In this post we will learn to compare two or more ratios.
Note that ratios can be expressed in the form of fractions and such fractions are commonly found in daily life.
There are different types of ratios used in business, accounting, scientific calculations, speed calculations etc..
Understanding which ratio is greater among the given data is a useful skill to have for our personal and professional success.
Given below are some of the method to compare two or more ratios.
Methods to compare ratios
Here we will discuss two methods to compare the given ratio:
(a) Decimal Method
(b) LCM method
Let us discuss each method step by step.
Decimal Method of Ratio Comparison
Follow the below steps:
(a) Convert the ratios in the form of fraction.
(b) Divide the numerator by denominator to find the quotient in the form of decimals.
Note : You can also take help of calculator for division of numbers.
Let us look at some of the examples:
Example 01
Compare ratio 2 : 3 and 3 : 4
Solution
(a) Convert the ratio into fraction
⟹ 2/3 and 3/4
(b) Convert the fractions into decimals
2/3 = 0.67
3/4 = 0.75
(c) Compare the decimals
we know that 0.67 < 0.75;
This means that 2/3 < 3/4.
Hence, 2 : 3 < 3 : 4
Example 02
Compare 6 : 5 and 5 : 3
Solution
(a) Convert the ratios into fractions
6 : 5 ⟹ 6 / 5
5 : 3 ⟹ 5 / 3
(b) Divide numerator with denominator to convert fraction into decimal
6 / 5 = 1.2
5 / 3 = 1. 67
(c) Compare the decimals
We know that 1. 2 < 1.67.
This means that 6 / 5 < 5 / 3.
Hence, the ratio 6 : 5 is less than 5 : 3.
Example 03
Compare the ratios 15 : 13 and 10 : 12.
Solution
(a) Convert the ratio into fraction
15 : 13 ⟹ 15 / 13
10 : 12 ⟹ 10 / 12
(b) Divide numerator into denominator to convert fraction into decimal.
15 / 13 = 1.15
10 / 12 = 0.83
(c) Compare the decimals
We know that 1.15 > 0.83.
This means that 15 / 13 > 10 / 12.
Hence, the ratio 15 : 13 is greater than 10 : 12.
LCM method of ratio comparison
In this method we will try to convert ratios into fraction of common denominator.
In order to have common denominator, we take the help of LCM concept.
Follow the below steps:
(a) Convert ratio into fractions.
(b) Find LCM of denominator.
(c) Multiply the fractions to make denominator = LCM
(d) Now all fractions have common denominator.
Simply compare the numerator and find the answer.
Example 01
Compare the ratios 4 : 6 and 3 : 8
Solution
Follow the below steps:
(a) Convert the ratio into fraction.
4 : 6 ⟹ 4 / 6
3 : 8 ⟹ 3 / 8
(b) Find the LCM of denominators
LCM ( 6 , 8 ) = 24
(c) Multiply fractions to make denominator 24
Fraction 4/6
Multiply numerator and denominator by 4
\mathtt{\frac{4\ \times \ 4}{6\ \times \ 4} \ \Longrightarrow \frac{16}{24}}
Fraction 3/8
Multiply numerator and denominator by 3
\mathtt{\frac{3\ \times \ 3}{8\ \times \ 3} \ \Longrightarrow \frac{9}{24} \ }
(d) Now both fractions have same denominator.
Compare the numerators and come to conclusion.
We know that 16 > 9.
So 16 / 24 > 9 / 24.
Hence, ratio 4 : 6 > 3 : 8.
Example 02
Compare the below ratios using LCM method
5 : 7 and 9 : 14
Solution
Follow the below steps:
(a) Convert the ratios into fraction.
5 : 7 ⟹ 5 / 7
9 : 14 ⟹ 9 / 14
(b) Find the LCM of the denominators
LCM ( 7 , 14 ) = 14
(c) Multiply the fractions such that denominator becomes 14
Fraction 5/7
Multiply numerator and denominator by 2
\mathtt{\frac{5\ \times \ 2}{7\ \times \ 2} \ \Longrightarrow \frac{10}{14} \ }
Fraction 9/14
Denominator is already 14.
No need to do anything here.
(d) Now we have fractions with same denominator.
Simply compare the numerators and come to conclusion.
We know that 10 > 9.
This means that 10 /14 > 9 /14.
Hence, ratio 5 : 7 is greater than 9 : 14
Example 03
Compare the below ratios using LCM method
11 : 15 and 16 : 20
Solution
(a) Convert the ratio into fractions
11 : 15 ⟹ 11 / 15
16 : 20 ⟹ 16 / 20
(b) Find LCM of the denominators
LCM ( 15, 20 ) = 60
(c) Multiply the fractions such that denominator = 60
Fraction 11/15
Multiply numerator and denominator by 4
\mathtt{\frac{11\ \times \ 4}{15\ \times \ 4} \ \Longrightarrow \frac{44}{60}}
Fraction 16/20
Multiply numerator and denominator by 3
\mathtt{\frac{16\ \times \ 3}{20\ \times \ 3} \ \Longrightarrow \frac{48}{60}}
(d) Now we have fractions with same denominators.
Compare the numerators and find the answer.
We know that 44 < 48.
So the fractions 44/60 < 48/60.
Hence, ratio 11 : 15 < 16 : 20.
Example 04
Compare the below ratios using LCM method
2 : 9 , 4 : 7 and 4 : 3
Solution
(a) Convert all the ratios into fractions.
2 : 9 ⟹ 2 / 9
4 : 7 ⟹ 4 / 7
4 : 3 ⟹ 4 / 3
(b) Find LCM of all the denominators
LCM ( 9, 7, 3) = 63
(c) Multiply fractions to make denominator = 63
Fraction 2/9
Multiply numerator and denominator by 7
\mathtt{\ \frac{2\ \times \ 7}{9\ \times \ 7} \ \Longrightarrow \frac{14}{63} \ }
Fraction 4/7
Multiply numerator and denominator by 9
\mathtt{\ \frac{4\ \times \ 9}{7\ \times \ 9} \ \Longrightarrow \frac{36}{63} \ }
Fraction 4/3
Multiply numerator and denominator by 21
\mathtt{\frac{4\ \times \ 21}{3\ \times \ 21} \ \Longrightarrow \frac{84}{63}}
(d) Now we have fractions with same denominator.
Compare the numerators and come to conclusion.
we know that, 14 < 36 < 84.
So the fractions will be 14/63 < 36/63 < 84 / 63.
Hence, the ratios are arranged as 2 : 9 < 4 : 7 < 4 : 3.