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§ Fractions

Adding Fractions

CCSS.4.NFCCSS.5.NF3 min read

Adding fractions challenges Year 3-6 pupils across England, from simple same-denominator problems to complex mixed numbers with different denominators. Mastery requires understanding least common multiples and systematic conversion methods that build confidence through the primary years.

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§ 01

Why it matters

Adding fractions appears in 47% of Year 6 SATs questions and forms the foundation for GCSE algebra. Pupils use fraction addition when calculating cooking measurements (adding 14 cup flour to 38 cup), sharing pizza slices at birthday parties, or determining total distances in PE lessons. Construction apprentices add fractional measurements when cutting materials, whilst nurses calculate medication dosages by combining 12 tablet with 34 tablet prescriptions. Financial literacy depends on adding fractional portions of pocket money or calculating discount combinations. The UK National Curriculum progression from Year 3 same-denominators through Year 6 different denominators ensures pupils develop robust number sense before secondary mathematics.

§ 02

How to solve adding fractions

Adding fractions — how to

  • If denominators differ, find the least common multiple (LCM).
  • Convert each fraction to have the LCM as denominator.
  • Add the numerators. Simplify if possible.

Example: 13 + 14: LCM=12 → 412 + 312 = 712.

§ 03

Worked examples

Beginner§ 01

On Monday you ran 13 km. On Tuesday you ran 13 km. How far did you run in total?

Answer: 23

  1. Same denominator -- add numerators → 1/3 + 1/3 = 2/3 — Total distance is the sum of both days. When denominators match, just add the top numbers.
  2. Simplify → 2/3 — Reduce the fraction if you can.
  3. Verify → 2/3 ✓ — Final answer.
Easy§ 02

You eat 45 of a pizza. Your friend eats 35. What fraction did you eat together?

Answer: 1 25

  1. Add the numerators → 4/5 + 3/5 = 7/5 — Eating pizza is adding fractions. Same denominator -- just add the numerators.
  2. Verify → 1 2/5 ✓ — Fraction check.
Medium§ 03

You eat 812 of a pizza. Your friend eats 34. What fraction did you eat together?

Answer: 1 512

  1. Find a common denominator → LCM(12, 4) = 12 — Eating pizza is adding fractions. The least common multiple becomes the shared denominator.
  2. Rewrite both fractions → 8/12 + 9/12 — Scale each fraction up to the common denominator.
  3. Add the numerators → 17/12 — Same denominator -- add the numerators.
  4. Simplify → 1 5/12 — Reduce to lowest terms or mixed number.
  5. Verify → 1 5/12 ✓ — Final answer.
§ 04

Common mistakes

  • Adding denominators alongside numerators, writing 1/3 + 1/2 = 2/5 instead of 5/6
  • Forgetting to find common denominators, calculating 2/3 + 1/4 = 3/7 instead of 11/12
  • Converting incorrectly when scaling fractions, changing 1/2 to 2/8 instead of 4/8 when adding to thirds
  • Missing simplification opportunities, leaving answers as 6/8 rather than reducing to 3/4
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§ 05

Frequently asked questions

Why can't pupils just add the numerators and denominators separately?
Denominators represent the size of equal parts, not quantities to combine. Adding 1/3 + 1/2 means one-third plus one-half, requiring conversion to sixths (2/6 + 3/6 = 5/6). Direct addition creates meaningless results like 2/5.
What's the quickest method for finding common denominators in Year 5?
Start with the larger denominator and check multiples. For 1/4 + 1/6, test if 6 works (no), then 8 (no), then 12 (yes). This avoids complex LCM calculations whilst maintaining accuracy for most primary problems.
How should pupils check their fraction addition answers?
Convert answers to decimals using division: 5/6 = 0.833... Then verify by adding original fractions as decimals: 1/3 (0.333...) + 1/2 (0.5) = 0.833... This builds number sense and confidence.
When do Year 6 pupils need to convert mixed numbers before adding?
Always convert mixed numbers to improper fractions first: 2 1/3 + 1 1/2 becomes 7/3 + 3/2. Find common denominator (6), then add: 14/6 + 9/6 = 23/6 = 3 5/6.
Should pupils simplify fractions during addition or afterwards?
Simplify after adding to avoid confusion. Adding 2/6 + 1/4 means finding twelfths (4/12 + 3/12 = 7/12), then checking if 7/12 reduces further. Early simplification can create calculation errors in multi-step problems.
§ 06

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