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§ Fractions

Subtracting Fractions

CCSS.4.NFCCSS.5.NF3 min read

Year 6 pupils often struggle when subtracting fractions, particularly when denominators differ. The key breakthrough comes when students master finding common denominators and understand that subtraction means taking away parts of the same-sized whole.

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§ 01

Why it matters

Subtracting fractions appears throughout GCSE maths and real-world scenarios. In cooking, if a recipe calls for 34 cup of flour but you only have 12 cup, you need 34 - 12 = 14 cup more. Craftwork requires precise measurements—cutting 25 metre from 78 metre of ribbon leaves 2740 metre. Time management involves fractional hours: working 56 of an hour but taking a 14 hour break means 56 - 14 = 712 hours of actual work. Construction projects depend on accurate fractional measurements for materials. These skills build confidence for algebraic fractions in Key Stage 4 and prepare students for percentage calculations essential in business studies and science.

§ 02

How to solve subtracting fractions

Subtracting Fractions

  • If denominators differ, find the LCM.
  • Convert to common denominator.
  • Subtract numerators. Simplify.

Example: 34 − 13: LCM=12 → 912 − 412 = 512.

§ 03

Worked examples

Beginner§ 01

A ribbon is 23 m long. You cut off 13 m. How much is left?

Answer: 13

  1. Same denominator -- subtract numerators → 2/3 - 1/3 = 1/3 — Cutting a ribbon means subtracting lengths. Just subtract the tops.
  2. Simplify → 1/3 — Reduce.
Easy§ 02

A bottle was 56 full. You drank 46. How full is it now?

Answer: 16

  1. Same denominator -- subtract → 1/6 — Drinking from a bottle is subtraction. Subtract the numerators.
  2. Simplify → 1/6 — Reduce.
Medium§ 03

A bottle was 39 full. You drank 15. How full is it now?

Answer: 215

  1. Find common denominator → LCM(9,5) = 45 — Drinking from a bottle is subtraction. Find the LCM.
  2. Convert and subtract → 15/45 - 9/45 = 6/45 — Subtract the numerators.
  3. Simplify → 2/15 — Reduce.
§ 04

Common mistakes

  • Students subtract both numerators and denominators, writing 3/4 - 1/2 = 2/2 = 1 instead of finding the common denominator to get 1/4.
  • Pupils find common denominators but forget to convert both fractions, calculating 3/4 - 1/2 as 3/4 - 1/4 = 2/4 instead of 3/4 - 2/4 = 1/4.
  • When subtracting mixed numbers, students subtract whole numbers and fractions separately without borrowing, getting 2 1/3 - 1 2/3 = 1 (-1/3) instead of converting to 1 4/3 - 1 2/3 = 2/3.
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§ 05

Frequently asked questions

Why can't I subtract fractions with different denominators directly?
Different denominators represent different-sized pieces. You can't subtract 1/3 from 1/2 directly because thirds and halves aren't the same size. Convert both to sixths first: 3/6 - 2/6 = 1/6. Think of it like subtracting 3 apples from 2 oranges—you need the same units.
How do I find the least common multiple for denominators?
List multiples of each denominator until you find a match. For 4 and 6: multiples of 4 are 4, 8, 12, 16... and multiples of 6 are 6, 12, 18... The LCM is 12. Alternatively, multiply denominators if they share no common factors.
What's the easiest way to subtract mixed numbers?
Convert mixed numbers to improper fractions first. For 2 1/4 - 1 3/4, convert to 9/4 - 7/4 = 2/4 = 1/2. Alternatively, if the fractional part of the second number is larger, borrow 1 from the whole number.
When should I simplify my answer?
Always check if your answer can be simplified by finding common factors. If your answer is 6/8, divide both numerator and denominator by their greatest common factor (2) to get 3/4. GCSE marking schemes typically require simplified answers.
How do I check my subtraction is correct?
Add your answer to the number you subtracted. If 3/4 - 1/4 = 2/4, then 2/4 + 1/4 should equal 3/4. This reverse operation catches most calculation errors and builds confidence in your working.
§ 06

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