Ratio and proportion

The idea

A ratio like 3 : 5 compares parts of a whole. It does not mean 3 out of 5 — it means the whole is split into 3 + 5 = 8 equal parts. To share an amount in a ratio: add the parts, divide the total by that number to find one part, then multiply to get each share.

Two quantities are in proportion when they grow at the same rate — double one and the other doubles too. Recipes are the classic example: find the amount for one item first (divide), then scale up (multiply) to any number you need.

Always check your shares add back up to the original total, and that the bigger share matches the bigger number in the ratio.

Worked example

Share 40 counters between two boxes in the ratio 3 : 5. How many counters are in each box?

1. Add the parts: 3 + 5 = 8 parts altogether.
2. Find one part: 40 ÷ 8 = 5 counters.
3. First box: 3 × 5 = 15 counters.
4. Second box: 5 × 5 = 25 counters. Check: 15 + 25 = 40 ✓

Answer: 15 counters and 25 counters

Watch out

• Treating 3 : 5 as '3 out of 5' and taking 3/5 of the total for the first share.
• Forgetting to check the shares add back to the whole amount.
• In recipe problems, scaling one ingredient but not the others.