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Percentage change

Percentages are used to tell how a quantity will increase or decrease.

  • Percentage change from an old number $$\Tblue{O}$$ to a new one $$\Tgreen{N}$$ is $$ \Tred{p} = \frac{\Tgreen{N}- \Tblue{O}}{\Tblue{O}} = \frac{\Tgreen{N}}{\Tblue{O}} - 1 $$

    The price of a shirt went from $$\Tblue{\$11}$$ to $$\Tgreen{\$12}$$. It increased by $$ \frac{\Tgreen{12}- \Tblue{11}}{\Tblue{11}} = \frac{1}{\Tblue{11}} =\Tred{0.09} = \Tred{9\%}. $$

  • To know a value after the change $$p$$, multiply by $$1+p$$ $$ \Tgreen{N} = \Tblue{O} \times (1+\Tred{p})$$

    A population of $$\Tblue{35}$$ million increased by $$\Tred{2\%}$$. It is now $$ \Tblue{35}\cdot (1+\Tred{2\%}) = \Tblue{35} \times 1\Tred{.02} = \Tgreen{35.7} $$

  • To find the value before the change, divide by $$1+p$$. $$ \Tblue{O} =\Tgreen{N} \div (1+\Tred{p})$$

    After a $$\Tred{20\%}$$ discount, the price of a toy is $$\Tgreen{\$ 8}$$. Before, it was $$ \frac{\Tgreen{8}}{1\Tred{-20\%}}=\frac{\Tgreen{8}}{1\Tred{-0.2}} = \frac{\Tgreen{8}}{0.8} = \Tblue{\$ 10} $$

Discounts in sales are often described using percentages. The new price is sometimes not given, so you need to know how to work it out.
Discounts in sales are often described using percentages. The new price is sometimes not given, so you need to know how to work it out.