Learning pack · Foundation · CIE Core

Fractions

What's in this pack: printable worksheet PDF, matching answers PDF (Foundation · CIE Core depth). Fraction arithmetic — equivalence, addition with common denominators, multiplication and division — appears across algebra and probability.

Resources at the top · full summary · videos with short notes below.

🎒 Resources in this pack

Jump straight to the printable files, or scroll to the summary and videos.

Scaffolded Learning Sheet — attempt the worksheet, then use the Answers for a full written solution.

📝 Open Learning Sheet ✅ Open answers 🎬 More topic videos (6)📖 Full summary

Files: foundation-19 Fractions handout.pdf · foundation-19 Fractions handout answers.pdf

Full topic summary

Fraction arithmetic — equivalence, addition with common denominators, multiplication and division — appears across algebra and probability.

Key learning points

Equivalent fractions: multiply/divide numerator and denominator by the same number.
Add/subtract: common denominator; multiply: numerators and denominators; divide: multiply by the reciprocal.
Mixed numbers: convert to improper fractions before calculating.

Worked example 1 — Equivalent fractions

Write three fractions equivalent to $\tfrac{2}{5}$ .

Working

\tfrac{4}{10},\ \tfrac{6}{15},\ \tfrac{8}{20}

Multiply numerator and denominator by the same integer.

Worked example 2 — Simplifying

Simplify $\tfrac{16}{20}$ .

Working

\tfrac{16\div4}{20\div4}=\tfrac{4}{5}

Divide by the HCF of 16 and 20, which is 4.

Worked example 3 — Addition

Calculate $\tfrac{2}{3}+\tfrac{1}{4}$ .

Working

\tfrac{8}{12}+\tfrac{3}{12}=\tfrac{11}{12}

LCD of 3 and 4 is 12.

Worked example 4 — Subtraction

Calculate $\tfrac{5}{6}-\tfrac{1}{4}$ .

Working

\tfrac{10}{12}-\tfrac{3}{12}=\tfrac{7}{12}

LCD of 6 and 4 is 12.

Worked example 5 — Multiplication

Calculate $\tfrac{2}{5}\times\tfrac{3}{4}$ .

Working

\tfrac{2\times3}{5\times4}=\tfrac{6}{20}=\tfrac{3}{10}

Multiply numerators and denominators, then simplify.

Worked example 6 — Division

Calculate $\tfrac{3}{4}\div\tfrac{2}{5}$ .

Working

\tfrac{3}{4}\times\tfrac{5}{2}=\tfrac{15}{8}=1\tfrac{7}{8}

Multiply by the reciprocal of the divisor.

Worked example 7 — Mixed numbers

Calculate $1\tfrac{1}{2}+2\tfrac{1}{3}$ .

Working

\tfrac{3}{2}+\tfrac{7}{3}=\tfrac{9}{6}+\tfrac{14}{6}=\tfrac{23}{6}=3\tfrac{5}{6}

Convert to improper fractions before adding.

Worked example 8 — Fraction of an amount

Find $\tfrac{3}{5}$ of $£40$ .

Working

\tfrac{3}{5}\times40=24

Divide by the denominator, then multiply by the numerator.

🎬 Topic videos

A Fascinating Thing about Fractions - Numberphile
Numberphile · 8 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Funny Fractions and Ford Circles - Numberphile
Numberphile · 14 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Infinite Fractions - Numberphile
Numberphile · 7 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Infinite fractions and the most irrational number
Mathologer · 13 min
Enrichment / curiosity clip for Lower Secondary (Numberphile-style). Use for hooks, clubs, or stretch — not core exam content.
Math Antics - Comparing Fractions
Math Antics · 7 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Math Antics - Fractions Are Parts
Math Antics · 5 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.

More Lower Secondary packs

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