Page 81 - ICSE Math 5

Comparing Unlike Fractions

Unlike fractions with the same numerator

We can compare unlike fractions with the same numerator by comparing their denominators.

For example, look at the figures shown below.
1
2
1
3
1
4
1
5
1 1 1 1
, , and are unlike fractions with the same numerator. On comparing their denominators,
2 3 4 5 1 1 1 1
we have 2 < 3 < 4 < 5. So, > > > .
2 3 4 5
Thus, we can say that if two fractions have the same numerator and different denominators,
then the fraction with the smaller denominator represents the greater fraction and the fraction
with the greater denominator represents the smaller fraction.

Unlike fractions with different numerators

We can compare unlike fractions with different numerators by finding equivalent fractions using
the L.C.M. or cross-multiplication method.
L.C.M. Method

To compare unlike fractions with different numerators using L.C.M. method, we follow the given
steps.

• Find the L.C.M. of the denominators of the given fractions.
• Find an equivalent fraction of each given fraction with denominator equal to the L.C.M.
• Compare the numerators of the fractions obtained in above step.

Cross-multiplication Method

To compare unlike fractions with different numerators using cross-multiplication method, we
do not find the L.C.M. of the denominators. Instead, we cross-multiply to compare the given
fractions.
3 2
Example 9: Compare and using the L.C.M. method.
4 5
Solution: Step 1: Find the L.C.M. of the denominators 4 and 5. 2 4, 5

L.C.M. of 4 and 5 = 2 × 2 × 5 = 20. 2 2, 5
Step 2: Find an equivalent fraction of each fraction with 5 1, 5
denominator equal to the L.C.M. 1, 1
3 3 × 5 15 2 2 × 4 8
= = and = =
4 4 × 5 20 5 5 × 4 20

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