Ratio Basics & Sharing in a Ratio –

Ratios appear on every GCSE Maths paper at both Foundation and Higher tier. They are used to compare quantities, share amounts fairly, and solve real-world problems involving recipes, maps and money. Despite being one of the most practical topics in maths, many students lose marks through simple errors — particularly when sharing an amount in a given ratio. This guide covers simplifying ratios, sharing in a ratio, and converting between ratios and fractions, with fully worked examples and exam-ready tips.

What Is a Ratio?

A ratio compares the sizes of two or more quantities. It tells you how much of one thing there is compared to another.

Ratios are written using a colon. For example, if there are 3 boys and 5 girls in a group, the ratio of boys to girls is:

Simplifying ratios

Ratios can be simplified just like fractions — divide all parts by their highest common factor (HCF).

Example: 12 : 8 → divide both by 4 → 3 : 2

Unit ratios

A unit ratio has 1 on one side. To find it, divide both parts by the smaller number.

Example: 5 : 8 → divide both by 5 → 1 : 1.6

Ratios and fractions

If the ratio is a : b, then the fraction of the total that is a is:

For example, in the ratio 3 : 5, the fraction that is boys is 3/(3 + 5) = 3/8.

Step-by-Step Method

How to share an amount in a given ratio

1. Add up the parts of the ratio. For 3 : 5, the total number of parts is 3 + 5 = 8.
2. Divide the total amount by the total number of parts to find the value of one part.
3. Multiply each ratio part by the value of one part.
4. Check that your shares add up to the original total.

How to simplify a ratio

1. If both values are whole numbers, find the HCF and divide both by it.
2. If the ratio involves fractions, multiply all parts by the lowest common denominator to clear the fractions first.
3. If the ratio involves decimals, multiply all parts by 10 (or 100) to make them whole numbers, then simplify.

Worked Example 1 — Foundation Level

Question: Share £240 between Ali and Ben in the ratio 3 : 5.

Step 1: Total parts = 3 + 5 = 8.

Step 2: Value of one part = £240 ÷ 8 = £30.

Step 3: Ali gets 3 × £30 = £90. Ben gets 5 × £30 = £150.

Step 4: Check: £90 + £150 = £240 ✓

Worked Example 2 — Higher Level

Question: The ratio of red to blue to green beads in a bag is 2 : 5 : 3. There are 18 more blue beads than green beads. How many beads are there in total?

Step 1: The difference between blue and green parts is 5 − 3 = 2 parts.

Step 2: These 2 parts represent 18 beads: 1 part = 18 ÷ 2 = 9 beads.

Step 3: Total parts = 2 + 5 + 3 = 10.

Step 4: Total beads = 10 × 9 = 90 beads.

Check: Red = 2 × 9 = 18, Blue = 5 × 9 = 45, Green = 3 × 9 = 27. Total = 90 ✓. Blue − Green = 45 − 27 = 18 ✓

Common Mistakes

• Dividing the amount by a ratio number instead of the total parts. If the ratio is 3 : 5, divide the total by 8 (not by 3 or 5).
• Getting the ratio order wrong. The question says "Ali to Ben = 3 : 5", so Ali gets 3 parts and Ben gets 5. Read the order carefully.
• Not simplifying fully. 6 : 9 should be simplified to 2 : 3 (divide by HCF of 3), not left unsimplified.
• Forgetting to check. Always verify that the shares add up to the original total. This catches arithmetic errors.
• Struggling with fractional ratios. To simplify ½ : ⅓, multiply both by 6 (the LCM of 2 and 3) to get 3 : 2.

Exam Tips

1. Always add up the parts first and write this number down. It prevents errors and shows the examiner your method.
2. Use the "one part" method consistently — it works for any number of ratio parts and is easy to follow.
3. On AQA papers, ratio questions often include context (recipes, mixtures, money). Read the question twice to identify which quantity the ratio refers to.
4. If given a difference (e.g., "Tom gets £20 more than Sam"), find the difference in parts first, then calculate the value of one part from there.

Practice Questions

Question 1 (Foundation): Simplify the ratio 45 : 30.

Question 2 (Foundation): Share £600 between three friends in the ratio 1 : 2 : 3.

Question 3 (Higher): The ratio of cats to dogs in a shelter is 4 : 7. There are 24 more dogs than cats. How many animals are there?

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Related Topics

• Ratio Problem Solving in Context
• Direct and Inverse Proportion
• Percentages: Increase and Decrease
• Fractions, Decimals and Percentages

Summary

• A ratio compares two or more quantities using a colon (e.g., 3 : 5).
• Simplify ratios by dividing all parts by the HCF, just like simplifying fractions.
• To share an amount in a ratio: add the parts, find the value of one part, then multiply.
• The ratio a : b means a has a fraction of a/(a + b) of the total.
• To simplify ratios with fractions or decimals, multiply to clear them first.
• Always check that your shares add up to the original amount.
• Read the question carefully to ensure you assign the correct part to the correct person or quantity.