Page 30 - ICSE Math 7

Comparison of Fractions

For comparison of fractions, there are two cases:

(a) If the fractions to be compared are like fractions, then the fraction with the greatest numerator is
the largest.

(b) If the fractions to be compared are unlike fractions, then convert them into like fractions and then
compare.

Maths Info
• If the fractions to be compared having same numerators, then the fraction with the smaller denominator is the largest.
7
For example, > 7
9 11
• If the fraction to be compared having same numerators then the fraction with the larger denominator is the smallest.
For example, 6 < 6
13 11

5 21
Example 7: Arrange , and 11 in ascending order.
6 24 18
Solution: We will first convert the given unlike fractions into like fractions.
LCM of the denominators 6, 24 and 18 is 72.

Now, 5 = 5 × 12 = 60 ( 72 ÷ 6 = 12)
6 6 × 12 72

21 = 21 × 3 = 63 ( 72 ÷ 24 = 3)
24 24 × 3 72
11 = 11 × 4 = 44 ( 72 ÷ 18 = 4)
18 18 × 4 72

,
So, the like fractions are 60 63 and 44 .
72 72 72
<
Since 44 < 60 < 63, so 44 60 < 63 .
72 72 72
5
Thus, the given fractions in ascending order are 11 < < 21 .
18 6 24
Inserting a Fraction between Two Fractions
c
a
a
c
Consider two fractions and such that < . We can insert a fraction between them such that
d
b
b
d
c
a < a + c < .
b b + d d
4
3
Example 8: Insert two fractions between and .
5 7
Solution: We will first convert the given unlike fractions to like fractions.
LCM of 5 and 7 is 35.
3 3 × 7 21
Now, = = ( 35 ÷ 5 = 7)
5 5 × 7 35
4
= 4 × 5 = 20 ( 35 ÷ 7 = 5)
7 7 × 5 35

16