Elementary Mathematics
Addition of Fractions Observe the Picture-A to the right. How many segments in this picture are coloured ? Two segments out of four equal segments are coluored. Each of these segments constitute one-fourth of the picture; the two coloured portions constitute one-half of the picture. So Picture-A 1 4
1 4
2 4
1 1 4
1 2
Observe the Picture-B. From the picture it is clear that 1 9
1 9
Example 1. Add : Solution :
1 11
Example 2. Add : Solution :
1
1 9
9 7
1 1 9
1 11
3 11
3 9 5 11
10 7 9 10 7 27 7 6 3 7
10 7
Picture-B
The sum of two or more fractions with a common denominator is a fraction with the same denominator. Its numerator is the sum of the numerators of the given fractions.
3 5 11 11 1 3 5 11 9 11 9 7
1 3
8 7
8 7
If the sum is an improper fraction, it is generally expressed as a mixed fraction.
8
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