Percentages

Percent means out of one hundred, so $18\%$ is $0.18$. Converting to a decimal first makes nearly every question here mechanical.

To increase by $20\%$, multiply by $1.2$; to decrease by $20\%$, multiply by $0.8$. Using multipliers rather than working out the change and adding it separately avoids most errors and makes repeated changes easy.

That picture shows the most tested idea in the topic. An increase followed by a decrease of the same percentage does not return you to where you started, because the second percentage is taken of a larger number.

Percent change compares the change to the original amount Dividing by the new value instead is the single commonest mistake, and that wrong answer is always offered.

Reverse questions give you the final amount and ask for the original. Divide rather than multiply: if a price after a $25\%$ rise is $\$50$, the original was $\frac{50}{1.25} = \$40$.

A price of $\$80$ rises by $15\%$. What is the new price?
Multiply by the increase multiplier

A value goes from $40$ to $52$. What is the percent increase?
Compare the change with the original Dividing by $52$ instead gives about $23\%$, which will be among the choices.