Sheet № 33 · Foundation + Higher · AQA · Edexcel · OCR
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 amoun
§Key definitions
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 ✓
§Formulas to memorise
boys : girls = 3 : 5
a / (a + b)
Add up the parts — of the ratio. For 3 : 5, the total number of parts is 3 + 5 = 8.
Divide the total amount — by the total number of parts to find the value of one part.
Multiply — each ratio part by the value of one part.
Check — that your shares add up to the original total.
Worked example
Share £240 between Ali and Ben in the ratio 3 : 5.
Step 1: Total parts = 3 + 5 = 8.
⚠ 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
- →Always add up the parts first and write this number down. It prevents errors and shows the examiner your method.
- →Use the "one part" method consistently — it works for any number of ratio parts and is easy to follow.
- →On AQA papers, ratio questions often include context (recipes, mixtures, money). Read the question twice to identify which quantity the ratio refers to.
- →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.
Bonus
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