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Chapter Contents

Add, Subtract, Multiply and Divide Fractions

Back to Number System
Found in topics: Fractions
Maths Query > Unit > Arithmetic > Number System

Introduction

As in previous chapter, discussed about what is fraction and what are the types of fractions. Now in this chapter, here is topic operations on fractions. All basic operations can be done on fractions i.e addition, subtraction, multiplication and division of fractions. In this chapter, addition, subtraction, multiplication and division of fractions will be discussed.

Addition of fractions

1. Addition of like fractions

In addition of fractions of like fractions, only numerators are added and keep the value of denominator as it is.

Example

Example 1: Add 58 and 68
As the denominator is 8 and add numerator of both fractions only
= 58 + 68
= 5 + 68 = 118

Example 2: Add 14, 24 and 64
Here, as denominator is 4 for all fractions, so add numerators of all fractions only.
= 14 + 24 + 64
= 1 + 2 + 64 = 94

2. Addition of unlike fractions

To add unlike fractions, convert unlike fractions into like fractions by taking LCM of their denominators.

Example

Example 1: Add 34 and 56
Step 1: Take LCM of denominators of fractions. 34 and 56. LCM of 4, 6
Step 2: Multiply both fractions by numbers to make their denominators same equal to LCM 12.
34 × 33 = 912
56 × 22 = 1012
Step 3: Add the like fractions 912 and 1012.
= 912 + 1012
= 9 + 1012 = 1912
∴34 + 56 = 1912

Example 2: Add 23 , 46 and 14
Step 1: Take LCM of denominators of fractions 23 , 46 and 14 LCM of 3, 6, 4
Step 2: Multiply all fractions by numbers to make their denominators same equal to LCM 12.
23 × 44 = 812
46 × 22 = 812
14 × 33 = 312
Step 3: Add the like fractions 812 , 812 and 312
= 812 + 812 + 312
= 8 + 8 + 312 = 1912
∴ 23 + 46 + 14 = 1912

Subtraction of fractions

1. Subtraction of like fractions

In subtraction of like fractions, only numerators are subtracted and keep the value of denominator as it is.

Example

Example 1: Subtract 89 from 109
As these are like fractions and denominator is 9 for both fractions.
So, subtract numerator of both fractions only.
109 – 89
10 – 89 = 29

Example 2: Subtract 1112 from 1512
Here, the two fractions are like fractions and their denominator is 12.
So, subtract numerators of both fractions only.
= 1512 – 1112
15 – 1112 = 412 = 13

2. Subtraction of unlike fractions

To subtract the unlike fractions, convert unlike fractions into like fractions by taking LCM of their denominators.

Example

Subtract 64 from 83
Step 1: Take LCM of denominators of fractions.
LCM of 4, 3
LCM of 4 and 3 is 12
Step 2: Convert unlike fractions into like fractions by multiplying a number which makes denominator equal to LCM 12.
83 × 44 = 3212
64 × 33 = 1812
Step 3: Subtract 1812 from 3212
= 3212 – 1812
= 32 – 1812 = 1412 = 76
∴ 83 – 64 = 1412

Multiplication of fractions

1. Multiplication of fraction with whole number

To multiply a fraction with whole number, multiply only numerator by the given whole number and keep the denominator same. Then reduce it to its the lowest term.

Example

Example 1: 75 × 2
Here, 75 is a fraction and 2 is a whole number.
2 is written as 21
= 75 × 21
= 7 × 25 × 1 = 145

Example 2: 65 × 4
= 65 × 41
= 6 × 44 × 1 = 245

2. Multiply a fraction by another fraction

To multiply a fraction by another fraction, multiply their corresponding numerators and denominators. Then reduce the obtained fraction into its the lowest form.

Example

Example 1: Multiply fraction 75 by 34
Here, multiply numerators 7 and 3. Also, multiply their denominators 5 and 4.
75 × 34
= 7 × 35 × 4 = 2120

Example 2: Multiply fractions 25 , 46 and 32
25 × 32 ×
multiply numerators 2, 4 and 3 and also multiply denominators 5, 6 and 2.
= 2 × 4 × 35 × 6 × 2 = 2460
Now 2460 should be reduced to its the lowest term by dividing with the common factor 12.
2460 = 25

Division of fractions

To divide a fraction with another fraction, first the division is changed into multiplication by changing the division sign into multiplication and taking reciprocal of the second fraction.
Let’s learn it by following examples.

Example

Example 1: Divide 23 by 57
= 23 ÷ 57
= 23 × 75
= 2 × 73 × 5 = 1415

Example 2: Divide fraction 45 by whole number 6
= 45 ÷ 61
= 45 × 16
= 4 × 15 × 6 = 430
430. should be reduced into its the lowest term by dividing with common factor 2
= 215

Example 3: Divide 5 by 67
= 5 ÷ 67
= 5 × 71 × 6
= 356

Frequently Asked Questions

1) How to add fractions in maths?

Step I: Add the numerator of fractions.
Step II: Keep the value of common denominator as it is.
Step III: Value of fraction = Sum of all numeratorsValue of common denominator

2) How to add unlike fractions in maths?

Step I: Convert the unlike fractions into like fractions by taking LCM of all denominators.
Step II: Add the numerator of each equivalent fraction.
Step III: Value of fraction = Sum of numeratorsDenominator of equivalent fractions

3) How to subtract like fractions in maths?

Step I: Subtract the numerator of each fraction.
Step II: Keep the value of common denominator as it is.
Step III: Value of fraction = Difference of all numeratorsValue of common denominator

4) How to subtract unlike fractions in maths?

Step I: Convert the unlike fractions into like fractions by taking LCM of all denominators. Step II: Subtract the numerator of each equivalent fraction.
Step III: Value of fraction = Difference of all numeratorsDenominator of equivalent fractions

Solved Examples

1) Add 14 , 74 and 114.

As the denominator of of all fractions is same, then add only numerators of all fractions. 1 + 7 + 114 = 194

2) Add 34 , 53 and 92.

Here, denominators of all fractions are different.
So, first take LCM of all denominators.
LCM of 4, 3, 2
LCM of 4, 3 and 2 is 12.
Now, make denominator as 12 for all fractions.
34 × 33 = 912
53 × 44 = 2012
92 × 66 = 5412
Add the fractions with same denominator of 12
= 912 + 2012 + 5412
9 + 20 + 5412
8312

3) Simplify the fraction 53 + 34 - 32

Take LCM of all denominators 3, 4 and 2.
LCM of 3, 4, 2
LCM of 3, 4 and 2 = 12
Make denominator as 12 for all fractions.
53 × 44 = 2012
34 × 33 = 912
32 × 66 = 1812
Add the fractions
= 2012 + 912 - 1812
20 + 9 - 1812
29 - 1812
1112

4) Solve 32 - 213 - 215

= 32 - 73 - 115
Take LCM of all denominators 2, 3 and 5.
LCM of 2, 3, 5
LCM of 2, 3 and 5= 30
Make denominator as 30 for all fractions.
32 × 1515 = 4530
73 × 1010 = 7030
115 × 66 = 6630
32 - 73 - 115 can be written as
4530 - 7030 - 6630
45 - 70 - 6630
45 - 13630
- 9130

5) Solve the following
a) 34 × 12
b) 215 × 217

a) 34 × 12
= 34 × 12
38
b) 215 × 217
115 × 157
111 × 37 = 337
= 457

6) Solve
a) 37 ÷ 73
b) 123 ÷ 312

a) 37 ÷ 73
= 37 × 37
= 949
b) 123 ÷ 312
53 ÷ 72
53 × 27
= 1021

Worksheet 1

Download PDF 1

Fill in the blanks.

  1. 58 + 68 = ___________
  2. 34 - 24 = ___________
  3. 74 - 34 = ___________
  4. 48 × 14 = ___________
  5. 92 + 12 = ___________
  6. 65 × 306 = ___________
  7. 93 × 1 = ___________
  8. 43 ÷ 1 = ___________
  9. 214 ÷ 34 = ___________
  10. 68 + 78 - 18 = ___________
Help iconHelp box
7
32
14
5
43
118
1
18
6
3

Worksheet 2

Download PDF 2

Multiple choice questions

1) Choose the correct option for the sum of 43 and 13 is
  1. 53
  2. 63
  3. 73
  4. 43
2) Sum of 95 and 0 is
  1. 0
  2. 95
  3. 145
  4. 455
3) 173 × 0 is
  1. 13
  2. 73
  3. 173
  4. 0
4) The value of 52 ÷ 2 is
  1. 54
  2. 5
  3. 2
  4. 45
5) 74 - 34 gives
  1. 1
  2. 34
  3. 74
  4. 7
6) 57 ÷ 2549 is
  1. 57
  2. 2549
  3. 2
  4. 75
7) The reciprocal of 65 is
  1. 65
  2. 56
  3. 5
  4. 6
8) A man covered 38 m on bicycle and 34 m by car. The total distance covered by man is
  1. 78 m
  2. 3612 m
  3. 98 m
  4. 612 m
9) 01 × 34 gives
  1. 34
  2. 43
  3. 1
  4. 0
10) 15 ÷ 15 gives
  1. 1
  2. 5
  3. 15
  4. 125
MCQs Answer Key chevron-right icon
Last updated on: 22-02-2025

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