Percentages summary

Key learning points

• Percentage of an amount: $\frac{p}{100}\times\text{amount}$.
• Increase by $p\%$: multiply by $1+\frac{p}{100}$; decrease by $1-\frac{p}{100}$.
• Reverse percentage: divide by the multiplier that created the new amount.

Worked example 1 — Percentage of an amount

Find $15\%$ of $£80$.

Working

Use a decimal multiplier.

Worked example 2 — Percentage increase

Increase $£50$ by $12\%$.

Working

Multiplier $1+\frac{p}{100}$.

Worked example 3 — Percentage decrease

Decrease $200$ by $25\%$.

Working

Multiplier $1-\frac{p}{100}$.

Worked example 4 — Reverse percentage

After a $20\%$ increase a price is $£72$. Find the original.

Working

Divide by the increase multiplier.

Scaffolded Learning Sheet and answers (PDFs)

This page is a short, searchable overview for revision and search engines. Use the Scaffolded Learning Sheet first, then the Answers PDF for a full written solution. The printable PDFs remain the main classroom resource.