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.

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

$$\text{Percentage increase}=\frac{15}{50}\times 100=30\mathrm{\%}$$

Percentage decrease

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

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

$$\text{Percentage increase}=\frac{20}{80}\times 100=25\mathrm{\%}$$

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.

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

$$\text{Percentage profit}=\frac{5000}{20000}\times 100=25\mathrm{\%}$$