Percentage change

It is useful for mathematicians to be able to calculate how much something has changed, and we can do this with percentage change.

Percentage change formula

\[\text{Percentage change} = \frac{\text{new value} - \text{original value}}{\text{original value}} \times 100\]

\[\text{Percentage change} = \frac{\text{change}}{\text{original}} \times 100\]

When we have an original value and a new value we can use the formula above to find the percentage change.

Percentage increase

If a product's price increases from 50 to 65 we can use the formula to find the percentage increase.

\[\text{Percentage increase} = \frac{\text{change}}{\text{original}} \times 100\]

\[\text{Percentage increase} = \frac{15}{50} \times 100 = 30\%\]

Percentage decrease

If the price decreases from 80 to 60 we can use the formula to find the percentage decrease.

\[\text{Percentage decrease} = \frac{\text{change}}{\text{original}} \times 100\]

\[\text{Percentage increase} = \frac{20}{80} \times 100 = 25\%\]

Percentage profit

Businesses track percentage change when looking at aspects of their business.

If a business bought goods for £20000 and sold them for £25000 we can use the formula to find the percentage profit.

\[\text{Percentage profit} = \frac{\text{change}}{\text{original}} \times 100\]

\[\text{Percentage profit} = \frac{5000}{20000} \times 100 = 25\%\]