An increase of r% retains the original 100% and adds r%, giving multiplier 1+ r100. A decrease gives 1- r100. Successive changes act on the latest amount, so multiply their multipliers. Example A $250 item is discounted by 20%, then its discounted price increases by 10%. Final price=250(0.80)(1.10)=$220. The combined multiplier is 0.88, so the overall decrease is 12%. Adding the signed rates would incorrectly give a 10% decrease. Equal percentage increases and decreases do not cancel: 1.2 x 0.8=0.96, because they use different bases.

An increase of $r\%$ retains the original $100\%$ and adds $r\%$, giving multiplier $1+\dfrac r{100}$. A decrease gives $1-\dfrac r{100}$. Successive changes act on the latest amount, so multiply their multipliers.

A $\$250$ item is discounted by $20\%$, then its discounted price increases by $10\%$.

$\text{Final price}=250(0.80)(1.10)=\$220$.

The combined multiplier is $0.88$, so the overall decrease is $12\%$. Adding the signed rates would incorrectly give a $10\%$ decrease.

Equal percentage increases and decreases do not cancel: $1.2\times0.8=0.96$, because they use different bases.

Percentage multipliers and successive changes

Percentage multipliers and successive changes