Equivalent Fractions

Identify, generate, and justify equivalent fractions by multiplying or dividing the numerator and denominator by the same scale factor, including completing missing-value equivalents and using stacked bar/circle diagrams to see the same shaded length or area cut into finer or coarser parts.

Worksheet Builder All resources ☕ Shout us a flat white Download All

Te reo Māori terms

click each term to open in Te Aka

Learning objective overview

Master Teaching Guide coverage for this objective.

Current NZC (2007)
  • NA3-5
  • NA4-4
New NZC (2026)
  • NZC26-P4-NUM-NSO-P-Y9-03
  • NZC26-P4-NUM-NSO-K-Y9-04
  • NZC26-P3-NUM-NSO-K-Y7-16
  • NZC26-P3-NUM-NSO-P-Y7-20

Resources

Terminology

  • Equivalent
  • Fraction
  • Numerator
  • Denominator
  • Simplify
  • Scale factor

Task goals

  • Identify whether two fractions are equivalent using a stacked bar or circle diagram (same shaded length or area, different cut).
  • Generate an equivalent fraction by multiplying (or dividing) the numerator and denominator by the same scale factor.
  • Find a missing numerator or denominator to complete an equivalent-fraction statement, including chained multi-blank problems.
  • Justify whether two given fractions are equivalent by naming a common scale factor, not by guessing.
  • Identify and correct the "scaled only one number" misconception in someone else's reasoning.
  • Reason flexibly with equivalent-fraction families, including a "which does not belong" task.

Where this fits

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

You are here

Equivalent Fractions

Equivalent Fractions

Do

Finding equivalent fractions, simplifying fractions, and converting between improper fractions and mixed numbers

Statement▸
Year 9 · Number · Number structures and operations
NZC26-P4-NUM-NSO-P-Y9-03
Know

Multiplying a fraction by an equivalent form of 1, such as 3/3, results in an equivalent fraction.

Statement▸
Year 9 · Number · Number structures and operations
NZC26-P4-NUM-NSO-K-Y9-04

Explore the whole sequence →