Ratio and Percentages

Ratio and Percentage:

Ratio:  The ratio of two quantities 'a' and 'b' of the same kind and in the same units is a fraction   which shows that how many times one quantity is of the other and is written as a : b and is read as 'a is to b' where b ≠ 0. 

Terms of the ratio: In the ratio a : b, the quantities a and b are called terms of the ratio. Here, 'a' is called the first term or the antecedent and `b' is called the second term or consequent.  In the ratio 5 : 9, 5 is called the antecedent and 9 is called the consequent.

Properties of ratio:   If the first term and the second term of a ratio are multiplied / divided by the same non-zero number, the ratio does not change.

Ratio in the simplest form:  A ratio a : b is said to be in the simplest form if a and b have no common factor other than 1.

Example:   Express 15 : 10 in the simplest form.

Solution:    

In this we cancelled the common factor 5.  Thus, we have expressed the ratio

and the terms 3 and 2 have common factor only 1.

Percentages: The word percent means per hundred.

Conversion of Ratio into Percent: 

Example: Convert 3:4 into percent

Solution: 

Ratio and Percentage:  To express a ratio as percentage we add both the ratios. Then we divide the ratio with the sum of ratios and multiply it with 100.

Example: Express 2:3 as percentage

Solution: First we find the sum of ratios: 2+3 = 5

The divide the first ratio i.e. 2 with 5 and multiply with 100.

The divide the second ratio i.e. 3 with 5 and multiply with 100

Or The second ratio can also be found as 100% - 40% = 60%

Hence, we can express each part of ratio x:y as percentage