Reverse percentages

Topic summary

Reverse percentages are used to find the original amount before a percentage increase or decrease. This is helpful when you know the final amount after the change and need to determine the original value.

Finding the Original Value After an Increase

If a price after a 20% increase is 120, think about how we would have found out this answer if we knew the original price.

\[\text{original } \times \text{ multiplier } = \text{ final}\]

\[\text{original } \times 1.2 = \text{ final}\]

But we have the final amount, not the original.

\[\text{original } \times 1.2 = 120\]

To find the original price we need to do the inverse (or opposite) of \(\times 1.2\).

\[120 \div 1.2 = \text{original }\]

\[120 \div 1.2 = 100\]

We can use this after a percentage increase or decrease. We can even apply this to repeated percentage changes.