Sheet № 114 · Foundation + Higher · AQA · Edexcel · OCR
Sharing in a Ratio –
Sharing in a ratio is one of the most frequently tested skills in GCSE Maths. Whether you are splitting money between friends, dividing ingredients for a recipe, or working out how much paint to mix, the method is always the same. This guide covers every variation you will meet in the exam — sharing with a total given, sharing with a diff
§Key definitions
Question:
Share £360 between Amy and Ben in the ratio 4 : 5.
Answer:
Amy gets £160 and Ben gets £200.
Q1 (Foundation):
Share £540 between two charities in the ratio 2 : 7.
Q2 (Foundation):
Divide 72 marbles among three children in the ratio 1 : 3 : 5.
Q3 (Higher):
Sam and Jake share money in the ratio 4 : 9. Jake receives £35 more than Sam. How much does each person receive?
§Formulas to memorise
Value of one part = Total amount ÷ Sum of ratio parts
Each share = Number of parts × Value of one part
Add the parts — of the ratio together to find the total number of parts.
Divide — the given amount by the total parts to find the value of one part.
Multiply — each number in the ratio by the value of one part to find each share.
Check — your answers add up to the original total.
Worked example
Share £360 between Amy and Ben in the ratio 4 : 5.
Working: Total parts = 4 + 5 = 9. Value of one part = £360 ÷ 9 = £40. Amy receives 4 × £40 = £160. Ben receives 5 × £40 = £200. Check: £160 + £200 = £360 ✓
⚠ Common mistakes
- ✗Dividing by a ratio part instead of the total. If the ratio is 3 : 5 and you are given the total, divide by 8 (the sum), not by 3 or by 5.
- ✗Mixing up the order. "Alice to Bob in the ratio 2 : 7" means Alice gets 2 parts. Read the names and the numbers in the same order.
- ✗Forgetting to check. Always verify your shares add up to the total. This catches arithmetic slips before they cost you marks.
✦ Exam tips
- →Write "Total parts = ..." as your first line of working. Examiners look for this and award a method mark.
- →When given a difference, find the difference in parts first, then calculate one part from there.
- →If one share is given directly, divide that share by its number of parts to find the value of one part immediately.
- →Questions sometimes express ratios using fractions (e.g., ½ : ⅓). Multiply both sides by the LCM to clear fractions before sharing.