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Comparing Ratios

We compare two ratios in the same manner as we compare two fractions.
To compare the given ratios, follow the following steps:
1. Express each ratio in its fractional form.
2. Find the LCM of the denominators of the fractions.

3. Convert each fraction to its equivalent fractions with the denominator equal to the LCM.
4. Compare the numerators of the equivalent fractions having the same denominator.
5. Hence, the fraction having a larger numerator will be greater.
6. Write them into the ratio form.

Example 9: Which is greater?
( a) 2 : 5 or 3 : 4 (b) 5 : 3 or 3 : 5
Solution: (a) Write the given ratios in their fractional form.
2 3
2 : 5 = and 3 : 4 =
5 4
LCM of the denominators 5 and 4 = 20
2 3
Write the equivalent fractions of the fractions and , as
5 4
×
24 8 35 15
×
×
54 = 20 and 45 = 20
×
Clearly, 8 < 15
8 15
So, < (Fraction with greater numerator is greater)
20 20

2 3
Therefore, <
5 4
Thus, 2 : 5 < 3 : 4

( b) Write the given ratios in their fractional form.
5 3
5 : 3 = and 3 : 5 = We can also compare ratios
3 5
LCM of the denominators 5 and 3 = 15 by cross multiplication
method. Let us compare
5 5
3
Write the equivalent fractions of the fractions and the fractions and by this
3 3 5
3 5 55 25 3 33 9 method.
×
×
, as = = and = = 5 3
5 3 35 15 5 53 15
×
×
3
5
Q 25 > 9 Q 5 × 5 = 25, 3 × 3 = 9
25 9 25 > 9
\ >
15 25 \ 5 > 3
5 3 3 5
> 5 : 3 > 3 : 5
3 5
Thus, 5 : 3 > 3 : 5

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