Maths Zone book 4 2077

Area

Class Discussion

It is a square having the
length of a side 1 cm.

1 cm

1 cm

The part of a plane enclosed by this square is 1 square cm.

It is written as 1 sq cm or 1 cm2.

So, 1 cm2 is the area of this square.

We can find the area of a plane surface by counting the number of
unit square in it.

Area of Rectangle

In the given rectangle, there 4 units
are 6 unit squares along the breadth
length and 4 unit square
along the breadth.

6 units
length

There are total 24 unit square boxes in this rectangle.
So area of rectangle = 24 sq. unit

We can also find the area of this rectangle by multiplying length and
breadth. So, area of rectangle = 6 × 4 = 24 sq.unit.

∴ Area of rectangle = length × breadth = l × b

Maths Zone – Grade 4 129

Area of Square

Take a square with side 5 cm.

Number of unit square contained 5 cm
in this square = 25

So area of square is 25 cm2. 5 cm 5 cm

This area is also obtained by multiplying 5 cm by 5 cm.

Area of square = 5 cm× 5 cm

= 25 cm2
∴ Area of square = (side)2 = l2
Example 1

Find the area of a rectangular play ground having length
90 m and breadth 50 m.

Solution:

Length (l) = 90 m

breadth (b) = 50 m

Area of rectangular ground (A) = l × b

= 90 m × 50 m

= 4500 m2
∴ Area (A) = 4500 m2



Example 2

Find the area of a square room whose length is 8m.

Solution:

Length (l) = 8 m

Area of square room (A) = l2

=l×l

=8×8
= 64 m2 ∴ Area (A) = 64 m2


128 Maths Zone – Grade 4

Exercise 6.2

1. Count the no of square and find the area of following
shapes.

Maths Zone – Grade 4 129

2. Find the area of following rectangle.
a. b.

5 cm 6 cm

7 cm 8 cm 4 cm
c. d.

12 cm 6 cm

3. Find the area of following squares. 8 cm
a. b.

6 cm 9 cm
c. d.

12 cm 7 cm

4. Find the area of rectangle having following dimension.
a. length (l) = 7 cm, breadth (b) = 5 cm
b. length (l) = 11 cm, breadth (b) = 8 cm
c. length (l) = 15 cm, breadth (b) = 12 cm

128 Maths Zone – Grade 4

5. Find the area of square having following dimension.

a. length (l) = 9 cm b. length (l) = 15 cm

c. length (l) = 13 cm d. length (l) = 11 cm

6. Measure the length and breadth of the following shapes
and find their area.
a. Surface of your desk
b. Black board/white board
c. Surface of your math book
d. Door of your classroom

Maths Zone – Grade 4 129

Volume

Class Discussion
The measure at the space occupied by a solid object is called its
volume.

Let's take a cube with 1 cm length, l cm breadth 1
and 1 cm height. The amount of space occupied 11
by this cube is called 1 cubic centimetre or 1 cm3.

We can find the volume of solid object by counting the no.of unit cubes
contained in it.

1 cm3 2 cm3 3 cm3 4 cm3

Volume of Cuboid

3 cm

2 cm
4 cm

In bottom layar there are 4 × 2 = 8 cubes and there are 3 such layers.
So total number = of unit cubes are 8 × 3 = 24. The volume of the
cuboid is 24 cm3. We can calculate the volume by multiplying 4 cm,
2 cm and 3 cm.
Volume = 4 cm × 2 cm × 3 cm = 24 cm3

∴ Volume of cuboid = length × breadth × height
V=l×b×h

128 Maths Zone – Grade 4

Example 1 4cm3cm
6cm
Find the volume of cuboid.
Here, length (l) = 6cm

breadth (b) = 3cm

height (h) = 4cm

We have volume (v) = l × b × h

= 6cm × 3cm × 4cm
= 72cm3

∴ Volume (v) = 75cm3



Example 2

Find the volume of cuboid having length 5cm, breadth
4cm and height 2cm.

Here, length (l) = 5cm
breadth (b) = 4cm
height (h) = 2cm
∴ We have volume (v) = l × b × h
= 5cm × 4cm × 2cm
= 40cm3

∴ Volume (v) = 40cm3



Volume of Cube

Length breadth and height of cube are equal.

∴ Volume of cube = length × length × length l
ll
=l×l×l

= l3

∴ v = l 3



Maths Zone – Grade 4 129

Example 3

Find the volume of cube having length 8cm.

Here, length (l) = 8cm

volume of cube (v) = l3

= 83

= 512cm3

∴ Volume (v) = 512cm3



Exercise 6.3

1. Find the volume of following solid object by counting the
unit cubes.

a. b.

c. d.

2. Find the volume of following cuboids.
a. b.

4 cm 3 cm 4 cm

c. 4 cm 3 cm
1 cm
5 cm

4 cm d. 5 cm

4 cm

2 cm 4 cm

128 Maths Zone – Grade 4

3. Find the volume of following cube.
a. b.

4 cm 5 cm
c. d.

6 cm 7 cm

4. Find the volume of cubes whose sides are given below.
a. 3 cm b. 9 cm c. 8 cm d. 11 cm

5. Find the volume of cuboid whose dimension are as follows.
a. length (l) = 4 cm, breadth (b) = 3 cm, height (h) = 3 cm
b. length (l) = 5 cm, breadth (b) = 4 cm, height(h) = 2 cm
c. length (l) = 6 cm, breadth (b) = 5 cm, height (h) = 1 cm
d. length (l) = 4 cm, breadth (b) = 2 cm, height (h) = 3 cm

6. Count number of unit box and find the volume.
a. b.

Maths Zone – Grade 4 129

Maths Fun

How many triangles are there in the given figure? Write
your answer below.

128 Maths Zone – Grade 4

Practice Zone

Group 'A'

Circle the correct option

1. Perimeter of a rectangle is obtained by using formula.

a. l × b b. 2(l + b) c. 4l

2. Area of a square is 16cm2. What is it's length of sides

a. 4cm b. 8cm c. 6cm

3. Volume of a cuboid having length 5cm, breadth 2cm and height
2cm is

a. 20cm3 b. 14cm2 c. 9cm3

4. Area of base of a cuboid is 15cm2 & height is 3cm. What is it's
volume?

a. 45cm3 b. 18cm3 c. 12cm3

5. What is the area of square having length 3.5 cm?

a. 7cm2 b. 12.25cm2 c. 14cm2

6. What is the volume of cube having 4cm length?

a. 64cm3 b. 16cm3 c. 32cm2

7. The volume & Area of base of a cuboid are 75cm3 and 25cm2
respectively find its height.

a. 3cm b. 1875cm c. 5cm

8. What is the area of Table of length 2m breadth 50cm?

a. 100m2 b. 1m2 c. 100cm2

Group 'B'

1. The perimeter of a rectangular garden is 100m if length is 30m
find its breadth.

Maths Zone – Grade 4 129

2. What is the Area of a rectangular garden having length 15m and

breadth 10m? The cost of paving the stone on 1m2 is Rs. 250. What
is the cost of paving the stone in whole garden.
3. A water tank have length 5m, width 4m and height 3m.
i. Find it's volume.
ii. Find the total water (in litre) containing in it. [1m3 = 1000l]
4. Find the volume of the cuboids having following dimension.
a. l = 7cm, b = 5cm, h = 4cm

b. l = 8cm, b = 4cm, h = 3cm

5. Find perimeter the given figure.

a. b. c.

5cm 7cm 8cm

10cm 6cm 10cm

6. The perimeter of a triangle is 40cm if two sides are 12cm and
15cm respectively. Find the other sides.

7. Measure the length, breadth and height of the given cuboid and
also find the volume.

a. b.

8. Two cuboid are given here.
a. Compare their volume.
b. Examine that in which vessles contain more water?


a. b.
2 cm
3 cm

3 cm 8 cm 4 cm 4 cm
128 Maths Zone – Grade 4

Answers of Unit 6

Exercise 6.1 b. 30cm c. 18cm d. 14cm
b. 18cm c. 16cm d. 22cm
1. a. 22cm b. 20cm c. 24cm d. 28cm
2. a. 18cm b. 20cm c. 16cm d. 40cm
3. a. 30cm b. 17cm c. 56cm d. 37cm
4. a. 12cm b. 25cm c. 34cm d. 25cm
6. a. 24cm b. 34cm c. 36cm d. 20cm
7. a. 25cm b. 28cm c. 36cm d. 26cm
8. a. 28cm
9. a. 20cm 11. Show to your teacher.

10. 50m

Exercise 6.2

1. a. 15 sq. unit b. 15 sq. unit c. 8 sq. unit d. 6 sq. unit
e. 9 sq. unit f. 7 sq. unit g. 11 sq. unit h. 12 sq. unit
i. 12 sq. unit
2. a. 35cm2 b. 24cm2 c. 96cm2 d. 48 cm2
3. a. 36cm2 b. 81cm2 c. 144cm2 d. 49 cm2
4. a. 35cm2 b. 88cm2 c. 180cm2
5. a. 81cm2 b. 225cm2 c. 169cm2 d. 121 cm2
6. Show to your teacher.

Exercise 6.3

1. a. 48cm3 b. 25cm3 c. 16cm3 d. 60cm3
2. a. 48cm3 b. 60cm3 c. 32cm3 d. 20cm3
3. a. 48cm3 b. 125cm3 c. 216cm3­ d. 343 cm3
4. a. 27cm3 b. 729cm3 c. 512 cm3 d. 1331 cm3
5. a. 36cm3 b. 40cm3 c. 30cm3 d. 24cm3
6. a. 105cm3 b. 91cm3

Maths Zone – Grade 4 129

7 Fraction, Decimal
and Percentage

Specific Objective Prescribed by CDC

 To give the concept of numerator and denominator.
 To distinguish and write the fraction from the shaded.
 To write the given like fractions in ascending and descending order.
 To add and subtract the like fractions.
 To give the introduction of tenths and hundredths from the figures.
 To convert the fractions with denominators 10 to 100 in to decimal

numbers.
 To give the concept of percentage.

164 Maths Zone – Grade 4

Fraction

Class Discussion 3 Numerator
Parts of a whole 4 Denominator

‰‰ The top number (the numerator) says how many parts we have
or shaded.

‰‰ The bottom number (the denominator) says how many parts the

whole divided into.

Words and their fractional representation.

Half Two third One third One fourth

1 2 1 1
2 3 3 4

Two fifth One ninth Four Tenths Quarter

2 1 4 1
5 9 10 4

Revision Exercise c.

1. Write the shaded part in fraction. =

a. b.
==

d. e. f.
= ==

Maths Zone – Grade 4 165

2. Color the given objects to show the given fraction.

a. b. c.

= 1 = 4 = 1
4 9 5

d. e. = One Eight
= One third

f. g. = Two fifth
= Quarter

3. Write the fractions from the given numerator and
denominators.

Numerator Denominator Fraction

25

37

48

39

166 Maths Zone – Grade 4

Equivalent Fractions

Class Discussion

Let's see the example.

= 1 [ Half part is shaded]
2

= 2 [ Half part is shaded]
4

= 3 [ Half part is shaded]
6

= 4 [ Half part is shaded]
8

Here the fractions 21, 42, 3 and 4 show the equal shaded part so they
6 8
are equivalent fractions.

The fractions which represent the equal value are called equivalent
fractions.

Methods of Finding Equivalent Fractions

First method

Multiplying both numerator and denominator by the same number

at the same time.

×2 ×3 ×4

2 = 4 2 = 6 2 = 8
5 10 5 15 5 20

×2 ×3 ×4

2 = 2 × 2 = 4 2 = 2 × 3 = 6 2 = 2 × 4 = 8
5 5 × 2 10 5 5 × 3 15 5 5 × 4 20

Second Method

Maths Zone – Grade 4 167

Dividing both numerator and denominator by the same number of

the same time.

÷3 ÷2 ÷2

3 = 1 4 = 2 10 = 5
6 2 6 3 12 6

÷3 ÷2 ÷2

Exercise 7.1

1. Color the required number of parts to make the next
fraction equivalent to the given fraction.

a. 1 b. 1
2 4
= =

==

c. 3 d. 1
6 3
= =

==

2. Multiply both numerator and denominator by the same
number to find three equivalent fractions.

a. 1 = 1 × 2 = 2 = 1 × 3 = 3 = 1 × 4 = 4
3 3 × 2 6 3 × 3 9 3 × 4 12

b. 3 = = =
4

c. 4 = = =
5

168 Maths Zone – Grade 4

d. 2 = = =
5

3. Divide both numerator and denominator by the
same number to find one equivalent fraction.

a. 4 = 4÷4 = 1 or 4÷2 = 2
12 12 ÷ 4 3 12 ÷ 2 6

b. 4 = c. 6 =
6 10

d. 8 = e. 9 =
12 12

4. Write the missing multipliers to find equivalent

fractions.

a. 2 = 2 × ............. = 182 b. 3 = 3 × ............. = 9
3 3 × ............. 5 5 × ............. 15

c. 4 = 4 × ............. = 12 d. 2 = 2 × ............. = 10
7 7 × ............. 21 6 6 × ............. 30

5. Find the missing numerator and denominator in each

of these equivalent fractions.

a. 2 = 6 ........... b. 4 = 12
3 5
...........

c. 1 = 27 ........... d. 4 = 1
3 3
...........

e. ........... = 5 f. 12 = 2
7 18
21 ...........

6. Write first four equivalent fractions for each of the

following fractions. 5
1 b. 23 c. 45 6 1
a. 2 d. e. 7

Maths Zone – Grade 4 169

Test of Equivalent Fractions

Class Discussion

Let's take the examples of two equivalent fractions

3 and 6
6 12

Then, 1st Numerator × 2nd denominator = 3 × 12 = 36

} same

2nd Numerator × 1st denominator = 6 × 6 = 36

So, Test the product of 1st Numerator × 2nd denominator with 2nd Numerator
× 1st denominator. If both products are same, they are equivalent fractions. If
products are not equal, they are not equivalent fractions.

Reduction of a Fraction to its lowest Term

First Method : Find the prime factors of both numerator and
denominator and cross out the common factors.

Example : Reduce 9 into its lowest term.
12

Solution:

3 9 and 2 12

33 26

1 33
1

Now, 9 = 2 3 × 3 × 1 1 = 3
12 × 2 × 3 × 4

170 Maths Zone – Grade 4

Second Method : Divide both numerator and denominator by a

common number. 12
18
Example : Reduce into its lowest term.

Solution: 12 = 12 6 2 First divided by 2
18 18 9 3 Second divided by 3

= 2
3
Third Method: Divide both Numerator and Denominator by Highest

Common Factor. 18
24
Example : Reduce into its lowest term

Solution:

18 = 18 ÷ 6 = 3 18 = 1, 2, 3, 6 , 9, 18
24 24 ÷ 6 4 24 = 1, 2, 3, 4, 6 , 12, 24

The fractions having zeros in both e.g.: 111128820000a. nCdrofsoslloowut the same
the above
number of zeros from both. = 1200 =
1800

method.

Exercise 7.2

1. Check whether the following pair of fractions are
equivalent or not ?

a. 2 and 4 b. 5 and 7
3 6 6 9

Maths Zone – Grade 4 171

c. 3 and 12 d. 3 and 6
4 16 7 14

e. 4 and 3 f. 4 and  23
5 8 6

2. Reduce the following fractions to their lowest term.

a. 182 b. 69 c. 1152 d. 2184 e. 3482 f. 30
45

3. First cross out equal number of zeros from both Numerator
and Denominator and reduce to its lowest term.

a. 5300 b. 4600 c. 430000 d. 325000 e. 1950000 f. 2000
8000

172 Maths Zone – Grade 4

Proper Fractions, Improper Fractions and Mixed Numbers

Class Discussion Nr < Dr ⇒ Proper Fraction
= 41, = 32

11 1 1 1 1 4
3 3 3 3 3
13 3  + + +  Dr < Nr  Improper Fraction
31

3

123  Mixed number 1 1 21 + 1 = 22 Improper Fraction
2 2 2

One Whole one over three

11 11 1  41 + 1 + 1 + 1 + 1 + 1 + 1 + 1 + 1
44 44 4 4 4 4 4 4 4 4 4

11 11 = 49 = Dr < Nr  Improper Fraction
44 44

214  Mixed number
Two Whole one over four

Proper Fractions: A proper fraction is a fraction which has the

numerator smaller than denominator.

Eg. 1 , 3 , 5 , 4 are some proper fractions.
2 4 7 8
Improper Fractions: An improper fraction is a fraction which has the

numerator larger than or equal to the denominator E.g., 3 , 5 , 6 , 7 ,
2 5 4 7
9 12
7 , 8 are some Improper fractions.

Mixed Numbers : A mixed number is a combination of a whole

number and a proper fraction.

E.g, 221 , 323 , 412 , 525 are some mixed numbers. (Mixed fraction)

Maths Zone – Grade 4 173

Conversion of Improper Fraction to Mixed Number
Let's take an example of improper fraction.

11 ⇒ 4 11 2 ⇒ 243 Q R
4 –8 D

11 234 3 234 = 2 + 3
4 4
∴ =

Conversion of Mixed Number to Improper Fraction

Let's take an example of Mixed number.

253 ⇒ 2 × 5 + 3 = 13
5 5

Q×D+R 253 = 13
D 5

Interesting Fact

7 → 312 → 3+ 1 Improper Mixed Sum of
2 2 Fraction Number whole
number
3+ 1 →2 1 → 9 and proper
2 4 4 fraction.

Exercise 7.3

1. Write proper fraction for the shaded part. (Using pencil
write in the box)

a. b. c.

2. Write improper fraction for the shaded parts.
a. b. c.

174 Maths Zone – Grade 4

3. Write mixed number for the shaded parts.
a. b. c.

4. Write the mixed number and improper fraction of the
following.
AB

a. A B Mixed
0123 Number
Improper

Fraction

5. Classify the following fractions as proper fraction,
improper fraction and mixed number.

31, 55, 54, Proper Fraction
253, 37, 112 Improper Fraction
Mixed Number

6. Convert the following improper fractions into mixed
numbers.
a. 130 b. 25 c. 165 d. 94 e. 273 17
f. 9

7. Convert the following mixed numbers into improper
fractions.
a. 221 b. 3 13 c. 451 d. 837 e. 5 28 f. 619

Maths Zone – Grade 4 175

Like and Unlike Fractions

Class Discussion

= 1
4

Same  Like Fractions

= 3
4

= 3
8

Different  Unlike Fractions

= 2
6

Like fractions: Fractions with the same denominators are called like

fractions.

Eg. 25, 35, 1 are like fractions.
5

Unlike fractions: Fractions with the different denominators are called

unlike fractions.

E.g. 52, 73, 4 are unlike fractions.
6

Comparison of like fractions

Class Discussion

= 1
4
2 1
Same 1 < 2 4 > 4

= 2
4

176 Maths Zone – Grade 4

If two fractions have the same denominator, the fraction with greater
2 1
numerator is greater. Therefore, 4 > 4

Conversion of unlike fractions into like fractions and their comparision

Class Discussion

Let's take two unlike fractions 1 and 2
2 3

= 1 = 2
2 3

= 3 = 4
6 6

3 < 4
6 6

∴ 12 ⇓ 2
3
<

1 and 2 are unlike fractions but their equivalent fractions 3 and 4 are
2 3 6 6
3 4 1 32.
like fractions. So, comparing like fractions, we get 6 < 6 ⇒ 2 <

First Method: Compare 2 and 3 and put < or >.
5 4

Solution:

2 , 3 Multiply Nr. and Dr. of
5 4 first fraction by 2nd Dr. and
2 × 44, 3×5 Multiply Nr. and Dr. of
5 × 4×5 second fraction by 1st Dr. and
compare them.
280, 15 [They are like fraction.]
20 ∴280 < 15
20 2 3
Now, ⇒ ∴ 5 < 4

Maths Zone – Grade 4 177

Second Method: Compare 3 and 5 and put < or >.
8 12

Solution:

Here, 8 = 2 × 2 × 2 Find LCM of both
12 = 2 × 2 × 3 denominators and multiply
first and second fraction with
LCM of 8 and 12 = 2 × 2 × 2 × 3

= 24 a suitable number to make

Now, 83 = 3 × 3 = 9 denominator equal to LCM.
8 × 3 24

5 = 5×2 = 10 Find LCM by multiples of
12 12 × 2 24 Denominators.

∴ 9 < 10 M8 = 8, 16, 24, 32 ....
24 24

⇒ 3 < 5 M12 = 12, 24, 36, 48 .....
8 12 LCM = 24

Arrangement of Fractions in order

Class Discussion

Let's take three like fractions 15, 53, 2
5
15, 2 3
Arranging them in ascending order, 5 , 5

If the denominators are same, fraction with greater numerator is

greater.

Let's take three unlike fractions.

72, 23, 2 [Unlike fractions but their numerator is same]
5
72, 2 2
Arranging them in ascending order, 5 , 3

If the numerators are same, fraction with smaller denominator is

greater.

178 Maths Zone – Grade 4

Exercise 7.4

1. Identify and write L for Like fractions and U for Unlike
fractions in the box.

a. 3 and 2 b. 4 and 3 c. 5 and 7
4 4 7 8 8 8

d. 1 and 8 e. 3 and 3 f. 5 and 7
9 9 2 3 10 12

2. Put < or > sign in the box to compare the like fractions.

a. 3 4 b. 3 2 c. 9 8 d. 9 1
5 58 8 17 17 12 12

e. 14 15 f. 7 5 g. 3 2 h. 4 1
20 20 15 18 6 69 9

3. Convert the given unlike fractions into like fractions.

a. 2 and 1 b. 2 and 1 c. 2 and 3 d. 3 and 5
3 4 5 3 3 5 4 6

e. 4 and 3 f. 1 and 2 g. 4 and 5 h. 3 and 2
7 6 2 3 5 6 6 9
4. Convert the given unlike fractions into like fractions and
compare them (put < or >).

a. 1 and 3 b. 3 and 2 c. 4 and 3 d. 4 and 3
3 4 5 4 6 4 8 7

5. Rewrite and circle the greater fraction.

a. 2 , 3 b. 59, 7 c. 37, 3 d. 85, 5
4 4 9 6 6

6. Write the following like fractions in ascending order.

a. 3 , 15, 2 b. 98, 93 , 6 c. 73, 71, 2 d. 46, 62, 5
5 5 9 7 6

7. Write the following unlike fractions in descending order.

a. 3 , 35, 3 b. 97, 87 , 7 c. 17, 41, 2 d. 82, 32, 2
4 6 11 5 5

Maths Zone – Grade 4 179

Addition and Subtraction of Fractions

Addition and Subtraction of like fraction

Class Discussion

Let's take two like fractions 3 and 2
6 6
3 2 3 + 2 5
∴ 6 + 6 = 6 = 6 +
2
3

To add like fractions, add 6 6

the numerators and keep 5
the denominator common. 6

Example 1

Add and express the sum into lowest term: 4 and 4
12 12
Solution:

4 + 6 = 4+6 = 10
12 12 12 12

Now, Reducing into lowest term.

10 = 2 2 × 5 3 = 5
12 × 2 × 6

Example 2

Subtract 4 from 170. –
10
Solution: 7 4
10 10
7 – 4 = 7-4 = 3
10 10 10 10

To subtract like fractions, 3
subtract the numerators 10
and keep the denominator

common.

180 Maths Zone – Grade 4

Addition and Subtraction of Unlike Fractions

Addition of Unlike Fractions

Class Discussion

Add : 3 and 5 .
6 8
First convert them into like fractions by

}3 = 3 × 4 = 12 Multiple of 6 = 6, 12, 18, 24 ...
6 × 4 24 Multiple of 8 = 8, 16, 24 ...
6 LCM = 24 = Denominator.
2 = 2 × 3 = 6
8 8 × 3 24

Now,

12 + 6 = 12 + 6 = 2148
24 24 24

Again, convert it into lowest term. (If necessary)

18 = 2 2×3×3 3 = 3
24 ×2×2× 4

Subtraction of Unlike fractions

Subtract 4 from 7
6 9
First convert them into like fraction.

}4 = 4 × 3 = 12 Multiple of 6 = 6, 12, 18 , 24 ...
6 × 3 18 Multiple of 9 = 9, 18 , 27 ...
6 LCM = 18 = Denominator.
7 = 7 × 2 = 14
9 9 × 2 18

Now, 7 - 4 = 14 - 12 = 14 - 12 = 2
9 6 18 18 18 18
2 2×1 1
Again, convert it into lowest term. 18 = 2 ×3× 3 = 9

Maths Zone – Grade 4 181

Addition and Subtraction of Mixed Number (Mixed fraction)

Class Discussion

Add: 352 and 2 1
5
First Method:
Convert
3 2 and 2 1 = 3 × 5 + 2 + 2×5+1 mixed number
5 5 5 5 into unlike fraction

= 17 + 11 Convert unlike
5 5 fraction into
17 + 11
= 5 mixed number.

= 28 Whole number is
5 added to whole
= 553 number and fraction
added to fraction

Second Method: Changing the
sum into mixed
3 2 + 2 1
5 5 number.

= (3 + 2) + 1 + 1
5 5
2+1
= 5+ 5

= 5 + 3
= 5 5
3
5

Subtract 2 2 from 4 3 .
7 7

First Method: Second Method:

4 3 - 2 2 4 3 - 2
7 7 7

= 4 × 7 + 3 - 2×7+2 = (4 - 2) + 3 - 2
7 7 7 7

= 31 – 16 = 15 = 217 = 2+ 3-2 = 2 + 71= 217
7 7 7 7

182 Maths Zone – Grade 4

Exercise 7.5

1. Find the sum of the following like fractions.

a. 3 + 15 b. 3 + 27 c. 4 + 130 d. 2 + 5
5 7 10 12 12
2. Find the difference of the following like fractions.

a. 4 – 36 b. 8 – 150 c. 11 - 175 d. 15 – 13
6 10 15 17 17
3. Find the sum of the following unlike fractions.

a. 3 + 61 b. 2 + 32 c. 3 + 150 d. 3 + 2
4 7 8 8 7
4. Find the difference of the following unlike fractions.
(Convert into lowest term wherever necessary)

a. 4 – 42 b. 5 – 16 c. 7 – 47 d. 7 – 4
5 8 10 10 15
5. Find the sum of the following fractions.

a. 3 2 + 4 52 b. 4 1 + 2 53 c. 627 + 437 d. 5 4 + 3 1
5 5 9 9
6. Find the difference of the following fractions.

a. 6 3 – 427 b. 554 – 4 35 c. 4 4 – 192 d. 458 – 2
7 9 8
7. Find the sum of the following fractions.

a. 4 + 5 + 122 b. 4 + 3 + 157 c. 3 + 6 + 8
12 12 17 17 19 19 19
8. Simplify the given fractions and convert into lowest term
wherever necessary)

a. 6 + 2 – 93 b. 8 – 2 + 130 c. 8 – 4 – 3
9 9 10 10 12 12 12
d. 237 + 374 – 472 5 294 191 8 5151 1121
e. 3 9 – + f. 6 11 – –

9. a. Bibek spent 3 of his money to buy a copy and 2 of his money
7 7
to buy a book. What fraction of income did Bibek spend?
3 382
b. Prizma had 5 8 meter of ribbon, she gave meters to her

sister Riya. Find the remaining part of the ribbon.

Maths Zone – Grade 4 183

Addition and Subtraction of Mixed Numbers of unlike fractions

Addition

Class Discussion

421 + 341 412 + 341 Converting Mixed

4 × 2 + 1 3 × 4 + 1 4 × 2 + 1 3 × 4 + 1 number into
2 4 2 4
⇒ + ⇒ + Improper fraction.

⇒ 9 + 13 ⇒ 9 + 13 Converting into
2 4 2 4 like fraction in a
9×4
⇒ 9×2 + 13 × 1 ⇒ 2×4 + 13 × 2 easy way.
2×2 4×1 4×2
13 36 26
⇒ 18 + 4 ⇒ 8 + 8
4
18 + 13 36 + 26
⇒ 4 ⇒ 8

⇒ 31 ⇒ 62
4 8
3 6231
⇒ 7 4 ⇒ 84

⇒ 31 Converting into mixed
4 term.

⇒ 734

184 Maths Zone – Grade 4

Subtraction

Class Discussion

732 – 4 5 Add: 732 – 4 5 Converting mixed
6 6 number into
7 × 3 + 2 4×6+5 Improper fractions.
= 7 × 3 + 2 – 4 × 6 + 5 = 3 – 6
3 6 Converting into
23 × 2 29 × 1 23 29 like fractions in a
= 3×2 – 6×1 = 3 – 6 easy way.

= 46 – 29 = 23 × 6 – 29 × 3 Converting into
6 6 3×6 6×3 lowest term.
138 87
= 46 – 29 = 18 – 18
6 =
17 138 - 87 5117 17
= 6 18 = 18 6 = 6

= 2 5 Converting into
6 mixed number.

Exercise 7.6

1. Add the following.

a. 5 2 + 8 61 b. 3 2 + 5 140
3 5
1 + 7 21 1
c. 6 9 d. 4 2 + 3 1
3
2. Subtract the following.

a. 353 – 2110 b. 8 1 – 6 3
2 4

c. 1031 – 2 16 d. 8 1 – 3 2
4 9

Maths Zone – Grade 4 185

Decimal Numbers

Class Discussion
Tenths

Figure Fraction Decimal Number Name
In Number Line 1
10 0.1 One tenths

3
10 0.3 Three tenths

2 1.2 One whole and
110 two tenths

0 0.1 0.3 1
Hundredths

Figure Fraction Decimal Number Name

3 0.03 Three
100 Hundredths

25 Twenty five
100 0.25

Hundredths

186 Maths Zone – Grade 4

Let's take an example of decimal number.
27 . 35
}
}

Whole number Decimal number
Read it as twenty seven point three five.

Place value of Decimal Numbers

Let's take a number 325.467 then the place value table of this decimal
number is

Hundreds Tens Ones Tenths Hundredths Thousandths

3 25 4 6 7

Whole numbers Decimal numbers
325.467

Read it as, 1 4
10 10
Three hundred twenty five 4 tenths = 4 × =
point four six seven.
1 6
Now Expanded from, 6 Hundredths = 6 × 100 = 100

300 + 20 + 5 + 4 + 6 + 7 7 thousandths = 7 × 1 = 7
10 100 1000 100 100

Comparison of Decimal Numbers

Class Discussion

Let's take two decimal numbers 12.34 and 15.27.
Here, whole number 15 is greater than 12.
So, 15.27 > 12.34
If the whole numbers are same, then we need to compare the decimal
parts starting from tenths, then hundredths, then thousandths and so
on.

Maths Zone – Grade 4 187

Example

Compare 63.257 and 63.249

Solution: 63 . 249
63 . 257
}
}

= Finally, we do not
= need to compare 7
>
and 9
\ 63.257 > 63.249

Exercise 7.7

1. Rewrite and express into decimal number.

a. 120 b. 1090 c. 45 d. 63
10 100

e. 235 f. 130700 g. 15190 h. 1712030
10

i. 11130700 j. 347
1000
2. Rewrite and express into fraction.

a. 0.5 b. 0.07 c. 3.5 d. 0.74

e. 48.5 f. 0.083 g. 17.3 h. 24.36

i. 25.032 j. 0.793

3. Write the place name and place value of coloured digit.

a. 3.7 b. 57.82 c. 0.038 d. 7.234

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

a. 2.7 b. 42.35 c. 375.21 d. 817.246

5. Write in expanded form.

a. 4.6 b. 57.42 c. 315.82 d. 417.926

6. Write in short form.

a. 4 + 7 b. 20 + 5 + 6 + 2
10 10 100

188 Maths Zone – Grade 4

c. 300 + 80 + 7 + 3 + 2
10 100
t3h0e+g4iv+e1n10d+ec1im060a+ls 7
7. d. 500 + 1a0n0d0 put '>' '<' or = sign.
Compare

a. 1.5 and 2.5 b. 3.6 and 3.4

c. 5.42 and 5.47 d. 0.01 and 0.1

e. 0.45 and 0.54 f. 78.315 and 78.137

Conversion of Decimals into Fractions

Class Discussion

In converting decimals to fractions, use the following steps.

Step I : Obtain the decimal.

Step II : Remove the decimal points from the given decimal and
take 1 as numerator.

Step III : At the same time, write in the denominator as many zero

or zeros to the right of 1 (one) for eg. 10, 100, 1000 etc) as

there are number of digit or digits in the decimal part then

simplify it.

Let's take few examples of Decimals.

a. 0.3 b. 0.8 c. 0.25 d. 3.2 e. 5.45

Solution:

a. 0.3 = 3 [3 tenths]
10 [Both 8 and 10 are divisible by 2.]
84
b. 0.8 = 8 = 10 5
10

= 4
5

Maths Zone – Grade 4 189

c. 0.25 = 25 = 25 1 [25 and 100 both divisible by 25.]
100 100 4

= 1
4

d. 3.2 = 3 2 = 312015 Alternatively
10
32 3216 16 351
= 315 3.2 = 10 = 10 5 = 5 =

e. 5.45 = 5 45 = 5 45 9 Alternatively
100 100 20
545109
= 5 9 5.45 = 545 = 100 20 = 5290
20 100

Exercise 7.8

1. Convert the following decimals into fractions and reduce
them into lowest term . (wherever necessary)

a. 0.1 b. 0.5 c. 0.6 d. 0.22

e. 0.35 f. 4.5 g. 6.4 h. 1.25

i. 4.75 j. 6.125

Conversion of Fraction into Decimals

Class Discussion

Let's take few examples of fractions:

a. 25 b. 3 c. 4 51 d. 58 e. 7
4 20

Solution:

a. 2 = 2 × 2 = 4 = 0.4 Multiply Numerator and
5 5 × 2 10 denominator by 2, make
denominator 10
Alternatively

52 = 5 – 02200.4
20
×

190 Maths Zone – Grade 4

∴ 2 = 0.4
5

b. 34 = 3 × 25 = 75 = 0.75 Numerator (4) cannot
4 × 25 100 be made 10 multiplying
by any whole number
Alternatively so, multiply 4 by 25
to get denominator 100.
3 =4 3 0.75
4 –0

30
– 28
20
20
×

∴ 3 = 0.75
4

c. 451 = 4 1 × 2 = 4 2 = 4.2
5 × 2 10

4 1 = 4 × 5 + 1 = 21 = 21 × 2 = 42 = 4.2
5 5 5 5×2 10

d. 58 = 5 × 125 = 625 = 0.625 Numerator (8) cannot be
8 × 125 1000 made 10, 100 multiplying

by any whole number

Alternatively so, multiply 8 by 125 to
get denominator 1000
58 =8 5
–0 0.625

50
– 48
20
16
40
40
×
∴ 5 = 0.625
8

Maths Zone – Grade 4 191

e. 7 = 7×5 = 35 = 0.35 Alternatively
20 20 × 5 100 20 7 0.35
7 –0
∴ 20 = 0.35 70
– 60
Exercise 7.9 100
100
×

1. Convert he following fractions into decimals.

a. 130 b. 35 c. 21 d. 352 e. 412
f. 290 g. 2115 h. 5230 i. 2 34
j. 3
8

Additional and Subtraction of Decimal Numbers

Addition and subtraction of decimals 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.

Let's take few examples of decimals.

Example - 1 b. 0.8 + 0.3 c. 3.42 + 0.23

Add :
a. 0.2 + 0.5

Solution:

Whole numbers
Tenths
Hundredths

a. 0.2 b. 0.8 c. 3.42 Write down the
0.5 0.3 0.23 digits at the same
1.1 3.65 place in the same
0.7 column.

192 Maths Zone – Grade 4

Example - 2

Subtract:

a. 0.8 - 0.4 b. 2.32 - 1.41

Solution: 1 13 Borrowing and carry
over is done as in the
a. 0.8 b. 2.32 whole numbers.
– 0.4
– 1.41 Add or subtract
0.4 0.91 the numbers in the
respective columns
Example - 3 and sort out decimal
point appropriately.
Simplify:

5.321 + 3.437 – 4.237

Solution:

}5 .321 first

+ 3.437 adding
8.758

Now,

8.758
– 4.237

4.521

∴ 5.321 + 3.437 – 4.237 = 4.521

Exercise 7.10

1. Add the following.

a. 0.9 + 0.3 b. 3.2 + 5.3 c. 0.54 + 0.47
f. 0.001 + 0.009
d. 7.032 + 0.125 e. 12.75 + 15.92 i. 18.25 + 19.755

g. 0.674 + 0.364 h. 11.984 + 7.7 43

Maths Zone – Grade 4 193

2. Add the following.

a. 0.5 b. 0.35 c. 3.257 d. 10.05
0.3 0.23 2.518 7.23

+ 0.4 + 0.89 + 3.823 + 8.09

3. Subtract the following.

a. 0.7 – 0.4 b. 1.2 – 0.5 c. 0.45 – 0.15
f. 25.325 – 15.126
d. 4.37 – 0.09 e. 75.35 – 0.85

4. Subtract the following.

a. 0.8 b. 0.71 c. 3.74 d. 10.579
– 0.2 – 0.34 – 2.85 – 5.388

5. Simplify the following. b. 2.325 + 3.729 – 4.812
a. 1.345 + 0.322 – 0.421

c. 8.257 – 6.814 + 3.223 d. 18.937 – 9.425 – 2.222

6. Find the sum of all sides of the following figures.

a. b. 3.2cm
4.2cm
3.5cm

2.7cm 6.5cm

c. d. 3.1 cm
3.3 cm
3.2cm 6.6 cm
2.1 cm 2.2 cm

2.3 cm 1.1 cm
7.5 cm

194 Maths Zone – Grade 4

Use of Decimals

Class Discussion

We see decimals all around us. Decimal numbers break down whole
numbers into smaller parts. They always have a decimal point.

You can see decimal prices on the market.

Money

Receipts Use of Decimals
in money eg. Rs
1. Rice Rs. 115.00 17.50.
2. Wheat Rs. 75.50
Total Rs 190.00

Length

11.5 km Use of Decimals
in Length 11.5 km.

Weight

2.5 kg Capacity Use of Decimals
2.5 l 1.25 l in weight 2.5 kg.

Use of Decimals
in Capacity 2.5 l,
1.5 l.

Maths Zone – Grade 4 195

Temperature

Use of Decimals
in Temperature
98.52° F, 37.5° C.

34.5° F or 1.38° C
Relation
Paisa and rupees

1 rupee = 100 paisa Rs. 5 and 40 paisa = 5 + 40
100
1 paisa = Rs. 1 = Rs. 0.01
100 = Rs. 5.40
7
7 paisa = Rs. 100 = Rs. 0.07

Centimeter, Meter and Kilometer

1 m = 100cm 100 m = 1km

1cm = 1 m = 0.01m 1m = 1 = 0.001km
100 1000
5 6
5cm = 100 m = 0.05m 6m = 1000 = 0.006km

5m. 30cm = 5 + 30 = 5.30m 7km. 500m = 7+ 500 = 7.500km
100 1000

Gram and Kilogram

1000 gram = 1 kilogram

1 gram = 1 kg = 0.001kg
1000
2
2 gram = 1000 kg = 0.002kg

3kg and 300 gm = 3 + 30 kg = 3.300kg
1000

196 Maths Zone – Grade 4

Milliliter and liter

100ml = ll

1ml = 1 = =0.001 l
1000
7
7 ml = 1000 = 0.007l

8l 400ml = 8 + 400 = 8.400l.
1000

Exercise 7.11

1. Write in rupees.

a. 5 paisa b. 25 paisa

c. 75 paisa d. 2 rupees 40 paisa

e. Rs. 7 and 80 paisa f. Rs. 20 and 50 paisa

2. Write in rupees and paisa.

a. Rs. 0.07 b. Rs. 0.40 c. Rs. 0.75
d. Rs. 5.25 e. Rs. 15.75 f. Rs. 17.05
3. Write in meter.

a. 6 cm b. 15 cm c. 80 cm
f. 50 m 20 cm
d. 3 m 55 cm e. 25 m 5 cm

4. Write in meter and centimeter.

a. 0.05 m b. 0.50 m c. 0.85 m
d. 7.35 m e. 15.60 m f. 18.07 m

Maths Zone – Grade 4 197

5. Write in kilometer.

a. 8 m b. 22 m c. 90 m
f. 65 km 370 m
d. 5 km 65 m e. 35 km 9 m
c. 0.375 km
6. Write in kilometer and meter. f. 44.008 km

a. 0.007 km b. 0.025 km c. 80 gram
f. 75 kg 385 g
d. 4.265 km e. 27.037 km
c. 0.428 kg
7. Write in kilogram. f. 42.007 kg

a. 9 gram b. 27 gram c. 60 ml
f. 54 l 475 ml
d. 3 kg 45 g e. 47 kg 8 g
c. 0.675 l
8. Write in kilogram and gram. f. 55.002 l

a. 0.004 kg b. 0.037 kg

d. 5.437 kg e. 37.035 kg

9. Write in liter.

a. 5 ml b. 23 ml

d. 4 l 35 ml e. 32 l 3 ml

10. Write in liter and milliliter.

a. 0.003 l b. 0.054 l

d. 7.752 l e. 42.038 l

198 Maths Zone – Grade 4

Percentage

Class Discussion

Here, the square is divided into 100 equal

parts. 7 out of hundred parts are shaded.

The fraction of shaded part = 7
100
It is 7 out of 100 or 7 per 100.

7 = 7%
100

A percent can also be Per = out of
expressed as a Decimal or a cent = hundred (100)
fraction. ∴ Percent = out of 100

A half can be written Symbol of percent is %.

As a percentage : 50%

As a Decimal : 0.5

As a Fraction = 1
2

Revision Exercise

1. Write the shaded part and the unshaded part as a fraction,
as decimal and percentages.

a. Shaded part Unshaded part

== % == %
Maths Zone – Grade 4 199

b. Shaded Unshaded

== % == %

Conversion of Fraction into Percentage

Let's take few examples : a. 1080 b. 3 and c. 3 1
4 2
Solution:
8 If denominator is 100 the
a. 100 =8% numerator represents the
percentage.
b. First method:

3 = 3 × 25 = 75 = 75% Change the denominator
4 4 × 25 100 into 100 by multiplying both
Numerator and denominator
Second Method: by a suitable number.

3 = 3 × 25 = 3 × 25% = 75% Multiply the fraction by
4 4 100% [100% = 110000]
100%

1

c. First Method:

321 = 7 = 7 × 50 = 350 = 350% Express mixed number into
2 2 × 50 100 improper fraction and convert
into percentage.
Second Method

7 = 7 × 50 7 × 50% = 350%
2 2
100%=

200 Maths Zone – Grade 4