How Do I Calculate Percentages and Ratios?

By S. Mahandru, Head of Maths at Exam.tips

You will have seen percentages such as when you have gone to a shop and there is a sale. Items are reduced by a certain percentage. A percentage is a fraction out of 100. 

How to find a percentage

Suppose you want to find 20% of 80

1. You can write 20% as a fraction or decimal: 20\% = \frac{20}{100} = 0.20.
2. Multiply the fraction or the decimal by 80: 20\%\text{ of }80 = 0.20 \times 80.
3. Perform the calculation: 0.20 \times 80 = 16.

How to find a percentage increase

There is a very useful formula that you can use to find a percentage increase and also decrease.

\text{Increase \%} \;=\; \frac{\text{Change}}{\text{Original}} \times 100

What are ratios?

Ratios allow you to compare quantities. They are used quite a lot in baking and construction. For instance to make cement you need 3 parts water to 7 parts cement mix. 

Simplifying Ratios

Just as you can simplify a fraction you can simplify a ratio. This is done by dividing both ratios by the same number. 

Example

Simplify 8 : 12

Since 4 is the highest common factor, divide by 4

\frac{8}{4} : \frac{12}{4}  = 2 : 3.

Sharing Ratios

Suppose you want to share £60 in the ratio 2 : 3. Add the ratio parts 2 + 3 = 5.
Each ratio part = £60 ÷ 5 = £12.
So, £24 and £36.

You will find that percentages and ratios are vital in finance, recipes, and data analysis.