Ratio and Proportion summary

Key learning points

• Simplify ratios by dividing by the HCF.
• Share $N$ in ratio $a:b$: parts $a+b$, one part $N/(a+b)$.
• Direct proportion: $y=kx$; inverse: $y=k/x$.

Worked example 1 — Sharing

Share $£60$ in the ratio $2:3$.

Working

5 equal parts of $£12$.

Worked example 2 — Simplify ratio

Simplify $18:24$.

Working

Divide by HCF 6.

Worked example 3 — Unitary method

4 pens cost $£6$. Cost of 7?

Working

Find one, then multiply.

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.