Page 77 - ICSE Math 6

Comparison of Fractions

Comparison of like fractions

If the fractions to be compared have the same denominator, then the fraction with the greatest numerator
is the largest.
a b
Thus, if we have two like fractions namely, and then,
a b a b c c a b
(i) > , if a > b (ii) < , if a < b (iii) = , if a = b
c c c c c c
259 7
Example 13: Arrange , , and in ascending order.
13 13 13 13

Solution: The numerators of the given fractions are 2, 5, 9 and 7. The fraction with the greatest
2 5 7 9
numerator is the largest. Therefore, < < < .
13 13 13 13
Comparison of unlike fractions

Unlike fractions can be compared by converting them into like fractions.
We can also compare unlike fractions by converting them into fractions with the same numerator
following the given steps:
Step 1: Find the LCM of the numerators of the given fractions.

Step 2: Find the quotient by dividing the LCM by the numerator of each fraction.
Step 3: Multiply the numerator and the denominator of each fraction by the corresponding
quotient.
Step 4: The fraction with the smallest denominator is the largest.
12 9 7 11
Example 14: Compare , , and .
15 5 16 20
Solution: LCM of all the denominators 15, 5, 16 and 20 = 240

12 12×16 192
\ = = (240 ÷ 15 = 16)
15 15×16 240
9 9×48 432
= = (240 ÷ 5 = 48)
5 5×48 240
7 7×15 105
= = (240 ÷ 16 = 15)
16 16×15 240
11 11×12 132
= = (240 ÷ 20 = 12)
20 20×12 240
9 12 11 7
 432 > 192 > 132 > 105 \ > > >
5 15 20 16
1 5 2 8
Example 15: Compare , , and by making their numerators the same.
1643 9
Solution: LCM of all the numerators 1, 5, 2 and 8 = 40
1 1×40 40
\ = = (40 ÷ 1 = 40)
16 16×40 640

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