Recalling Ratios and Percentages

Ratios

It shows the relation between two quantities or to compare two quantities.

Example

If there are 20 men and 40 women in a company then the ratio of the number of men to the number of women is 20: 40.

 \dfrac{20}{40}=\dfrac{1}{2}.

This shows that the number of men is half the number of women in the company.

It is written as 1: 2 and read as “1 is to 2”.

Percentage

In the fraction form if the denominator is 100 then the numerator is the percentage and is represented by a special symbol %, read as a percent.

There are two methods to find the percentage.

1. By Fraction Method

Example

If there are 20 boys out of 50 students in the class then find the percentage of boys.

To make the denominator hundred we need to multiply both the denominator and numerator with 2.

\dfrac{20}{50}\times\dfrac{2}{2}=\dfrac{40}{100}=40\%

So the percentage of boys is 40\%.

2. Unitary Method

In the unitary method, first, we need to find the value of one unit then multiply it with the required number of units.

Example

In the above example, there are 20 boys out of 50 students. Then out of 100 students, the number of boys will be
\dfrac{20}{50}\times100=40\%

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