Math 4

Objective Questions

Colour the correct alternative.

1. 4 tens + 8 tens + 15 tens is equal to

2 hundreds 2 hundreds 2 tens
+ 7 ones
+ 4 tens + 7 tens

2. By how much 5264 is greater than 2719?

2545 7983 2525

3. What is the dividend if divisor is 13, quotient is 5 and remainder is 10?

65 85 75

4. How many times 8 should be subtracted from 72 to get 0?

9 times 8 times 5 times

5. The product of 30 and 3 subtracted from 100 is 190

– 10 10

6. How many times 7 is added to itself to get the result 56?

6 3 12

7. The value of 20 ÷ 4 + 3 × 4 – 17 is -104

0 15

8. The value of 10 – 2 {8 ÷ (16 ÷ 4)} is 8

16 6

9. The mathematical expression of the statement "the quotient of 60
divided by 15 added to the product of 5 and 3" is

60 ÷15 + 5 × 3 60 × 15 ÷ 5 × 3 60 + 15 ÷ 5 × 3

10. Which of the following is not true?

Any number Zero divided by Any number
divided by 1 is the any number is divided by 0 is 0

number itself. zero.

Oasis School Mathematics Book-4 101

Unit Test Full marks -20

1. Add: 2
a. 7682653
+ 2744768 b. 3254617 + 274168 + 6492 + 62

2. Subtract: 2
a. 6374281
- 21493 b. 526486 - 231874

3. Multiply: 2

a. 73564 b. 27460 × 8
× 26

4. Divide: 2
a. 4562 ÷ 8
b. 58318 ÷ 53

5. Solve the following problems: 3×2=6

a. Monthly expenses of a household are as follows: Food: Rs.
4687, clothes: Rs. 8562 and miscellaneous: Rs. 5469. What is
the total expenditure of the household?

b. There are 24 hours in a day. How many hours are there in 365
days?

c. The cost of 125 watches is Rs. 123125. What is the cost of a
watch?

6. Simplify: 2×2=4
a. 28 ÷ 7 - 4 × 8 + 6 - 12 2×1=2
b. 16 - [20 ÷{20 - 3(10 - 5)}]

7. Find the value of:
a. 24 × 10 b. 6400 ÷ 400

102 Oasis School Mathematics Book-4

UNIT

4 Fraction

12 Estimated Teaching Hours: 15
93

6

Contents • Concept of fraction
• Like and unlike fractions
• Comparison of like fractions
• Equivalent fractions
• Proper, improper and mixed fractions
• Addition and subtraction of fractions
• Multiplication of fraction by a whole number and

by a fraction
• Reciprocal of a fraction
• Division of fraction by a whole number and by

fraction
• Division of a fraction by a whole number

Expected Learning Outcomes

Upon completion of the unit, students will be able
to develop the following competencies:

• To recognise the fraction as part of a whole
• To identify the like and unlike fractions
• To compare the like fractions
• To recognise the equivalent fractions and find the equivalent of

given fraction using multiplication and division
• To identify the proper fraction, improper fraction and mixed

fraction
• To add and subtract the like fractions
• To add and subtract the unlike fractions
• To solve the simple verbal problems in addition and subtraction

of fractions
• To multiply the fraction by whole number
• To multiply two fractions
• To divide a whole number by a fraction
• To divide fraction by a whole number
• To divide a fraction by a fraction

Materials Required: Flash cards, paper models of different fractions, etc.

Oasis School Mathematics Book-4 103

Fraction

Review

A fraction is a part of one whole or of a group of objects.
1 , 3 , 5 , etc. are fractions.
1
227

In the given figure, 1 out of 3 equal parts 3

is shaded.

\ Fraction represented by the shaded 2 Remember !
part = 1 3
3
3
three fourths = 4
Fraction represented by the remaining 5
part = 2 6

3

A fraction is a part of a group of objects.

five sixths =

2

two fifths = 5
1
In the given figure 2 flowers out of 5 are red.
one thirds = 3
\ 2 flowers are red. 1
5 one tenths = 10

Again, 3 flowers out of 5 are white. 3

\ 3 flowers are white. three tenths = 10
5

Note:

In the fraction 1 , 1 is the numerator and 2 is the denominator.

2

Denominator represents how many parts of a whole is divided and the
numerator tells how many parts are taken out of the whole.

Exercise 4.1

1. Write the fraction for the shaded parts in each figure:
a. b.

c. d.

104 Oasis School Mathematics Book-4

2. Copy the following figures in your copy and shade the given fraction:

a. 3 b. 3

7 10

a. b. c. 4
6
5 5
8 6

3. Write the fraction of the coloured circles: c.
a. b.

4. Write the fraction for each of the following:

a. two-thirds b. four-sevenths c. five-eighths

d. one-seventh e. three-tenths f. eight-nineths

5. Write the given fraction in word:

a. 1 b. 2 c. 3 d. 3 e. 7
4 3 7 10 9

6. Write the numerator and denominator of the following fractions.

a. 2 b. 3 c. 5 d. 7
7 8 9 11

7 a. Out of 40 students in class IV, 25 are boys and the rest are girls.
What fraction of students are boys and what fraction of students are
girls?

b. In a shop, there are 50 candles. Out of them, 20 are red, 25 are white
and the rest are yellow. Find, what fraction of candles are red, white
and yellow?

c. Out of 25 balloons, 15 are red, 6 are blue and the rest are green.

(i) What fraction of balloons are red?
(ii) What fraction of balloons are blue?
(iii) What fraction of balloons are green?

Answer: Consult your teacher.

Oasis School Mathematics Book-4 105

Like and unlike fractions (Review)

When there are two or more fractions, all with same denominators, they are like

fractions.

3 , 4 , 2 and 1 , are like fractions.
7 7 7 7

When the fractions have different denominators, they are unlike fractions.

3 , 1 , 2 are unlike fractions.
5 6 9

Comparison of like fractions (Review)

Shaded part is 3 Shaded part is 5
8 8

In the second figure more parts are shaded than in the first figure.

Therefore, 3 < 5 Like fractions having greater
8 8

Similarly, numerator is greater than

4 < 5 ( ∵ 4< 5) the fraction having smaller
7 7 numerator.

8 > 3 (∵8> 3) I understand!
11 11

My focus should be on the
numerator.

Class Assignment

1. Colour the like fractions with the same colour.

2 3 4 1 2 5 2 5
5 7 9 5 7 7 9 9

36 68 1 3 4
59 79 7 7 5

106 Oasis School Mathematics Book-4

2. Colour the circle of the right statement with green and the circle of the
wrong statement with red.

a. Like fractions have same numerator.

b. Denominator of like fractions is same.

c. 3 is smaller than 4
5 5

d. Like fraction having greater numerator is greater than the

fraction having smaller numerator.

e. 1 > 6
7 7

Teacher's Signature

Exercise 4.2

1. Find out the like fractions from the given sets.

a. 2 , 3 , 1 , 1 , 4 , 2 b. 3 , 4 , 2 , 1 , 1 , 5 , 6
3 5 5 4 5 5 4 7 7 3 2 7 7

c. 5 , 3 , 4 , 8 , 6 , 1 d. 5 , 5 , 7 , 7 , 2 , 1
11 7 9 11 11 2 8 8 10 8 5 7

e. 7 , 2 , 3 , 4 , 8 , 10
11 5 14 7 11 11

2. Put > and < in the box.

a. 2 1 b. 3 5 c. 3 5
5 5 7 7 11 11

d. 1 1 e. 5 2 f. 6 3
7 7 8 8 13 13

3. Arrange the following fractions in an ascending order.

a. 5 , 2 , 3 , 4 , 6 b. 3 , 2 , 4 , 7 , 6
7 7 7 7 7 8 8 8 8 8

4. Arrange the following fractions in an descending order.

a. 3 , 7 , 4 , 2 , 9 , b. 5 , 7 , 9 , 1 , 6 ,
11 11 11 11 11 10 10 10 10 10

Answer: Consult your teacher.

Oasis School Mathematics Book-4 107

Equivalent fractions

Is there any difference between the shaded part of these three figures?

1 is shaded.
2

2 is shaded.
4

3 is shaded.
6
1 2
Same quantity in all figures are shaded, but they are called differently i.e. 2 , 4
3
and 6 .

These fractions 1 , 2 and 3 are equivalent fractions.
2 4 6

Class Assignment

Shade the two given diagrams in such a way that they represent equivalent fractions.
a.

c.



b. d.



Making equivalent fractions Teacher's Signature

Method I,

Let’s take a fraction 1 .
2

Multiply both numerator and denominator by the same number.

1 × 2 = 2
2 2 4

1 × 3 = 3
2 3 6

1 × 4 = 4
2 4 8

1 , 2 , 3 and 4 are equivalent fractions.
2 4 6 8

108 Oasis School Mathematics Book-4

Method II,
Let’s take a fraction 12/18.
Divide both numerator and denominator by the same number.

12 ÷÷22= 6 To find the equivalent fraction, divide
18 9 both the numerator and the denominator
by the same number.
12 ÷÷33= 4
18 6

12 ÷÷66= 2
18 3

\ 12 , 6 , 4 , 2 are equivalent fractions.
18 9 6 3

Class Assignment

Find three equivalent fractions of 2 .
3

2 = 2 × 2 = 4 2 = 2 × ... = 2 = 2 × ... =
3 3 2 6 3 3 ... 3 3 ...

Find three equivalent fractions of 20 .
30

20 = 20 ÷ 2 = 10 20 = 20 ÷ ... = 20 = 20 ÷ ... =
30 30 ÷ 2 15 30 30 ... 30 30 ...

Test of equivalent fractions Teacher's Signature

Let's take any two fractions and test whether they are equivalent fractions or not.

3 and 6 3 6 10 × 3 = 5 × 6 \ 3 and 6 are equivalent fractions.
5 10 5 10 30 = 30 (true) 5 10

Again, look at one more example Multiply the numerator of the first
by the denominator of the second
If the products are equal, the given fractions and numerator of the second by
are equivalent and if the products are not the denominator of first.
equal, the given fractions are not equivalent.

1 and 3 1 3 1×7=3×3
3 7 3 7 7 = 9 (false)

\ 1 and 3 are not equivalent fractions.
3 7

Oasis School Mathematics Book-4 109

Exercise 4.3

1. Using multiplication, find three fractions equivalent to the following
fractions.

a. 1 b. 3 c. 2 d. 4 e. 2
2 5 3 7 11

2. Using division, find three fractions equivalent to the following
fractions:

a. 12 b. 18 c. 24 d. 36 e. 36
18 24 36 32 54

3. Copy the given diagram in your copy and colour them in such a way
that they form equivalent fractions.
a. b.

c. d.

4. Identify whether the given pair of fractions are equivalent or not.

a. 1 and 6 b. 3 and 15 c. 3 and 9 d. 1 and 3
2 12 5 25 5 12 5 16

e. 5 and 10 f. 1 and 3 g. 7 and 3 h. 3 and 9
9 18 3 9 9 12 4 12

5. Find the missing numerators and denominators in the following

equivalent fractions.

a. 1 = .... b. 4 = 8 c. 2 = .... d. 4 = 6 e. 4 = ....
10 20 6 .... 5 10 .... 12 6 27

Answer: Consult your teacher.

Proper, improper and mixed fractions (Mixed number)

Proper fraction
The fraction in which the numerator is less than the denominator is called a proper
fraction.
1 , 2 , 4 , 7 are proper fractions.
2 3 5 12

110 Oasis School Mathematics Book-4

Improper fraction

The fraction in which numerator is greater than the denominator is called an

improper fraction. Just compare the numerator
4 , 7 , 5 , 9 are improper fractions. and denominator to identify the
3433 proper or improper fraction.

Mixed numbers
Improper fraction can also be expressed as mixed numbers.

In the above figure, there are five half apples.
It can be written as 5 .

2

Five half apples

= 5 apples
2

2 and a half apples

=2 1 apples
2

\ 5 = 2 1
2 2

Improper fraction Mixed numbers

Remember !

When we combine a whole number with a fraction we get a mixed number.

Again, 1 and a half apples
1 apple
= 1 1 apples
2

1 apple
2

Oasis School Mathematics Book-4 111

3 half apples

= 3 apples
2

1 apple 1 apple 1 apple
2 2
1 apple 1 apple
2 2
1
1 2 = 3
2

Mixed number Improper fraction

Class Assignment

1. Colour the proper fraction with blue and improper fraction with yellow.
27316
55247

12 17 9 1 12
13 6 4 15 5

2. Using mixed number answer the following questions.

How many biscuits?

How many biscuits?

How many bottles of milk?

3. Write the answer in improper fraction.

How many biscuits?
How many biscuits?

Teacher's Signature

112 Oasis School Mathematics Book-4

Conversion of mixed number into improper fraction.
1

Let's take a mixed number 1 2

2 × 1 = 2 Multiply the whole number with the denominator.

1 + 2 = 3 Add the numerator to the product.

\1 1 = 3 Write the sum above denominator.
2 2

Example:

Convert 3 5 into mixed number.
7

Here, 3 5 = 3×7+5 = 21 + 5 = 26
7 7 7 7

Conversion of improper fraction into mixed number

Let’s take an improper fraction 5
2

To convert, this improper fraction into mixed number

divisor 2 ) 5 (2 quotient Remainder
–4 remainder Divisor
\ Mixed number = Quotient
1

11
2

Class Assignment

1. Convert into improper fraction:

1 1 = 2 3 = 3 2 = 3 1 =
2 4 3 3

5 1 = 5 2 = 6 1 = 7 1 =
2 5 3 2

2. Convert the following imporper fraction into mixed number.

13 = 3) 13 (4 Divisor = 3
3
- 12
1 Quotient = 4 \ 13 =4 1
Remainder = 1 3 3

15 = 4) 15 ( Divisor = .......
4 Quotient = .......
Remainder = .......
\ 15 = .................
4

Oasis School Mathematics Book-4 113

23 = 5) 23 ( Divisor = .......
5
Quotient = .......
23
Remainder = ....... \ 5 = .................

Teacher's Signature

Exercise 4.4

1. Make separate lists of proper and improper fractions from the given sets of fractions:

2 , 5 , 1 , 3 ,12, 5 ,13, 2 , 5
323758659
2. Use the pictures to write the improper fractions and the mixed number.
a. b.

Improper fraction = 3 Improper fraction = ..........
Mixed number = 1212 Mixed number = ..........
d.
c.

Improper fraction = .......... Improper fraction = ..........

Mixed number = .......... Mixed number = ..........

3. Convert the following fractions into mixed numbers. i. 51
a. 4 b . 7 c. 10 d. 13 e. 12 f. 36 g . 28 h . 43 7
323 45798

4. Convert the following mixed numbers into improper fractions:

a. 2 3 b. 3 1 c. 2 13 d. 3 1 e. 5 2
4 7 4 6 3

f. 5 6 g. 4 3 h. 3 i. 7 5 j. 9 1
7 8 10 6 3

Answer: Consult your teacher.

114 Oasis School Mathematics Book-4

6

Addition and subtraction of like fractions

In the given figure, fraction of the green part = 3 3
8 8
2
In this figure, fraction of the red part = 8 2
8
3 2 5
\ Fraction of the coloured part = 8 + 8 = 8

Example:

Add:

4 + 2 Keep the denominator same, add
7 7 the numerator only.

= 4 + 2
7
6
= 7

Subtraction of like fractions

2 taken out
8

5 3 left
8 8

5 – 2 = 3
8 8 8

I understand, to subtract like fractions, keep
the denominator same, subtract only the
numerator.

Oasis School Mathematics Book-4 115

Class Assignment

Complete the given table.

Figure Fraction of Fraction of Fraction of Result
red green coloured part \2 +1=3

2 1 3 8 88
8 8 8

Complete the given table.

Figure Fraction of Fraction of Remaining fraction Result
total part red colour of green colour
3 –2=1
32 1 4 44
44 4

Teacher's Signature

116 Oasis School Mathematics Book-4

Example 1: Example 2:

Subtract: Simplify:
4 1 3
7 – 7 = 8 3 1 + 4 3 + 2 4 3 1 = 3 × 5 + 1= 16
5 5 5 5 5 5

= 4 – 1 = 3 = 16 + 23 + 14 = 53 =10 3
7 7 5 5 5 5 5

Example 3:

Simplify: Convert the mixed number
into improper fraction.

5 2 – 1 6 + 2 5
7 7 8

= 37 – 13 + 19 = 37 – 13 + 19 = 56 – 13 = 43
7 7 7 7 7 7

Exercise 4.5

1. Add: 1 2 2 5
2 5 4 9 8 13 6 15
a. 5 + b. 9 + c. 13 + d. 15 + e. 1 + 5
6 6

2. Subtract:

a. 3 – 1 b. 2 – 1 c. 8 – 3 d. 7 – 3 e. 4 – 1
5 5 3 3 13 13 12 12 13 13

3. Add:

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

4. Subtract:

a. 4 3 –3 1 b. 5 3 – 2 1 c. 7 2 – 6 4 d. 4 1 –2 1 e. 8 2 – 6 1
5 7 8 8 9 9 6 6 3 3

5. Simplify:

a. 6 – 2 + 7 b. 4 + 3 – 1 c. 1 1 + 3 3 – 3 1 d. 7 1 + 2 2 –1 1
11 11 11 13 13 13 4 4 4 3 3 3

Answers: 2 10 11 2 1 5
3 3 15 5 3 13
3
5 3 1 61 1 3 2
13 4 78 6 4 3
1
3 1 7 1 6
1 4 9 3 13
7

Oasis School Mathematics Book-4 117

Addition and subtraction of unlike fractions

While adding or subtracting two or more fractions with different denominators,
first we change all the fractions to their equivalent fraction with common
denominator, then we add or subtract.

Example 1:

1 + 3
2 4
1 2
Equivalent fraction of 2 is 4

Now, 1 3 Equivalent fractions of 1 are
2 4 2
+ 2 3 4
4 6 8
2 3 , , , etc.
4 4
= + Equivalent fractions of 3 are
4
= 5 6 , 192,1162, etc.
4 8
1
= 1 4

Example 2:

Add: 2 3 + 3 1 + 2 1
4 3 2
Solution:

2 3 + 3 1 + 2 1
4 3 2

= 11 + 10 + 5
4 3 2

= 11 × 3 + 10 × 4 + 5 × 6 Convert all the mixed numbers into improper fraction.
4 3 3 4 2 6
Take L.C.M. of 4, 3, and 2. It is 12.
= 33 + 40 + 30 Convert all three fractions into like fraction
12 12 12 having each denominator 12.

= 33 + 40 + 30 Follow the addition rule of like fractions.
12

= 103 = 8 7
12 12

118 Oasis School Mathematics Book-4

Example 3:

Subtract: Subtract: Subtract:

2 1 – 1 1 3 – 1 6 3 – 3 1
4 2 4 6 4 5

= 9 – 3 = 3 – 3 – 1 – 2 =247 – 16
4 2 4 6 6 2 5

= 9 × 1 – 3 × 2 = 9 – 2 = 27 × 5 – 16 × 4
4 × 1 2 × 2 12 12 4 5 5 4

= 9 – 6 = 9–2 = 135 – 64
4 4 12 20 20

= 9–6 = 3 = 7 = 135–64 = 71 = 3 11
4 4 12 20 20 20

Exercise 4.6

1. Add:

a. 2 + 1 b. 2 + 3 c. 1 + 5 d. 1 + 3
3 6 5 10 3 9 4 8

e. 1 + 2 + 1 f. 2 + 1 + 5 g. 1 + 3 + 7 h. 1 2 + 1 5
2 3 4 3 2 6 2 4 8 3 6

i. 2 1 +3 1 j. 5 1 + 3 1 + 1 5 k. 1 3 + 2 5 + 3 1
4 2 2 4 4 4 6 3

2. Subtract:

a. 5 – 1 b. 2 – 1 c. 3 – 1 d. 3 – 1 e. 2 – 1
6 2 3 2 4 2 4 8 5 10

f. 2 3 –1 1 g. 3 1 – 2 1 h. 5 1 – 2 2 i. 5 5 –4 1 j. 6 1 –3 1
4 2 2 4 6 3 6 4 8 4

3. Simplify:

a. 5 – 1 + 2 b. 1 + 5 – 1 c. 2 + 1 – 1 d. 3 – 1 + 3
6 2 3 4 8 2 3 2 4 4 2 8

e. 2 3 + 1 1 – 3 5 f. 7 2 – 1 1 + 2 1 g. 2 5 – 4 2 – 1 1 h. 2 2 + 3 1 – 4 1
4 2 8 3 4 2 6 3 2 3 4 2

Answers:

1. a. 56 b. 7 c. 8 d. 5 e. 1 5 f. 2 g. 2 1 h. 3 3 i. 5 3 j. 10 7 k. 711
10 9 8 12 8 6 4 12 12

2. a. 13 b. 1 c. 1 d. 5 e. 130 f. 1 1 g.1 1 h.2 1 i.5 3 j.2 7
6 4 8 4 4 2 8 8

3. a. 1 b. 3 c.1112 d. 5 e. 4 7 f. 81112 g. -3 1 h. 1152
8 8 8 3

Oasis School Mathematics Book-4 119

Simple verbal problems in fraction

Prabesh bought 2 1 kg of potatoes and 5 1 kg of cauliflower. How much
3 2
vegetable did he buy altogether?

Solution: Here, total weight of vegetable is

2 1 + 5 1
3 2

= 7 + 11 = 7 × 2 + 11 × 3
3 2 3 2 2 3

= 14 + 33 = 14 + 33 kg = 467kg = 7 5 kg
6 6 6 6

\ He bought 7 5 kg of vegetable.
6

Exercise 4.7

1. a. A man bought 1 kg of Basmati rice and 2 kg of Mansuli rice. How
4 5
much rice did he buy altogether?

b. A man mixes 2 3 kg of sugar with 4 2 kg of better quality sugar.
7 7
Find the weight of the mixture so formed?

2. a. From 11 kg rice 2 kg is sold. How much rice is left now?
13 13

b. A man has to walk 8 2 km. In one hour he walked 5 1 km. Find the
3 3
distance left to walk?

3. a. A milkman mixes 2 1 litres of milk with 1 1 litres of water. Find the
4 2
quantity of the mixture.

b. A boy did 1 of his homework on Sunday and 1 of his homework
4 3
on Monday. How much of the homework did he do?

4. a. If 3 2 metres is cut from a ribbon which is 5 1 meters long, what
3 2
length of ribbon is left?

b. A shopkeeper had 2 2 m of cloth. He sold 1 1 m of the cloth. How
much cloth is left? 3 4

Answers:

1. a. 13 b. 6 5 kg 2. a. 9 b. 3 1 km 3. a. 3 3 litre b. 7 4. a. 1 5 m b. 1152 m
20 7 13 3 4 12 6

120 Oasis School Mathematics Book-4

Multiplication of a fraction by a whole number

Look and learn.

33 33

4 3 s, 4 44
Here are four 4
3 Remember !
To find its value, it is 4 × 4
2 2 2 2 6
3 3 3 3 • 5 + 5 + 5 = 3 × 5 = 5
4 4 4 4
+ + + 1 1 1 1 1 4
3 3 3 3 3 3
3 + 3 + 3 + 3 12 • + + + = 4 × =
4 4
= = = 3

We can obtain value by using this method also.

4 × 3 =? Steps:
4
4 3 12 • Write the whole number as fraction
= 1 × 4 4
= = 3 1 × 3
4 4
• Multiply the numerators
Remember !

• When we multiply a • Multiply the denominators and simplify.

fraction by zero, the

result is always zero.

Whole number × fraction = whole number × numerator of fraction
denominator of fraction

Class Assignment

1. Complete as shown:

a. 1 + 1 + 1 + 1 = 4 × 1 = ....2...............
2 2 2 2 2

b. 1 + 1 + 1 + 1 + 1 = ................... = ...................
3 3 3 3 3

c. 2 + 2 + 2 = ................... = ...................
7 7 7

d. 3 + 3 + 3 + 3 + 3 = ................... = ...................
5 5 5 5 5

e. 1 + 1 + 1 + 1 = ................... = ...... .............
5 5 5 5

Oasis School Mathematics Book-4 121

2. Multiply:

a. 2 × 3 = 6 1 × 3 =
5 5 2

b. 5 × 1 = 3 × 3 =
2 7

c. 6 × 3 = 1 × 0 =
5 2

d. 4 × 1 = 4 × 0 =
3 5

e. 2 × 1 = 4 × 3 =
3 5

f. 1 × 3 = 1 × 7 =
4 5

Teacher's Signature

Multiplication of a fraction by another fraction

The shaded part of the given figure represents 3 . of means ‘ × ‘
4

If we divide it into half, then half of the

shaded part is 1 of 3
2 4

= 1 × 3 Steps:
2 4
• To multiply a fraction by another fraction
1 × 3
= 2 × 4 • Multiply the numerator by the numerator 1 × 3 = 3

3 • Multiply the denominator by the denominator 2 × 4 = 8 3
8 8
= • Reduce the fraction into the lowest term (if possible) =

Class Assignment

2 × 1 = ........................... 2 × 2 = ...........................
5 3 3 5

4 × 2 = ........................... 3 × 1 = ...........................
5 3 7 2

6 × 1 = ........................... 4 × 2 = ...........................
7 5 9 3
Teacher's Signature

122 Oasis School Mathematics Book-4

Look at this example,

Example 1: Example 2:

Multiply: 3 1 × 1 × 3 1 Find the value of 1 of 24.
4 3 3
3
12 Solution:

= 13 × 1 × 10 = 1 of 24
2 5 3 3

= 13 = 1 8 3 divides 24 into 8
3 3
× 24

= 4 1 =8
3

Class Assignment

1 × 3 = 1×3 = 3
5 2 = 5×2 10
=
2 × 5 = .. .............. = ...........................
3 6 =
=
1 × 1 × 2 ................ = ...........................
2 3 5

3 × 5 × 1 ................ = ...........................
7 6 3

1 × 2 × 3 ................ = ...........................
4 7 11

3 × 2 × 1 ................ = ........................... Teacher's Signature
5 3 2

Exercise 4.8

1. Multiply:

a. 2× 1 b. 3× 2 c. 4× 1 d. 5× 2
4 7 6 9

e. 6× 1 f. 4 ×2 g. 1 × 3 h. 1 ×3
3 2 6 10

2. Multiply:

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

e. 2 × 3 f. 5 × 4 g. 2 1 × 3 2 h. 6 1 × 3 3
3 4 15 9 2 5 2 5

Oasis School Mathematics Book-4 123

3. Simplify:

a. 3 × 2 × 5 b. 1 × 2 × 3 c. 1 × 3 × 4 d. 2 1 ×1 3 ×2 1
4 3 6 2 3 5 3 7 9 2 4 4

e. 1 2 ×4 1 ×2 1 f. 2 × 5 1 ×3 1 g. 3 1 × 2 × 1 4
3 2 4 7 2 4 4 5 7

4. Find the value of:

a. 1 of 20 b. 1 of 12 c. 3 of 30 d. 2 of 21 e. 1 of 90 f. 1 of 24
4 3 5 7 3 4

1. a. 42 b. 6 c. 2 d. 1 1 e. 2 f. 4 g. 1 h. 3
2. a. 31 7 3 9 2 10
3. a. 152
4. a. 5 b. 3 c. 5 d. 5 e. 1 f. 4 g. 8 1 h. 23 2
8 12 8 2 27 2 5

b. 1 c. 4 d. 9 17 e. 16 7 f. 5 3 g. 2 3
5 63 32 8 28 70

b. 4 c. 18 d. 6 e. 30 f. 6

Reciprocal of a number

Let’s take a number 2. Reciprocal of a number can be obtained
dividing 1 by the given number.
Its reciprocal is 1
2
Similarly, reciprocal of 3 is 1
3

Again,

Reciprocal of 3 is 4 Reciprocal of a fraction can be
4 3 obtained by simply interchanging

Reciprocal of 5 is 6 numerator and denominator.
6 5

Note: Reciprocal of a number is also known as multiplicative inverse.

multiplicative number × multiplicative inverse = 1

Class Assignment

Find the reciprocal of

4 = 1 3 = .............
4 4
4
5 = ............. 7 = .............

7 = ............. 2 = ............. Teacher's Signature
5

124 Oasis School Mathematics Book-4

Dividing a whole number by a fraction

Let's take a whole number and a fraction.

Now, 3 ÷ 1 ; what does it mean?
It means 4
that how many 1 s are in 3?
4
To find its value, we have to multiply the whole number by the reciprocal of the divisor.

Example :

Divide: 3 whole number ÷ fraction
4÷ 5 = whole number × reciprocal of fraction

= 4× 5
3
20 2
= 3 = 6 3

Class Assignment

2 ÷ 2 = ................ = ................ 3 ÷ 1 = ................ = ................
1 2

5 ÷ 2 = ................ = ................ 3 ÷ 1 = ................ = ................
5 3

6 ÷ 3 = ................ = ................ 8 ÷ 2 = ................ = ................
4 5

6 ÷ 1 = ................ = ................
3

Teacher's Signature

Dividing a fraction by a whole number

Take a fraction 3 and a whole number 2
4
Now,
3
4 ÷2 Divisor

Dividend

To calculate the value, follow the following steps.

Oasis School Mathematics Book-4 125

Steps:

• Write the whole number as a fraction 3 ÷ 2 .
• 4 1
1
Find the reciprocal of divisor; reciprocal of 2 = 2

• Multiply the fraction by the reciprocal of divisor.

3 × 1 = 3
4 2 8

Example :

Divide: ÷5 = 2 × 1 = 2 fraction ÷ whole number
2 3 5 15 = fraction × reciprocal of whole number
3

Class Assignment

3 ÷ 4 = 3 × 1 = 3
5 5 4 20

2 ÷ 3 = ................ = ................ 5 ÷ 2 = ................ = ................
7 8

3 ÷ 5 = ................ = ................ 4 ÷ 3 = ................ = ................
11 7

5 ÷ 3 = ................ = ................
9
Teacher's Signature

Dividing fractions by fractions

Take any two fractions. Say 1 and 3
2 4

Now, 1 3
2 4
÷ Divisor

Dividend

To calculate the value, follow the following steps.

Steps:

• Find the reciprocal of divisor;

• Multiply the dividend by the reciprocal of divisor

1 3 1 4 2 2
2 4 2 3 3
÷ = × =

126 Oasis School Mathematics Book-4

Example :

Divide: 2 ÷ 3 dividend ÷ divisor
5 5 = dividend × reciprocal of divisor
2 5 2
= 5 × 3 = 3

Class Assignment

3 ÷ 1 = 3 × 3 = 9
4 3 4 1 4

5 ÷ 1 = ................ = ................ 3 ÷ 2 = ................ = ................
7 2 11 5 = ................

4 ÷ 2 = ................ = ................ 5 ÷ 2 = ................
13 7 9 3

Teacher's Signature

Exercise 4.9

1. Find the reciprocal of:
a. 3 b. 7 c. 1 d. 2 e. 3 f. 2 g. 1
8 5 7 11 6

2. Divide:

a. 4 ÷ 3 b. 2 ÷ 1 c. 5 ÷ 2 d. 6 ÷ 1 e. 2 ÷ 1
5 2 3 5 10

f. 10÷ 3 g. 3 ÷ 1 h. 6 ÷ 2 i. 15 ÷ 1
5 2 3 5

3. Divide:

a. 3 ÷5 b. 1 ÷6 c. 1 ÷2 d. 3 ÷4 e. 2 ÷3
4 2 3 5 3

f. 3 ÷2 g. 1 ÷4 h. 3 ÷8 i. 1 ÷ 3
7 3 8 20

4. Divide:

a. 1 ÷ 1 b. 2 ÷ 1 c. 3 ÷ 2 d. 2 ÷ 3 e. 5 ÷ 2
23 34 45 11 73 77

f. 6 ÷ 2 g. 5 ÷ 1 h. 3 ÷ 1 i. 2 ÷ 1 j. 1 ÷ 2
13 7 62 43 34 43

Oasis School Mathematics Book-4 127

1. a. 1 b. 1 c. 8 d. 5 e. 7 f. 11 g. 6 2. a. 6 2 b. 4 c. 7 1 d. 30
3 7 2 3 2 3 2

e. 20 f. 50 g. 6 h. 9 i. 17 1 3. a. 3 b. 1 c. 1 d. 3 e. 2 f. 3 g. 1
3 2 20 12 6 20 9 14 12

h. 3 i. 1 4. a. 1 1 b. 2 2 c. 1 7 d. 146 e. 2 1 f. 1 8 g. 1 2 h. 2 1 i. 8 j. 3
64 60 2 3 8 33 2 13 3 4 3 8

Activity

Multiplication of fractions

Multiply: 1 × 2
3 5

Here two denominators are 3 and 5.

Draw a rectangle, divide it into 3 equal parts horizontally and 5 equal parts
vertically as shown in the figure.

5

3

Shade 2 of the rectangle. Shade 1 of the rectangle.
5 3

What fraction of the rectangle is shaded twice?

Here 2 parts out of 15 boxes are shaded.

i.e. 2 parts is shaded.
15
1 2 2
\ 3 × 5 = 15

Try this to multiply.

a. 2 × 1 b. 3 ÷ 2 c. 1 ÷ 2
3 4 4 3 4 3

128 Oasis School Mathematics Book-4

Anasuya has Rs 1500 for shopping. She
1
spent 3 of her money to buy fruits.

Her expenditure on fruits.

= 1 of 1500
3

= ....................

= ....................

She bought 2 kg
3
4
mango and 5 kg

apple.

What is the total
weight of fruits?

She spent 1 of her money to buy food
5
items.

Her expenditure on food = 1 of 1500
5

= ....................

= ....................

She bought 1 1 kg rice
and 2
1
2 4 kg of sugar.

What is the total

weight of rice and

sugar?

What is the total weight of fruits and
food?

On which item she spent more money?

Oasis School Mathematics Book-4 129

Objective Questions

Colour the correct alternatives.
1. Which of the following statement is not true?

1 , 2 , 4 , and 3 , 1 , 2 and 3 , are 5 , 8 and 4 , are
555 5 24 6 13 13 13
unlike fractions
are like fractions equivalent fractions

2. What does the following figure represent?

2 1 2 3 2 1
4 4 4

3. 1 + 1 + 1 + 1 + 1 is
2 2 2 2 2

5 two's 5 halves 5 1
2

4. What is the reciprocal of 2 ?
5

5 1 2
2 5

5. Which of the following statement is not true?

5 ÷ 2 =5× 3 3 ÷4= 5 ×4 1 ÷ 2 = 1 × 3
3 2 5 3 2 3 2 2

6. Which of the following pairs are equivalent fractions?

2 and 4 3 and 9 1 and 2
3 5 5 15 2 3

130 Oasis School Mathematics Book-4

7. The sum of 1 + 2 is
2 3

2 5 7
5 6 6

8. The product of 2 × 4 is 6
3 5 8

8 10
15 12

9. The value of 4 ÷ 10 is
5

8 2 4
25 50

10. A day is what fraction of a week? 1
12
11
7 30 1
60
11. An hour is what fraction of a day?

11
12 24

12. A month is what fraction of a year? 1
12
11
7 60

13. A finger is what fraction of total fingers of your hand and feet?

111
5 10 20

Number of correct answers

Oasis School Mathematics Book-4 131

Unit Test Full marks -20

1. Write any two equivalent fractions of: 2

a. 2 b. 3
3 4

2. Convert the following mixed number into improper fraction and

improper fraction into mixed number.: 2

a. 3 2 b. 36
7 7

3. Add or subtract: 2

a. 3 + 2 b. 8 – 3
8 8 13 13

4. Simplify 2×2=4

a. 1 + 2 + 1 b. 2 5 – 4 2 + 1 1
2 3 4 6 3 2

5. Multiply: 2

a. 3 × 1 b. 5 × 4
6 12 9

6. Divide: 3

a. 2 ÷ 5 b. 5 ÷ 15 c. 5÷ 2
3 26 6 3

7. Simplify: 3

a. 2 × 1 × 3
3 2 4

b. 2 1 × 1 3 × 3 4
2 4 5

8. A milkman mixes 3 1 litres of milk with 1 1 litres of water. Find the quantity
of mixture. 2 2 2

132 Oasis School Mathematics Book-4

UNIT

5 Decimal

12 Estimated Teaching Hours: 15
93

6

Contents • Decimal as a part of the whole

• Conversion of decimal into fraction and
fraction into decimal

• Place value of decimal number

• Comparison of decimal numbers

• Addition and subtraction of decimal
numbers

• Multiplication and division of decimal
number by a whole number

• Use of decimal in the measurement of money,
length, weight and capacity

Expected Learning Outcomes

Upon completion of the unit, students will be
able to develop the following competencies:

• To understand the meaning of decimal
• To understand the relation between decimal and fraction
• To put the decimal number in the place value chart and

compare the decimal number
• To add and subtract decimal number
• To multiply and divide the decimal number by whole number
• To understand the application of decimal number in various

measurement

Materials Required: Graph paper, paper models showing hundredths, tenths, etc.

Oasis School Mathematics Book-4 133

Decimal as a part of whole

Tenths

In the given figure, one whole is divided into
ten equal parts. One part is shaded.

Fraction represented by the shaded part is one

tenth i.e. 110.

Fraction 110can also be written as 0.1 and read as ‘zero decimal one’.

Fraction represented by the shaded part = 120
( two tenths)

Decimal represented by the shaded part = 0.2.

If one whole is divided into 10 equal parts, fraction
1
represented by each part is 10 and the decimal

represented by each part is 0.1.

one whole two tenths six tenths

Fraction = 2 Fraction = 160
10 Decimal = 0.6

Decimal = 0.2

The fractions 1 , 2 , 130, etc having the denominator 10 are called tenths.
10 10

Hundredths

Here one whole is divided into 100 equal parts.
4 parts out of 100 are shaded. The fraction
represented by the shaded part = 1040.

134 Oasis School Mathematics Book-4

It is also written as 0.04 and read as zero decimal

zero four.
Fraction represented by the shaded parts = 11050.
Decimal represented by the shaded parts = 0.15.

If a whole is divided into 100 equal parts, the fraction represented by a
1
part is 100 and the decimal represented by each part is 0.01.

The fractions 1100, 1300, 15 etc. having the denominator 100 are called
hundredths. 100

Thousandths

If a whole is divided into thousand equal parts, the fraction represented by
1
each part is 1000 and the decimal represented by each part is 0.001.

\3 = 0.003 15 = 0.015 465 = 0.465 etc. are called thousandths.
1000 1000 1000

A decimal point separates a whole number and a decimal fraction:

one whole 3 tenths 1.3 decimal part

Remember ! decimal point
the whole part

Fraction Fraction Decimal Number name
0.2 zero point two
2 tenths 2 0.18 zero point one eight
18-hundredths 10 0.025 zero point zero two five
25-thousandths
18
100

25
1000

How to read the decimal? Take 1.3, how to read it?
It is read as ‘one decimal three’ or ‘one point three’.

If there is no whole number, we have to write ‘0’ in the whole number
position before the decimal.

Oasis School Mathematics Book-4 135

Class Assignment

1. Write the fraction and decimal represented by the shaded part.

a. Fraction Decimal

2 0.2
10

b. Fraction Decimal

12 0.12
100

c. Fraction Decimal

d. Fraction Decimal

136 Oasis School Mathematics Book-4

2. Shade the following figure to represent the given decimal.

0.64 0.15

0.4 0.8

0.7

3. Write as you would read.

a. 0.31 .................................................................

b. 0.05 .................................................................

c. 0.84 .................................................................

d. 0.45 .................................................................

e. 0.92 .................................................................

Fractions

As we know that 1 = 0.1, 2 = 0.2, 1 = 0.01, 12 = 0.12, we have to use this
10 10 100 100

concept to convert other fractions into decimal.

Let's convert 4 into decimal.
5
Example 1:
I have to make
Divide: 4 denominator 10.
5
To convert fraction into decimal, I
= 4×2 have to make denominator either
5×2
8 10 or 100.
= 8 = 0.8 10 = 0.8
10

Example 2:

Convert 4 into decimal.
25

Oasis School Mathematics Book-4 137

Solution:

4 = 4×4 Denominator 25 is a factor of 100. So multiply
25 25 × 4 both numerator and denominator by 4.

= 16
100

= 0.16

Conversion of decimal number into fraction

Let’s learn to convert decimal into fraction.

0. 4 = 4 Steps:
10
• Count the number of digits after decimal.
0. 12 = 12 • Remove the decimal.
100 • Write 10 in the denominator, if there is 1 digit after decimal.
• Write 100 in the denominator, if there are 2 digits after
0. 225 = 225
1000 decimal.

Note: 1.25 = 112050 3.75 = 317050 2.6 = 2 6
10

Class Assignment

Convert into fractions:

0.2 = 0.35 = 0.5 = 0.625 =

0.16 = 0.75 = 0.125 = 2.01 =

Exercise 5.1

1. Write the decimal represented by the given figure.
a. b. c.

2. Write the following decimal numbers in word:

a. 0.45 b. 0.03 c. 2.36 d. 3.005 e. 0.675

138 Oasis School Mathematics Book-4

3. Write the following in fraction and then in decimal:

a. six tenth b. two tenths c. five hundredths

d. four thousandths e. twenty five thousandths

f. three hundred sixty thousandths

4. Express the following fractions in decimals:

a. 2 b. 3 c. 45 d. 63 e. 216030 f. 512010
10 10 100 100

5. Convert the denominators into 10 or 100 and express them in decimal:

a. 3 b. 1 c. 1 d. 3 e. 3 f. 23
5 2 20 20 25 50

6. Express the following decimals in fractions:

a. 0.01 b. 0.12 c. 0.314 d. 3.56 e. 4.5

f. 5.25 g. 6.5 h. 10.2 i. 9.05 j. 7.215

Consult your teacher.

Place value of decimal numbers

A decimal number consists of two parts, a whole number part and a decimal
number part. The two parts are separated by a dot called decimal point.

Take a number 2738.125 2738.125

Thousands Thousandths
Hundreds Hundredths
Tenths
Tens
Ones

Decimal point

Whole number parts Decimal parts
Thousands
Hundreds

Tens
Ones
Decimal (.)
Tenths

Hundredths
Thousandths

1000 100 10 1 111
2 7 3 8 10 100 1000
. 125

Oasis School Mathematics Book-4 139

The digit 2 is in thousands place. So its place value is 2 × 1000 = 2000

The digit 7 is in hundreds place. So its place value is 7 × 100 = 700

The digit 3 is in tens place. So its place value is 3 × 10 = 30

The digit 8 is in ones place. So its place value is 8 × 1 = 8

The digit 1 is in tenths place. So its place value is 1 × 1 = 1
10 10
1 2
The digit 2 is in hundredths place. So its place value is 2 × 100 = 100

The digit 5 is in thousandths place. So its place value is 5 × 10100 = 5
1000

\ 2738.125 = 2 thousands + 7 hundreds + 3 tens + 4 ones + 1 tenths +

2 hundredths + 5 thousandths.

= 2000 + 700 + 30 + 8 + 110+ 2 + 5
100 1000

\ 2738.125 = 2000 + 700 + 30 + 8 + 0.1 + 0.02 + 0.005

Short form Expanded form

Short form of decimal numbers

50 + 8 + 6 + 7 = 50 + 8 + 0.6 + 0.07
10 100
= 58.67 Short form

4 hundreds + 3 tens + 5 ones + 3 tenths + 8 hundredths

= 400 + 30 + 5 + 3 + 8
10 100

= 400 + 30 + 5 + 0.3 + 0.08

= 435.38 Short form

Class Assignment

1. Write the place value of each of the digits of given number:
283.63

140 Oasis School Mathematics Book-4

2. Write in the short form:

200 + 10 + 6 + 1 + 2 =
10 100

500 + 20 + 7 + 3 + 1 =
10 100

500 + 20 + 7 + 3 + 1 =
10 100

Exercise 5.2

1. Show the following numbers into place value chart.

a. 0.873 b. 12.81 c. 8.92 d. 5.184

e. 23.86 f. 26.814 g. 254.81 h. 56.24

2. Write the following decimal numbers in hundreds, tens, ones, tenths
and hundredths.

a. 0.82 = 8 tenths + 2 hundredths

b. 2.75 c. 7.65 d. 0.96 e. 5.74

f. 23.82 g. 39.85 h. 85.46 i. 127.94 j. 385.64

3. Write the place value of coloured digits.

a. 0.94 b. 6.84 c. 23.86 d. 87.34

e. 27.62 f. 43.215 g. 96.159 h. 23.164

4. Write the following decimals in expanded form.

a. 56.75 b. 0.81 c. 6.84 d. 23.96 e. 136.94

f. 224.93 g. 0.082 h. 5.093 i. 58.123 j. 8.146

5. Write the following in the short form of decimal number.

a. 170 + 1800 b. 3 + 110 + 5 c. 20 + 5 + 130 + 7
100 100

d. 300 + 20 + 5 160 + 7 e. 400 + 10 + 1 + 120 + 3
100 100

f. 5 hundreds + 6 tens + 2 ones + 3 tenths + 6 hundredths

Consult your teacher.

Oasis School Mathematics Book-4 141

Comparison of decimal numbers

While comparing two decimal numbers, follow the steps given below.

Take any two numbers 82.36 and 48.63 and compare them
eg. 82.36 > 48.63

since, 82 > 48 Compare whole number part

• If the whole number parts are equal, compare the digits in the tenths place.
Let's compare

45.57 and 45.63

compare tens : 4 = 4

compare ones : 5 = 5

compare tenths : 5 < 6

Since 5 < 6, 45.57 < 45.63

• If the whole number parts as well as the digits in the tenths place are

equal, compare the digits in hundredths place.
Example :

25.84 and 25.874

compare tens :2=2 Compare whole number parts tenths place,
hundredths place and thousandths place in order
compare ones : 5 = 5 to compare the decimal numbers.

compare tenths : 8 = 8

compare hundredths : 4 < 7

\ 25.84 < 25.874

Relation between ones, tenths, hundredths and thousandths.

10 tenths = 1 ones

10 hundredths = 1 tenths

10 thousandths = 1 hundredths

100 hundredths = 1 ones

1000 thousandths = 1 ones

Exercise 5.3

1. Compare the following decimal numbers. c. 123.08 and 75.98
a. 18.623 and 24.825 b. 63.12 and 52.65 f. 0.96 and 0.85
i. 15.84 and 15.83
d. 12.15 and 12.63 e. 315.64 and 315.82

g. 0.72 and 0.76 h. 2.03 and 2.01

142 Oasis School Mathematics Book-4

2. Write the following decimal numbers in an ascending order.

a. 2.31, 0.52, 1.65 b. 2.45, 8.95, 4.63 c. 0.123, 0.101, 0.314

d. 12.65, 12.67, 12.61 e. 123.801, 123.807, 123.802

3. Write the following decimal numbers in an descending order.

a. 5.83, 2.94, 7.68 b. 2.25, 3.86, 1.23 c. 2.25, 3.86, 16.96

d. 72.64, 72.54, 72.89 e. 83.76, 83.01, 83.24 f. 0.31, 0.37, 0.32

g. 23.86, 23.88, 23.84 Consult your teacher.

Addition and subtraction of decimal numbers

The process of addition and subtraction of decimal numbers is same as that
of the whole numbers.

Follow the following steps to add or subtract the decimal numbers.

Steps:
• Put the digits according to the place value so that the decimals are

also exactly one below the other, ones below ones, tens below tens,
tenths below tenths and so on.
• Add or subtract as in the whole numbers.
• Place the decimal points in the answer in the same place as the numbers
above it.

Let's add two decimal numbers.

Example 1:

2.183 + 0.540 I have to place decimal in a 2 . 1 8 3 Decimal points one
straight line. + 0 . 5 4 0 below the other.
Solution: 2.723

2 . 183
+ 0 . 540
2 . 723

Example 2: I understand!
I can write zeros in tenths, hundredths and
Add: 2.631 + 15.14 + 0.6
thousandths place to make like decimal.
Solution:
Oasis School Mathematics Book-4 143
2.631
15.140
+ 0.600
18.371

Example 3: Example 4:

Subtract: 15.25 from 40.2 Simplify: 23.14 + 0.83 - 6.135

Solution: Solution:

40.20 23.14 Add the decimal numbers having
- 15.25 + 0.83 + sign.
24.95
23.97
Again, Subtract the number having
– sign from the sum.
23.970
- 6.135

17.835

\ 23.14 + 0.83 – 6.135 = 17.835

Exercise 5.4

1. Add: b. 2.81 c. 0.8 d. 12.63 e. 15.635
a. 0.823 + 12.35 + 12.86 + 9.6 + 137.8

+ 1.542

f. 86.92 g. 14.32 h. 132.5 i. 254.63 j. 56.89
+ 0.93 0.16 56.28 28.9 0.9
+ 132.6 + 0.9 + 0.814 + 4.763
2. Add:
a. 23.63 + 0.8 b. 10 + 3.83

c. 16.01 + 19.1 d. 0.825 + 6.24

e. 3.632 + 0.14 f. 15.6 + 0.814

g. 12.63 + 0.814 + 5.185 h. 13.01 + 1.1 + 1.98

i. 23.62 + 0.81 + 2.03 j. 0.316 + 2.46 + 15.1

3. Subtract: b. 35 c. 58.35
- 17.83 - 6.17
a. 26.85
- 12.63

d. 31.2 e. 132.63 f. 73.2
- 0.41 - 12.89 - 18.14

4. Subtract: b. 43.89 - 16.64 c. 37 - 12.85
a 36.84 - 24.28 e. 164.92 - 85.631 f. 57.64 - 18.9
d. 60.5 - 23.632

144 Oasis School Mathematics Book-4

5. Simplify: b. 18.35 + 12.26 - 19.39 c. 4.63 - 1.24 + 15.6
a. 7.35 + 9.82 - 3.45

d. 36.48 - 26.1 - 3.63 e. 18.314 + 0.678 - 12.1 f. 12.07 + 18.1 - 16.32

6. a. Amar runs 3.7 km in the morning and 2.75 km in the evening. What
distance does he run in all?

b. The thickness of a book is 4.23 cm and that of another book is 2.09
cm. What is the thickness of the two books when placed one on top
of the other?

c. A boy spent Rs. 35.5 to buy a pen and Rs 26.85 to buy a book. How
much did he spend altogether?

7. a. A man walked 382.63 m on Sunday and 290.8 m on Monday. How
much less metres did he walk on Monday?

b. Nisha had Rs 65.10. She spent Rs 35.55 to buy a book. How much
money does she have now?

8. Find the perimeter of given triangle and quadrilateral.

5.6cm 7.2cm
4.5cm
4cm
6.3cm 4.6cm 6.9cm

Consult your teacher.

Multiplication of decimals by whole numbers

Let’s take a decimal number and a whole number and learn how to multiply
a decimal number by a whole number.

Multiply: 3.26 × 6 Steps:

Solution: 3.26 • Multiply 326 and 6.
×6
19.56 • Count the number of digits after decimal in the
multiplicand.

• Put the decimal point in the product before the
same number of digits counting from the right.

Oasis School Mathematics Book-4 145

There are 2 digits in 3.26 after decimal. So the decimal Remember !
point in the product should be placed before 2 steps
Total decimal places in
counting from the right. factor = decimal places
is the product.

Multiplication and division of decimals by 10 and 100

Multiplication by 10 and 100

5.23 × 10 = 52.3 Shift decimal point It's simple. While multiplying a
one step right. decimal number by 10, we just have to

2.68 × 10 = 26.8 shift decimal point one step right.

Again, Shift decimal point one step right.

0.324 × 100 = 32.4

Shift decimal point two steps right.

5.634 × 100 = 563.4 5.74 × 10 = 57.4
Shift decimal point two steps right. 2.135 × 100 = 213.5

Class Assignment

Multiply:

2.314 × 10 = 62.16 × 10 = 0.125 × 10 =
0.0169 × 10 =
0.0314 × 10 = 528.62 × 10 = 0.215 × 100 =
0.540 × 100 =
45.231 × 100 = 3.149 × 100 =

0.071 × 100 = 0.23 × 100 =

Dividing by 10 and 100

34.6 ÷ 10 = 3.46 Shift decimal point one step left.
Shift decimal point one step left.
0.86 ÷ 10 = 0.086 Shift decimal point two steps left.
Again,
53.4 ÷ 100 = 0.534

264.83 ÷ 100 = 2.6483 Shift decimal point two steps left.

146 Oasis School Mathematics Book-4

Class Assignment 2.374 ÷ 10 =
37.32 ÷ 100 =
Divide: 432.83 ÷ 100 =
54.2 ÷ 10 = 36.14 ÷ 10 =
1.823 ÷ 10 = 0.416 ÷ 10 =
9.821 ÷ 100 = 0.614 ÷ 100 =

Division of decimal numbers by whole numbers

Dividing decimal numbers is just like dividing the whole numbers except
placing the decimal point.
Let’s see an example,
Divide 6.35 by 4.

Example 1:

4 4.36 1.09 Steps:
• Divide ones 4 ÷ 4 = 1

-4 • Put decimal in quotient
36 • Bring down 3
- 36 • 3 cannot be divided by 4
0 • Write 0 on the quotient
• Bring down 6, now it is 36

• 36 ÷ 4 = 9

Do not show the decimal in

the working of the sum.

Example 2: Example 3:

0.624 ÷ 8 2 ) 2.50 ( 1.25

8 ) 0.624 ( 0.078 -2

- 56 6 cannot be divided by 8, 5 Write extra zero to complete
64 so write 0 after decimal. -4 the division.
- 64
10

0 - 10

Again, look at one more example, 0

Oasis School Mathematics Book-4 147

Exercise 5.5

1. Multiply: b. 0.36 × 4 c. 0.284 × 5 d. 0.034 × 7 e. 2.374 × 4
g. 6.45 × 3 h. 9.047 × 8 i. 2.684 × 3 j. 0.034 × 7
a. 3.26 × 3 l. 5.642 × 7
f. 4.8 × 3
k. 3.04 × 6 b. 0.273 ÷ 3 c. 0.452 ÷ 4 d. 4.25 ÷ 5 e. 5.225 ÷ 5
g. 3.43 ÷ 7 h. 3.612 ÷ 3 i. 6.25 ÷ 5 j. 6.235 ÷ 5
2. Divide:

a. 0.326 ÷ 2
f. 6.9 ÷ 3

3. Multiply: b. 2.634 × 10 c. 0.0125 × 10 d. 56.23 × 10 e. 1.235 × 10
g. 0.375 × 10 h. 4.65 × 10
a. 0.355 × 10
f. 2.84 × 10

4. Multiply:

a. 0.0214 × 100 b. 0.316 × 100 c. 0.31 × 100 d. 1.08 × 100 e. 2.05 × 100
i. 5.09 × 100
f. 3.18 × 100 g. 5.27 × 100 h. 4.63 × 100
d. 0.463 ÷ 10 e. 15.14÷ 10
5. Divide: b. 4.623 ÷ 10 c. 8.14 ÷ 10

a. 3.14 ÷ 10

f. 26.37 ÷ 10 g. 23.64 ÷ 10 h. 2.54 ÷ 10

6. Divide:

a. 5.172 ÷ 100 b. 27.38 ÷ 100 c. 39.65 ÷ 100 d. 83.93 ÷ 100 e. 92.27 ÷ 100
f. 527.31 ÷ 100 g. 0.123 ÷ 100 h. 5.194 ÷ 100

7. a. The cost of one pencil is Rs 4.65. What is the cost of 7 such pencils?

b. The length of a ribbon is 2.15 m. What is the length of 4 such ribbons?

c. A man earns Rs 65.80 in five hours. How much does he earn in one hour?

Answer:

1. a. 9.78 b. 1.44 c. 1.42 d. 0.238 e. 9.496 f. 14.4 g. 19.35
h. 72.376 i. 8.052 j. 0.238 k. 18.24 l. 39.494

2. a. 0.163 b. 0.091 c. 0.113 `d. 0.85 e. 1.045 f. 2.3

g. 0.49 h. 1.204 i. 1.25 j. 1.247 3. Consult your teacher

4. Consult your teacher 5. Consult your teacher 6. Consult your teacher

7. a. Rs 32.55 b. 8.6 m c. Rs 13.16

148 Oasis School Mathematics Book-4

Use of decimal in measuring of money, length, weight and capacity

Decimal system is used in different types of measurement such as
measurement of money, length, weight and capacity. It is used in the
conversion of units.

Use of decimal in money

Example : 1

Convert 60 paise into rupees 100 Paise = 1 Rupee

Solution: 60 1 P = 1 Rupees
100 100
60 paise = rupees

= 0.6 rupees 60 P = 60 Rupees
100
Again, look at one more example.

Example : 2

Convert 15 rupees 45 paise into rupees. I know, I have to divide paise
by 100 to convert into rupees.
Solution:
I have to multiply rupees
15 rupees 45 paise by 100 to convert into
paise.
= 15 rupees + 45 rupees
100

= 15 rupees + 0.45 rupees

= 15.45 rupees

Example : 3

Convert 0.04 rupees into paise.

Solution:

= 0.04 × 100 paise
= 4 paise

Use of decimal in length

Example : 4

Convert 25 cm into metre.

Solution: 25 100 cm = 1 m
100
25cm = m 1 cm = 1 m
100

= 0.25 m 25 cm = 25 m
100

Oasis School Mathematics Book-4 149

Example : 5

Convert 6 m 35 cm into metre. I have to multiply m by 100 to
convert it into cm.

Solution: 6 m 35 cm

= 6 m + 35 cm
100

= 6m + 0.35 cm
= 6.35 cm
Example : 6

Convert 0.34 m into cm. I have to multiply m by 100
to convert it into cm.
Solution:

0.34 m
= (0.34 × 100) cm
= 34 cm

Use of decimal in weight While dividing by 1000,
decimal point shifts 3 steps left
Example : 7

Convert 425 gm into kilogram (kg).

Solution:

425 gm = 425 kg 1000 gm = 1 kg
1000
1 gm = 1 kg
1000
= 0.425 kg
425 gm = 425 kg
1000

Use of decimal in capacity

Example : 8

Convert 55 ml into litre (l). 1000 ml = 1 l

Solution: 425 1
1000 1000
55 ml = litre 1 ml = l

= 0.055 l. 55 ml = 55 l
1000

Example : 9 0.25 × 1000
= 250 ml
0.25 litre into ml.

Solution:

0.25 litre = (0.25 × 1000) ml
= 250 ml.

150 Oasis School Mathematics Book-4