
×

∴ 25.875 ÷ 15 = 1.725

Maths Zone -Grade 5 183

Solution:

c) 0.2975 ÷ 7

= 0.2975 By long division method. The tenths place
7 digit 2 cannot be
425 7 0.2975 0.0425 divided by 7. So,
2975 –0 write a zero at
= 1000 × 7 2 tenths place in
–0 the quotient then
= 425 29 divide 29 by 7.
1000 – 28
17
= 0.0425 - 14
35
- 35
×

Division of decimals by other decimals

Follow these steps

a. Make the divisor a whole number by multiplying the numerator and
denominator by the appropriate power of 10.

b. Perform by any division method.



Example 1

Divide 5.85 by 1.5 So,Numerator is also
multiplied by 10
Solution:

5.85 ÷ 1.5 = 5.85 = 5.85 × 10 = 58.5 Denominator is
1.5 1.5 × 10 15
Now, multiplied by 10 to

remove decimal of

15 58.5 3.9 denominator

–45

135

–135

×

\ 5.85 ÷ 15 = 3.9.

184 Maths Zone -Grade 5

Exercise 7.9

1. Find the quotients of the following by shifting the decimal point.
a. 15 ÷ 10 = ....... b. 25 ÷ 100 = ....... c. 45 ÷ 1000 = .......

d. 2.7 ÷ 10 = ....... e. 6.3 ÷ 100 = ....... f. 7.5 ÷ 1000 =.......

g. 3.75 ÷ 10 = ....... h. 52.76 ÷ 100 = ....... i. 115.32 ÷ 1000 = .......

j. 16.348 ÷ 10 = ....... k. 3.278 ÷ 100 = ....... l. 5.982 ÷ 1000 = .......

2. Find the quotient of :

a. 3.2 ÷ 8 b. 0.75 ÷ 5 c. 0.357 ÷ 3

d. 5.31 ÷ 9 e. 8.52 ÷ 12 f. 9.63 ÷ 15

g. 12.408 ÷ 22 h. 17.15 ÷ 7

3. Divide and find the quotient.

a. 0.8 ÷ 0.2 b. 0.15 ÷ 0.3 c. 0.55 ÷ 0.5

d. 7.28 ÷ 0.8 e. 36.4 ÷ 0.04 f. 28.56 ÷ 0.14

g. 0.35 ÷ 0.005 h. 7 ÷ 0.14 i. 15.75 ÷ 0.15

4. Convert the following.
a. 375 paisa into rupees. (Re. 1 = 100 paisa)

b. 1575 gram into kilogram (1 kg = 1000 gm)

5. Solve the following problems.
a. The cost of 7 pens is Rs. 89.25. Find the cost of 1 pen.

b. A rope of 230.64 m is cut into 8 equal pieces. What is the length
of a piece?

Maths Zone -Grade 5 185

Rounding off the Decimals

What is Rounding?
Rounding means making a number simpler but keeping its value close to
what it was. The result is less accurate but easier to use. 64 rounded to the
nearest ten is 60 because 64 is closer to 60 than to 70. But 66 goes up to 70.

Example 1

How to Round Numbers ?
a. Decide which is the last digit to keep.
b. Leave it the same if the next digit is less than 5.
(This is called rounding down)
c. But increase it by '1' if the next digits is 5 or more
(This is called rounding up)

To tens
524 'Here 4 is less than 5, So '2' stays the same
⇒ 520
Now, 576 'Here, '6' is more than 5 so, 7 is increase by 1.
⇒ 580

To hundredths 'Here '4' is less than 5 so '3' stays the same
2.7348 'Here '6' is greater than 5, so 4 increases to 5.
⇒ 2.7300
⇒ 2.73
Now,
2.8462
⇒ 2.8500
⇒ 2.85

186 Maths Zone -Grade 5

Example 2

Round 84 to the nearest 10.
• We want to keep the '8' (it is in the 10s position)
• The next digit is '4' which is less than 5, no change is needed to 8.
• 84 gets round down and becomes 80.

Example 3

Round 76 to the nearest 10.
• We want to keep the '7'
• The next digit is '6' which is more than 5. So increase the 7 by 1 to
'8'
• 76 gets rounded up to 80.

Rounding Decimals

‰‰ First work out which number will be left when we finish.
‰‰ Rounding to tenths means to leave one number after the decimal

point.
‰‰ Rounding to hundredths means to leave two numbers after the

decimal point and so on.

Example 4

Round off 3.1617 into tenths, hundredth and thousandths.
Solution :
3.1617 rounded to tenths is 3.2 as the next digit (6) more than 5.
3.1617 rounded to hundredths is 3.16
as the next digit (1) is less than 5.
3.1617 rounded to thousandths is 3.162
as the next digit (7) is more than 5.

Maths Zone -Grade 5 187

Exercise 7.10

1. Round off to the nearest whole number.

a. 32.3 b. 47.7 c. 110.8

d. 165.5 e. 240.4 f. 568.3

2. Round off to the nearest tenths (one decimal places)

a. 4.42 b. 7.57 c. 8.64

d. 12.63 e. 24.68 f. 50.45

3. Round off to the nearest hundredths (two decimal places)

a. 2.548 b. 3.672 c. 7.146

d. 11.165 e. 42.432 f. 63.689

4. Round off to the nearest thousandths (three decimal places)

a. 7.0529 b. 8.5264 c. 12.3047

d. 18.5623 e. 55.4918 f. 60.0155

5. Solve the followings problems.
a. The distance from Kalanki chowk to Balaju chowk is 5.47 km.
What is the distance to nearest in km?

b. One scientific team determined that the average thickness of a
chicken's egg shell is 0.311 millimeters. What is the thickness of
the shell to the nearest tenth.

188 Maths Zone -Grade 5

Lesson Percentage

3

Class Discussion

Percent means "for every 100" or out of 100". The (%) symbol as a quick
way to write a fraction with denominator of 100. For example: instead of
saying "It rained 15 days out of every 100." We say "It rained 15% of time."


Fraction of shaded part : 20 = 20%
100

25 out of 100 = 25 = 25% 40 out of 50 = 40 = 40 × 2
100 50 50 × 2

7 out of 20 = 7 = 7×5 = 80 = 80%
20 20 × 5 100

= 13050 = 35%

Percentages can be written as decimal number by moving the decimal two
places to the left.

Percent means per 100 or 27 = 0.27
d ivide d by 100. Divid ing b y 27 % = 100

100 moves the decimal point

two places to the left.

Maths Zone -Grade 5 189

Decimal number can be written as percentage by moving the decimal two
places to the right.

Changing a number to its 0.56 % = 0.56 × 100 % = 56%
percentage value requires the
op posi te oper ation -mu ltiply
by 100% or move the decimal
point two places to the right.

Formula for calculating percentage
To convert a fraction or decimal to a percentage, multiply by 100%

1M0 u0%ltipt loy givth eethef rarecstiuol nt asbya 1 = 1 × 100% = 25%
4 4

percentage value. 25

100 % = 100 and 1 = 1% 4 100 1
100 100 –8 ∴ 4 = 25 %
20
–20
×

To convert percentage to a fraction, divide by 100 and reduce the

fraction into its lowest term.

50 % = 50 = 51 = 1
100 10 2
2

190 Maths Zone -Grade 5

Example 1

Convert into percentage : =(a1)600053 (b) 4
= 60% 9
3 3 × 20
(a) Solution: 5 = 5 × 20 3 = 3 × 100 = 3 × 100%
5 5 100 5

= 300 = 60%
5
(b) Solution :

4 = 4 × 100 = 4 × 100% = 400 %
9 9 100 9 9

Example 2

Convert into fraction: 45 %

Solution : 45
100
45 % 45 % =

= 45 × 1 = 45 = 9 Remove % sign and divide by
100 100 20
100.

Example 3

Convert 65% into fraction and then into decimal.

Solution: 65 % = 65 = 0.65.
100

Example 4

Convert into percentage : (a) 0.75 (b) 0.7

(a) Solution: 0.75 = 75 First change decimal into
100 fraction.

= 75 × 100% = 75% Change fraction into
100 percentage.

(b) Solution: 0.7 = 7
10

Maths Zone -Grade 5 191

= 7 × 100% = 70%
10

Example 5

Convert into decimal : (a) 5% (b) 66%

(a) Solution: (b) Solution :

5 % = 5 66% = 66
100 100

= 0.05 = 0.66

Percent of Given Number

To find the percent of a given numbers, we have to multiply the given
percent and the number.

Example 1

Find 15 % of 200

Solution:

15% of 200

= 15% × 200 [ Remove 'of' by '×' sign]

= 15 × 200 [Convert percent into fraction]
100

= 15 × 2

= 30

Example 2

There are 40 students in a class. If 40% of the students are girls, find

the number of girls and boys of the class.

Solution:

Number of girls in the class

= 40 % of 40

= 40 × 40
100
= 40 × 4

192 Maths Zone -Grade 5

= 16
∴ The number of girls = 16.
And, the number of boys = Total students - Number of girls
= 40 – 16

= 24

Example 3

Find the percentage of 12 out of 20.
Solution:

12 [First convert into Fraction]
20

= 12 × 5 %[Convert into Percentage]
20
100

= 12 × 5%

= 60%

Exercise 7.11

1. Convert the following fractions into percentage.

a. 5 b. 12 c. 55 d. 80 e. 100
100 100 100 100 100

2. Convert the following fractions into percentage

a. 1 b. 2 c. 3 d. 7 e. 17
2 5 10 25 50

f. 3 g. 6 2 h. 7 3 i. 12 j. 3
20 5 4 15 8

3. Convert the following percentage into fractions and reduce them

into lowest term.

a. 8% b. 35% c. 75% d. 80% e. 125%

4. Convert the following percentage into decimal.

a. 6% b. 14% c. 44% d. 84% e. 215%

Maths Zone -Grade 5 193

5. Convert the following decimal into percentage.

a. 0.4 b. 0.05 c. 0.54 d. 0.94 e. 1.45

6. Find the value of

a. 40 % of Rs. 500 b. 15 % of 80 m c. 75% of 160 kg

d. 25% of 8 l e. 2 1 % of Rs.200.
2

7. Find the percentage.

a. 15 out of 50 b. 40 out of 160 c. 75 paisa out of Re 1

d. Rs. 42 out of Rs. 84 e. 25 minutes out of an hour

8. Solve the following problems.

a. There are 120 students in the class. If 40% of the students are

girls, how many students are girls and how many students are

boys?

b. 2 of the total population of a village are women. Find the
5
percentage of women, and percentage of men?

c. If you obtained 45 marks out of 50 marks in Mathematics,
what fraction and percentage of marks did you obtain?

d. Rajendra scores 85% in a spelling test out of 40 questions.
How many did he get right?

e. In a survey of 300 adults, 25% did not know how to ride a
bike. How many people can ride bike?

f. A toy car costing Rs. 600 is reduced by 15 % in the sale. How
much does it cost now?

194 Maths Zone -Grade 5

Maths Fun

Draw any 5 shapes (letters, digits, geometric figures etc.) of your choice
using different colors in the given worksheet and complete the table given
below.
(Do not use part of the square box of the worksheet)

Table

Color Shapes No. of Fraction Decimal Percentage

used box

Red 4 9 9 0.09 9%
100

1.

2.

3.

4.

5.

Maths Zone -Grade 5 195

Maths Songs of Rounding Decimals

2 7.5 → 28.0

• Find the place value and circle the digit.
• Move to the right and underline it.
• 0 – 4 the circle stays the same; 5 – 9 adding '1' is the game.
• Digits to the right turn into zero, all other numbers stay the same.

Multiply and place the answer in the cross-number puzzle.

Across Down a. b.

a. 4 × 0.06 a. 8 × 0.009

b. 3 × 0.3 b. 9 × 0.03 c.

c. 10 × 0.07 c. 7 × 0.07

d. 90 × 0.011 d. 5 × 0.16 d.
e. 0.252× 10 e. 10 × 0.02
e.

e.

196 Maths Zone -Grade 5

Practice Zone

Group A
A. Circle the correct answer.

1. Which of the following is an improper fraction?
2 . aA. fr52ac tion 4 8 1
b. 5 c. 7 d. 2
than the numerator
having denominator greater

is………………..fraction.

a. proper b. improper c. mixed d. none of these
3. What is the decimal number of 170? d. 7.0
a. 0.07 b. 0.7 c. 0.007

4. How many tenths are there in 432.567?

a. 5 b. 3 c. 4 d. 10

5. The decimal number 0.02 can be converted to fraction as 1
a. 1020 b. 120 20
6. Round off 67.91 to one decimal c. 20 d.
place is...1..0...............

a. 67.00 b. 67.10 c. 67.20 d. 67.90
3 c. 36 d. 9
7. Find the value of 9 ÷ 4 . c. 55% d. 85%

a. 12 3 b. 27
4
8. Express into percentage.

a. 65% b. 75%

9.. Find the value of 5% of 80.

a. 5 b. 4 1 c. 3 d. 6
2 c. 50% d. 500%
10. What is the percentage of ?

a. 0.5% b. 5%

11. The value of 3253 in decimal is……………
10000

a. 32.53 b. 325.3 c. 0.3253 d. 3.253

12. The equivalent fraction of 2 is 4 d. 8
3 8 5
a. 4 b. 8 c.
69

Maths Zone -Grade 5 197

Group B

Solve the following questions

1. Identify the types of given fractions and write:

2 5 , 2 , 3 , 100 1 , 21 , 8
7 3 2 4 17 3
a. Proper fractions : ………………..

b. Mixed fractions : ………………

c. Improper fractions: ………………….

d. Like fractions :……………………

2. Simplify the following:

a. 3 + 2 b. 12 ÷ 144 c. 9 1 of 120
4 8 11 121 6

d. 24 ÷ 1 3 e. 4 1 – 1 4
5 2 5

3. Which one is greater? 2 2
3 2 10 5
a. 9 and 3 b. and

4. Simplify:

a. 7.82 + 0.94 – 3.58 b. 0.047 × 1000 + 53

5. Simplify: 3 + 5 + 3
7 21 14

6. There are 400 students in a school. Among them 160 are girls, find the
percentage of boys.

7. Arrange 3.14, 4.75 and 2.69 in ascending order.

8. A rope of 3.92 m is cut into 4 pieces. What is the length of each piece?

9. If 3 of the length of a road is 81 km, what is the length of 1 of it?
10 2

10. Out of a class of 200 students, two-fifths studied Maths, how many

studied Maths?
11. There are 350 oranges in a basket. If 20% of them are rotten, how
many oranges are rotten?

198 Maths Zone -Grade 5

Answers of Unit 7

Exercise 7.1

1 and 2 solve and show it in your maths teacher.

3. Answer vary, show to your teacher.

4. (a) 43 (b) 32 (c) 190 (d) 43
5. (a) 53 (b) 371 (c) 361 (d) 681
4 5 1 7 5
6. (a) 3 7 (b) 3 9 (c) 7 6 (d) 10 8 (d) 4

7. (a) 2105 and 4 (b) 18 and 35
20 42 42
(c) 172 10 15 20
and 12 (d) 40 and 40

Exercise 7.2

1. (a) 54 (b) 17 or 1 (c) 22 or 1 3 (d) 9 or 1
17 19 19 27 3

(e) 6 or 3 (f) 33 or 4 5 (g) 11 7 (h) 7 7
2 7 7 12 17

(i) 3 7 (j) 5 4 (k) 20 15 (l) 11 3
9 13 17 4

2. (a) 95 (b) 2 (c) 6 (d) 7 or 1
19 23 21 3

(e) 3 1 (f) 4 1 (g) 3 1 (h) 5 5
3 7 4 19

(i) 172 or 1 5 (j) 60 or 6 2 (k) 59 or 4 11 (l) 86 or 5 11
7 9 3 12 12 15 15

3. (a) 9 or 3 (b) 20 or 1 (c) 7 (d) 10 or 2
12 4 20 10 15 3

(e) 6 6 (f) 8 (g) 2 8 or 2 4 (h) 2 2
7 10 5 9

4. (a) 5 (b) 3 (c) (i) 15 2 l (ii) 7 1 l
7 5 4 4

Maths Zone -Grade 5 199

Exercise 7.3

1. (a) 65 (b) 190 (c) 1 4 (d) 3 3 (e) 8 7
21 4 12

(f) 5 13 (g) 3 27 (h) 7 17 (i) 7 23
15 40 18 30

2. (a) 21 (b) 21 (c) 241 (d) 1 11 (e) 2 5
15 12

(f) 3 3 (g) 1 11 (h) 5 7 (i) 3 13
44 24 12 30

3. (a) 1370 (b) 23 (c) 8 1 (d) 7 11 (e) 2 15
60 4 15 16

(f) 8 7
12

3. (a) (i) 47 (ii) 13 (b) (i)5690 (ii) 1
60 60 60

Exercise 7.4

1. (a) 45 (b) 2 1 (c) 1 (d) 12 (e) 1 1
7 35 5

(f) 4 4 (g) 24 (h) 15 6 (i) 4 (j) 45
5 5

(k) 145 (l) 2 1
4

2. (a) 178 (b) 2 (c) 2801 (d) 1 (e) 45
5 6

(f) 11

3. (a) (i) 30 girls (ii) 20 boys

(b) (i) 50 km (ii) 150 km

(c) Bibek gets Rs. 630 and Rajesh gets Rs. 945.

Exercise 7.5

1. (a) 14 (b) 1 (c) 35 (d) 92 (e) 1
(f) pq 7 a

(g) no reciprocal (h) 5 (i) 15

200 Maths Zone -Grade 5