Because a ratio can be expressed as a fraction, we can compare the two ratios using fractions.
We can follow the steps given below to compare two ratios.
Step 1 :
Write the given two ratios as fractions.
Step 2 :
Find the least common multiple of the denominators of both the fractions (if the denominators are not same).
Step 3 :
Make the denominators of both the fractions same as the value of least common multiple found in step 1 using multiplication.
Step 4 :
After getting same denominator for both the fractions, compare the numerators and decide which fraction is greater.
The fraction which has larger numerator is greater in value.
Example 1 :
Compare 3 : 5 and 4 : 7.
Solution :
Write the given ratios as fractions.
3 : 5 = 3/5
4 : 7 = 4/7
The least common multiple of the denominators 5 and 7 is 35.
Make the denominators of the fractions as 35 using multiplication.
3/5 = (3 ⋅ 7) / (5 ⋅ 7) = 21/35
4/7 = (3 ⋅ 5) / (7 ⋅ 5) = 20/35
Compare the numerators.
21 > 20
Then,
21/35 > 20/35
3 : 5 > 4 : 7
So, 3 : 5 is greater than 4 : 7.
Example 2 :
Compare 2 : 3 and 3 : 4.
Solution :
Write the given ratios as fractions.
2 : 3 = 2/3
3 : 4 = 3/4
The least common multiple of the denominators 3 and 4 is 12.
Make the denominators of the fractions as 12 using multiplication.
2/3 = (2 ⋅ 4) / (3 ⋅ 4) = 8/12
3/4 = (3 ⋅ 3) / (4 ⋅ 3) = 9/12
Compare the numerators.
8 < 9
Then,
8/12 < 9/12
2 : 3 < 3 : 4
So, 2 : 3 is less than 3 : 4.
Example 3 :
Compare 4 : 5 and 5 : 7.
Solution :
Write the given ratios as fractions.
4 : 5 = 4/5
5 : 7 = 5/7
The least common multiple of the denominators 5 and 7 is 35.
Make the denominators of the fractions as 35 using multiplication.
4/5 = (4 ⋅ 7) / (5 ⋅ 7) = 28/35
5/7 = (5 ⋅ 5) / (7 ⋅ 5) = 25/35
Compare the numerators.
28 > 25
Then,
28/35 > 25/35
4 : 5 > 5 : 7
So, 4 : 5 is greater than 5 : 7.
Example 4 :
Compare 3 : 4 and 4 : 5.
Solution :
Write the given ratios as fractions.
3 : 4 = 3/4
4 : 5 = 4/5
The least common multiple of the denominators 4 and 5 is 20.
Make the denominators of the fractions as 20 using multiplication.
3/4 = (3 ⋅ 5) / (4 ⋅ 5) = 15/20
4/5 = (4 ⋅ 4) / (5 ⋅ 4) = 16/20
Compare the numerators.
15 < 16
Then,
15/20 < 16/20
3 : 4 < 4 : 5
So, 3 : 4 is greater than 4 : 5.
Example 5 :
Compare 5 : 12 and 7 : 18.
Solution :
Write the given ratios as fractions.
5 : 12 = 5/12
7 : 18 = 7/18
The least common multiple of the denominators 12 and 18 is 36.
Make the denominators of the fractions as 36 using multiplication.
5/12 = (5 ⋅ 3) / (12 ⋅ 3) = 15/36
7/18 = (7 ⋅ 2) / (18 ⋅ 2) = 14/36
Compare the numerators.
15 < 14
Then,
15/36 < 14/36
5 : 12 < 7 : 18
So, 5 : 12 is less than 7 : 18.
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