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Comparison of Unlike Fractions

Unlike Fractions Having the Same Numerators

If two unlike fractions with same numerator are given, the fraction with the smaller denominator
is greater than the fraction with larger denominator.
For example,
1 1 1
3 2 6
1 1
By looking at above figures we conclude that shaded portion of > shaded portion of > shaded
1 1 1 1 2 3
portion of . So, > > .
6 2 3 6
Unlike Fractions Having the Different Numerators

On comparing unlike fractions with different numerators, we first convert them into like fractions
and then compare them based on their numerators.

Method:
1. First find the LCM of the denominators of given unlike fractions.

2. Convert each fraction to its equivalent fraction with denominator equal to the LCM obtained
in first step.

2 3
For example, let us compare and . Here, both fractions are unlike fractions, so first we will
5 7
convert them into like fractions. Since, LCM of 5 and 7 = 35

2 27 14 3 35 15
×
×
∴ = = and = =
5 57 35 7 75 35
×
×
Clearly, 14 < 15.
Thus, on comparing these like fractions, we get
14 < 15 ⇒ 2 < 3
35 35 5 7
Example 12: Which of the following fractions is greater?
1 5 7 7 4 6
(a) or (b) or (c) 1 or 2
9 9 13 23 7 21
Solution: (a) Since both the fractions are like fractions with denominator 9, and comparing
numerators of fractions, we have 1 < 5.
5 1
∴ > .
9 9
(b) Here, fractions have same numerator but different denominators.

So, the fraction with smaller denominator is greater than the fraction with larger
denominator.
7 7
∴ >
13 23

217 Fractions