GCSE — mathsFoundation2 min read

Ratio and Proportion

Share amounts in a given ratio and solve proportion problems for GCSE Maths.

Tutor AI Team2026-02-25T01:46:49.374Z

Ratios compare quantities. Proportion problems involve scaling quantities up or down. Both are fundamental GCSE skills used in everyday contexts like recipes, maps, and sharing money.

Core Concepts

Simplifying Ratios

Divide all parts by the HCF: $12:18 = 2:3$ .

Sharing in a Ratio

Share £120 in the ratio 3:5.

Total parts: $3 + 5 = 8$ . One part: $120 \div 8 = £15$ .

Shares: $3 \times 15 = £45$ and $5 \times 15 = £75$ .

Given One Share, Find the Rest

The ratio is 2:3:5. The smallest share is £30.

$1$ part = $£15$ . Total = $10 \times 15 = £150$ .

Combining Ratios

$A:B = 2:3$ and $B:C = 4:5$ .

Make B the same: $A:B = 8:12$ and $B:C = 12:15$ .

$A:B:C = 8:12:15$ .

Worked Example: Example 1

Problem

Share 500g in the ratio 3:7. Parts = 10. One part = 50g. Shares: 150g and 350g.

Solution

Worked Example: Example 2

Problem

Orange juice and water mixed 1:4. 200ml juice used. Water needed: $200 \times 4 = 800$ ml.

Solution

Practice Problems

1. Share £240 in ratio 1:2:3.
1. Ratio of boys to girls is 3:5. There are 24 boys. How many girls?

Want to check your answers and get step-by-step solutions?

Key Takeaways

✓
Simplify ratios by dividing by HCF.
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Sharing: find total parts, then value per part.
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Given one share: work backwards to find the rest.
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Combine ratios by making the common term equal.

Tags:

#gcse#maths#ratio#proportion

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