Conversion of Ratios to Percentage

A ratio compares two topicIdentities or variables and is often expressed as a: b form. For example, if we say the ratio between boys and girls is 5:1. It means that boys are five times more than girls. A percentage is a very specific type of ratio. 

A percentage compares any part of the whole against the whole instead of making the comparison with indivtopicIdual parts with each other. 

For example, in a school, there are 40% girls and the remaining 60% are boys. 

To convert the ratio to percentage form we need to 1st topicIdentify the ratio. And then we have to apply the formula which is known as the ratio to percentage formula.

steps to convert the ratio to percentage:

divtopicIde the first number by the second number. For example, if the ratio is 3: 5 then write it as 3/ 5. 

Multiply it by hundred to convert in percentage  

            (3/ 5) * 100 = 3* 100/5 = 60

now put the percentage symbol % to the answer obtained. 

            =60%. 

Example 1: Convert 6: 5 ratio to percentage. 

 Ratio given = 6:5 

                    = ( 6/5) * 100

                    = 6* 100 / 5 

                    = 120 % 

Example 2: Convert 55% to ratio

55% = 55/100

        ( after reducing 55 by hundred we got )

         = 11/20 

         Therefore the ratio equivalent is 11: 20 

Example 3: Mr. Shah purchased oranges and apples in a ratio of 4:5. Find how many percent of oranges and apples are there in all? 

The ratio of oranges and apples are 4:5 

In order to write them in fraction, the denominator will be 4+5 = 9

Fraction of oranges = 4 / 9 

Fraction of apples= 5/ 9

Percentage of oranges = 4 /9 x 100 = 400/ 9 = 44.44%

Percentage of apples= 5 /9 x 100= 500/ 9 = 55.56 % 

Checking and writing equivalent ratios:

Equivalent ratios are ratios that can be simplified or reduced to some value. For example  4:8  it can further be reduced to 2:4, which can further be reduced to 1:2. 

So in mathematics, the definition of equivalent ratios is “ Two or more ratios that express the same relation or comparison of numbers are known as equivalent ratios.” 

Example4:  Find the equivalent ratio of 11:15. 

The equivalent ratios of 11:15 are 

22:30 ( both the numbers are multiplied by two)  or

33: 45 ( both the numbers are multiplied by three) 

Example 5: Are 2:3 and 12:18 equivalent ratios?

In order to find out whether both the ratios are equal or not

Let us reduce 12:18 

= 6*2/ 6*3 

= 2:3 

Yes, both the ratios are equivalent to each other. 

Steps to find the equivalent ratios: 

First, you have to write the given ratios

Then you have to multiply both numbers in the ratios with the same number. 

Sometimes if the ratio is given and if it is possible to reduce it by the same number then it’s possible to find an equivalent fraction. For example, 14:16 is given we can reduce it to 7:8.