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§ Fractions

Dividing Fractions

CCSS.6.NS3 min read

Dividing fractions challenges Year 6 pupils more than any other fraction operation, yet it appears frequently in SATs questions. The "keep, flip, multiply" method transforms what seems impossible into straightforward multiplication.

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§ 01

Why it matters

Dividing fractions appears in countless real-world situations that pupils encounter daily. When Oliver splits 34 of a chocolate bar among 6 friends, he's dividing fractions. Baking recipes require this skill constantly—if Amelia needs to halve a recipe calling for 23 cup flour, she divides 23 by 2. Construction workers divide materials: splitting 58 metres of timber into 14-metre pieces requires fraction division. In secondary school, pupils use this foundation for algebraic fractions and rate calculations. GCSE Foundation papers regularly test fraction division in problem-solving contexts, making mastery essential for mathematical progression. The reciprocal method—flipping the second fraction then multiplying—provides a reliable algorithm that works every time, building confidence for more complex fraction work ahead.

§ 02

How to solve dividing fractions

Dividing Fractions

  • Keep the first fraction.
  • Flip the second fraction (reciprocal).
  • Multiply. Simplify.

Example: 23 ÷ 45 → 23 × 54 = 1012 = 56.

§ 03

Worked examples

Beginner§ 01

How many 13-cup servings fit in 14 cup?

Answer: 34

  1. Invert and multiply → 1/4 x 3/1 = 3/4 — Finding how many servings is division. Flip the second fraction, then multiply across.
  2. Simplify → 3/4 — Reduce to lowest terms.
  3. Verify → 3/4 ✓ — Answer.
Easy§ 02

You have 45 of a pizza. You share it equally among friends who each get 15. How many shares?

Answer: 4

  1. Invert and multiply → 4/5 x 5/1 = 20/5 — Sharing equally means dividing. Flip the second fraction, then multiply across.
  2. Simplify → 4 — Reduce to lowest terms.
  3. Verify → 4 ✓ — Answer.
Medium§ 03

You have 69 of a pizza. You share it equally among friends who each get 910. How many shares?

Answer: 2027

  1. Invert and multiply → 6/9 x 10/9 = 60/81 — Sharing equally means dividing. Flip the second fraction, then multiply across.
  2. Simplify → 20/27 — Reduce to lowest terms.
  3. Verify → 20/27 ✓ — Answer.
§ 04

Common mistakes

  • Pupils divide straight across without using reciprocals, calculating 3/4 ÷ 1/2 as 3/8 instead of 3/2.
  • Students flip the wrong fraction, turning 2/3 ÷ 4/5 into 3/2 × 4/5 = 12/10 rather than 2/3 × 5/4 = 10/12.
  • Many forget to simplify final answers, leaving 12/16 instead of reducing to 3/4.
  • Pupils struggle with mixed numbers, attempting to divide 2 1/3 ÷ 1/2 without first converting to improper fractions.
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§ 05

Frequently asked questions

Why do we flip the second fraction?
Division by a fraction equals multiplication by its reciprocal. Dividing by 1/2 means finding how many halves fit into something, which equals multiplying by 2. This mathematical property makes the algorithm work consistently across all fraction division problems.
When should pupils learn dividing fractions?
Year 6 National Curriculum introduces dividing fractions by whole numbers first. Full fraction division typically appears in early KS3. Pupils need solid multiplication of fractions mastery before tackling division, as the reciprocal method relies on confident multiplication skills.
How do I help pupils remember the steps?
Use the rhyme "Keep, flip, multiply" or "Don't ask why, just flip and fly". Visual aids showing pizza slices or chocolate bars help contextualise the process. Regular practice with the same three-step routine builds automatic recall of the algorithm.
Should pupils always convert mixed numbers first?
Yes, always convert mixed numbers to improper fractions before dividing. Attempting division with mixed numbers leads to errors. For example, 2 1/3 becomes 7/3 before proceeding with the reciprocal method. This ensures accuracy every time.
What's the difference between dividing by fractions and whole numbers?
Dividing by whole numbers like 3 means multiplying by 1/3. Dividing by fractions like 2/5 means multiplying by 5/2. The reciprocal method works identically—flip the divisor (whatever you're dividing by) then multiply, regardless of whether it's whole or fractional.
§ 06

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