Learning pack · IGCSE handout

Algebraic Fractions

What's in this pack: printable worksheet PDF, matching answers PDF (IGCSE / Secure–Stretch practice). Algebraic fractions simplify by factorising, then cancelling common factors — never cancel terms across a sum until factorised.

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: 45_algebraic_fractions_handout.pdf · 45_algebraic_fractions_handout_answers.pdf

Full topic summary

Algebraic fractions simplify by factorising, then cancelling common factors — never cancel terms across a sum until factorised.

Key learning points

Factorise numerators and denominators fully before cancelling.
Multiply: factor then cancel across the product.
Add/subtract: common denominator (product of factors).

Worked example 1 — Simplify

Simplify $\tfrac{x^2-9}{x+3}$ .

Working

x-3\ (x\ne-3)

Difference of squares.

Worked example 2 — Multiply

Simplify $\tfrac{2}{x}\times\tfrac{x^3}{4}$ .

Working

\tfrac{x^2}{2}

Cancel common factors.

Worked example 3 — Add

Simplify $\tfrac{1}{x}+\tfrac{2}{x+1}$ .

Working

\tfrac{3x+1}{x(x+1)}

Common denominator.

🎬 Topic videos

Equations involving algebraic fractions - Corbettmaths
Corbettmaths · 11 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Simplifying Algebraic Fractions
Corbettmaths · 6 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Multiplying Algebraic Fractions
Corbettmaths · 8 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Equations: Advanced Algebraic Fractions
Corbettmaths · 11 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Algebraic Fractions (Simplifying) - GCSE Higher Maths
1st Class Maths · 11 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.
Simplifying Algebraic Fractions
Maths Genie · 6 min
Lower Secondary classroom-friendly explainer. Scaffold→stretch friendly; use with mixed-ability groups.

More Lower Secondary packs

Browse the hub Learning Packs & Summary, or open the compact Algebraic Fractions summary.