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§ Fractions

Fraction / Decimal / Percent

CCSS.6.RPCCSS.7.NS3 min read

Converting between fractions, decimals, and percentages forms the backbone of Year 6 numeracy and GCSE foundation skills. Students who master these conversions—like recognising that 3/4 equals 0.75 and 75%—unlock confidence in ratio problems, probability calculations, and real-world percentage applications from discounts to statistics.

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§ 01

Why it matters

These conversion skills appear everywhere in British education and daily life. Year 6 pupils encounter them in SATs questions about comparing fractions like 710 versus 0.68. GCSE students use percentage conversions to analyse data in science coursework or calculate compound interest in maths. Real-world applications include understanding that a 25% discount equals £12.50 off a £50 jacket, or recognising that 0.6 of pupils choosing football over cricket represents 35 of the class. Shop workers convert between decimal prices (£4.75) and percentage markups (15% profit margin). Sports statistics rely on these conversions—a cricket batting average of 0.45 means getting runs 45% of the time, or 9 times out of 20 attempts.

§ 02

How to solve fraction / decimal / percent

Fraction / Decimal / Percent

  • Fraction → decimal: divide numerator by denominator.
  • Decimal → percent: multiply by 100.
  • Percent → fraction: write over 100, simplify.

Example: 38 → 0.375 → 37.5%.

§ 03

Worked examples

Beginner§ 01

Convert 34 to a decimal.

Answer: 0.75

  1. Divide numerator by denominator → 3 ÷ 4 = 0.75 — Fraction means division.
  2. Verify → 3/4 = 0.75 ✓ — Check.
Easy§ 02

Convert 25 to a decimal.

Answer: 0.4

  1. Divide numerator by denominator → 2 ÷ 5 = 0.4 — Fraction means division.
  2. Verify → 2/5 = 0.4 ✓ — Check.
Medium§ 03

Convert 0.1818 to a fraction.

Answer: 211

  1. Write as fraction over power of 10 → 0.1818 → 2/11 — Then simplify.
  2. Verify → 2/11 ✓ — Check.
§ 04

Common mistakes

  • Students multiply instead of divide when converting fractions to decimals, writing 3/4 as 12 instead of 0.75 by calculating 3 × 4 rather than 3 ÷ 4.
  • When converting decimals to percentages, pupils forget to multiply by 100, incorrectly stating that 0.35 equals 35% instead of moving the decimal point two places right.
  • Converting percentages to fractions, students write 25% as 25/10 instead of 25/100, then fail to simplify to 1/4 using highest common factors.
  • Pupils confuse recurring decimals with exact ones, writing 1/3 as 0.33 instead of 0.333... or using the dot notation 0.3̄.
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§ 05

Frequently asked questions

Which fractions should Year 6 pupils memorise as decimal equivalents?
The UK National Curriculum emphasises benchmark fractions: 1/2 = 0.5, 1/4 = 0.25, 3/4 = 0.75, 1/5 = 0.2, 2/5 = 0.4, 1/10 = 0.1, and 1/3 ≈ 0.333. These appear frequently in SATs and provide mental maths shortcuts for comparison tasks.
How do I help students recognise when decimals terminate or recur?
Fractions with denominators containing only factors of 2 and 5 create terminating decimals (like 3/8 = 0.375). Other denominators produce recurring decimals (like 2/7 = 0.285714285714...). Teaching this pattern helps students predict decimal types before calculating.
What's the quickest method for converting between all three forms?
Start with the fraction as your base. Convert to decimal by dividing numerator by denominator, then multiply by 100 for percentage. This single pathway (fraction → decimal → percentage) reduces errors compared to memorising six different conversion rules.
How should students handle remainders when dividing for decimal conversion?
Continue dividing using long division until the decimal terminates or a pattern repeats. For 5/6, students get 0.8333... where the 3 repeats infinitely. Mark recurring digits with dots above them or use brackets: 0.8(3).
Which denominators create the trickiest conversion problems for GCSE students?
Sevenths, ninths, and elevenths produce complex recurring patterns. 4/7 = 0.571428571428... requires students to recognise the 6-digit repeat cycle. These appear in GCSE higher-tier questions testing pattern recognition alongside computational skills.
§ 06

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