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Converting recurring decimals to fractions

Number · Grade 7–9

Strand: Number Substrand: Fractions, decimals and percentages Sparx code: U689 Sparx levels: 3, 4, 5 Tier: Higher Only

Key steps (method)

  • Simplify fractions where possible before doing any calculations.
  • To add/subtract: use a common denominator, then combine numerators.
  • To multiply: multiply numerators and denominators (cancel common factors first).
  • To divide: multiply by the reciprocal.
  • Convert improper fractions to mixed numbers only at the end if asked.

Common mistakes

  • Adding denominators when adding fractions (you don’t).
  • Forgetting to use the reciprocal when dividing.
  • Not simplifying/cancelling, leading to messy arithmetic mistakes.

Quick notes

  • If you get stuck, try a simpler version of the problem first or plug in easy numbers to test your method.
  • For multi-step questions, label each step and keep intermediate results.
  • For exam questions, always aim to make your work “mark-scheme readable”.

Self-assessment

  • Can I define it? Write a one-sentence definition of Converting recurring decimals to fractions (or the key term in the question).
  • Can I do it? Do 3 questions: one easy, one standard, one harder. Don’t look at notes until you’ve tried.
  • Can I explain it? In 2–3 sentences, explain why the method works (or what would go wrong with a common mistake).
  • Can I check it? State one quick check (estimate, units, sign, reasonableness).

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Notes