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Operations on Fractions

Addition and Subtraction of Like Fractions

In order to add or subtract like fractions, first we will add or subtract numerators and then write
the sum or difference over the common denominator.

−
+
1 3 1 3 13 4 1 4 4 1 41 3
For example, addition of and = + = = ; Subtraction of from = − = =
7 7 7 7 7 7 5 5 5 5 5 5
3 5 4 9
Example 14: (a) Find the sum of and (b) Subtract from
13 13 47 47
−
+
3 5 35 8 9 4 94 5
Solution: (a) + = = (b) − = =
13 13 13 13 47 47 47 47
Addition and Subtraction of Unlike Fractions

In order to add or subtract the unlike fractions, first convert them into like fractions and then add

or subtract as usual.
Brahmagupta first explained this method for adding or subtracting any fractions in detail in 628 CE.

Brahmagupta’s method of adding or subtracting fractions involves the following steps:

1. Find equivalent fractions, which can be done by finding a common multiple of the
denominators, like the product of the denominators or the smallest common multiple of the
denominators.

2. Once the fractions have the same denominator, add (subtract) the numerators together and
keep the common denominator.

3. Simplify the result if necessary to get it into its simplest form.

3 2 1 5
Example 15: (a) Add the fractions and . (b) Subtract from .
8 3 5 6
Solution: (a) First convert the fractions into like fractions.

The LCM of the denominators 8 and 3 is 24.

×
3 33 9 2 28 16
×
∴ So, = = and = =
×
8 83 24 3 38 24 Get it right!
×
3 2 9 16 916 25 1
+
Now, + = + = = = 1 4 3 1
8 3 24 24 24 24 24 l − =
(b) First convert the fractions into like fractions. 5 10 10
l 4 − 3 = 5 or 1
The LCM of the denominators 5 and 6 is 30. 5 10 10 2
×
×
1 16 6 5 55 25
∴ = = and = =
×
5 56 30 6 65 30
×
5 1 25 6 25 6 19
−
Now, − = − = =
6 5 30 30 30 30
219 Fractions