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 fraction**s 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**.