Operations with Algebraic Fractions

Add or subtract two algebraic fractions that already share a common monomial denominator, and multiply or divide simple algebraic fractions with single-term numerators and denominators.

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Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • NA6-6
New NZC (2026)
  • NZC26-P4-ALG-ER-P-Y9-01

Resources

Terminology

  • Algebraic fraction
  • Numerator
  • Denominator
  • Common denominator
  • Factorise
  • Cancel a common factor

Task goals

  • Foundation: Add or subtract two algebraic fractions that already share a common monomial denominator, and multiply or divide simple algebraic fractions with single-term numerators and denominators.
  • Proficient: Add or subtract algebraic fractions with different binomial denominators by finding a common denominator, and multiply or divide algebraic fractions that require factorising a binomial before cancelling.
  • Excellence: Add, subtract, multiply or divide algebraic fractions involving quadratic expressions in the numerator or denominator, fully factorising each expression first and simplifying the combined result.

Where this fits

What leads into this objective, and where it goes next.

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Operations with Algebraic Fractions

Operations with Algebraic Fractions

Do

Simplifying and manipulating algebraic expressions involving sums, products, differences, and positive integer powers, by: collecting like terms; factorising using common factors; expanding products, including multiplying a single term by a bracketed term.

Statement▸
Year 9 · Algebra · Equations and relationships
NZC26-P4-ALG-ER-P-Y9-01

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