Introduction
The previous chapter Fractions, Types, Shaded Diagrams & Real Life Applications discussed about what a fraction is and what the various types of fractions are. This chapter, discusses the arithmetic operations like addition, subtraction, multiplication and division on fractions.
Addition of fractions
1. Add like fractions
In addition of fractions of like fractions, only numerators are added and keep the value of denominator as it is.
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. Add unlike fractions
To add unlike fractions, convert unlike fractions into like fractions by taking LCM of their denominators.
Example 1: Add 34 and
56
Step 1: Take LCM of denominators of fractions.
34 and
56.
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
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. Subtract like fractions
In subtraction of like fractions, only numerators are subtracted and keep the value of denominator as it is.
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. Subtract unlike fractions
To subtract the unlike fractions, convert unlike fractions into like fractions by taking LCM of their denominators.
Subtract 64 from
83
Step 1: Take LCM of denominators of fractions.
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. Multiply a 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 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 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 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 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
