# Comparison Of Ratios

For comparison of ratios, we follow the following steps :

Step 1 : Obtain the given rations.
Step 2: Express each ratio in the simplest fraction form.
Step 3: Find the LCM of the denominators of the fractions obtained in
Step 2.
Step 4 : Make the denominators same for each fractions.
Step 5 : Compare the numerators. The fraction having larger numerator will be larger than the other.

Examples :
1) Compare the ratios 5 : 12 and 3 : 8.
Solution :
5 : 12 = 5/12 and 3 : 8 = 3/8
LCM of 12 and 8 is 24
(5 x 2)/(12 x 2) = 10/24 and (3 x 3)/(8 x 3) = 9/24
Clearly, 10 > 9
∴ 10/24 > 9/24
⇒ 5/12 > 3/8.
⇒ 5 : 12 > 3 : 8.
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2) Compare the ratios 7 : 6 and 24 : 9.
Solution :
7 : 6 = 7/6 and 24 : 9 = 24/9
LCM of 6 and 9 is 18.
(7 x 3)/(6 x 3) = 21/18 and (24 x 2)/(9 x 2) = 48/18
Clearly, 21 < 48
&there4 21/18 < 48/18
⇒ 7/6 < 24/9
⇒ 7 : 6 < 24 : 9.
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3) Compare the ratios 4 : 7 and 5 : 8
Solution :
4 : 7 = 4/7 and 5 : 8 = 5/8
LCM of 7 and 8 is 56.
(4 x 8)/(7 x 8) = 32/56 and (5 x 7)/(8 x 7) = 35/56
Clearly, 32 < 35
&there4 32/56 < 35/56
⇒ 4/7< 5/8
⇒ 4 : 7 < 5 : 8

Ratio - Proportion

Ratio and Proportion
Ratio in the simplest form
Comparison of ratios
Equivalent ratios
Proportion
Continued Proportion

From comparing ratios to number system