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§ Fractions

Fraction Word Problems

CCSS.4.NFCCSS.5.NF3 min read

When Charlotte splits 16 sweets equally among 4 friends, she's solving a fraction word problem without realising it. These problems bridge the gap between abstract fraction calculations and real-world mathematical thinking that Year 7 students encounter daily.

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§ 01

Why it matters

Fraction word problems prepare students for GCSE maths by connecting numerical operations to practical scenarios. Whether calculating discounts during shopping (14 off £20), sharing pizza slices at a party, or determining ingredients for half a recipe, these skills appear in 73% of GCSE Foundation questions involving fractions. Students who master interpreting 'of' as multiplication and 'remaining' as subtraction perform 34% better on problem-solving assessments. The UK National Curriculum Year 7 emphasises using four operations with fractions in context because real-world applications require students to identify the operation needed, not just perform calculations mechanically.

§ 02

How to solve fraction word problems

Fraction Word Problems

  • Read carefully: identify what fraction of what quantity.
  • 'Of' usually means multiply: 23 of 12 = 23 × 12 = 8.
  • For remaining/left over: subtract the fraction from the whole.
  • Draw a diagram if the problem is hard to visualise.

Example: 34 of 20 students like maths: 34 × 20 = 15 students.

§ 03

Worked examples

Beginner§ 01

Lily has 12 cookies. She gives away 13 of them. How many did she gives?

Answer: 4

  1. Find 1/3 of 12 → 12 ÷ 3 = 4 — To find 1/3 of 12, divide 12 by 3.
  2. Answer → 4 — She gives 4 cookies.
Easy§ 02

A pizza is cut into 4 slices. Arthur eats 2 slices. What fraction did he eat?

Answer: 24 = 12

  1. Write as fraction → 2/4 — Eaten (2) over total (4).
  2. Simplify → 1/2 — Divide both by 2.
Medium§ 03

A rope is 36 m long. Another rope is 23 m long. How long are they together?

Answer: 1 16 m

  1. Find common denominator → LCM(6, 3) = 6 — The common denominator is 6.
  2. Rewrite and add → 3/6 + 4/6 = 7/6 — Convert both to 6ths and add.
  3. Simplify → 1 1/6 m — Simplify and express as a mixed number if needed.
§ 04

Common mistakes

  • Adding denominators when finding fractions of amounts: students calculate 2/3 of 15 as 2/(3+15) = 2/18 instead of (2×15)÷3 = 10
  • Confusing 'fraction eaten' with 'fraction remaining': when 3/8 of cake is eaten, writing 3/8 left instead of 5/8 remaining
  • Mixing up numerator and denominator in word problems: if 7 out of 12 pupils wear glasses, writing 12/7 instead of 7/12
  • Misinterpreting 'of' in compound problems: calculating 1/2 of 3/4 of 20 as (1/2 + 3/4) × 20 = 25 instead of 1/2 × 3/4 × 20 = 7.5
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§ 05

Frequently asked questions

How do I help students identify which operation to use?
Teach key phrases: 'of' means multiply, 'left over' or 'remaining' means subtract from the whole. Create a word bank showing '2/3 of 18 pupils' versus '2/3 eaten, how much left'. Practice with diagrams helps students visualise the operation needed.
Should students always simplify their fraction answers?
Yes, unless the context suggests otherwise. In GCSE marking, 6/8 loses marks when 3/4 is expected. However, if the problem involves 8 pizza slices, keeping the answer as 6/8 might make more sense contextually before simplifying.
What's the best way to teach 'finding a fraction of an amount'?
Start with unit fractions: 1/4 of 12 means 12÷4. Build to general fractions: 3/4 of 12 means 3×(12÷4). Use visual models like bar diagrams. Students should see that 2/5 of 20 = 2×4 = 8, not 2+5+20.
How can students check their fraction word problem answers?
Estimate first: 2/3 of 18 should be around 12. Use inverse operations: if 1/4 of amount equals 5, then 5×4 should give the original amount. Draw pictures for complex problems. The answer should make sense in context.
Why do students struggle with mixed number answers in word problems?
Students often leave improper fractions like 7/4 instead of converting to 1 3/4. Teach them to check if the numerator is larger than denominator. In context, 1 3/4 hours makes more sense than 7/4 hours when describing time spent on homework.
§ 06

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