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MathidiaMathematics Academy
Fractions
Lesson 21 of 75
Introduction

Equivalent fractions

Objective. Generate and recognise equivalent fractions.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Equivalent fractions represent the same value even though they are written with different numerators and denominators. You create an equivalent fraction by multiplying or dividing the numerator and denominator by the same whole number, since this scales the fraction without changing its size. For example, multiplying 2/3 by 4 top and bottom gives 8/12, which is equal to 2/3. Equivalent fractions are essential for comparing or combining fractions that currently have different denominators. A quick check is to cross-multiply: if 2×12=3×8, the fractions 2/3 and 8/12 are indeed equal.

Worked example

Find an equivalent fraction to 3/5 with a denominator of 20.

3/5
Fraction bar showing 3 out of 5 parts shaded
  1. 1Find the multiplier: 20÷5=4.
  2. 2Multiply the numerator by the same multiplier: 3×4=12.
  3. 3Write the new fraction: 12/20.
  4. 4Check by cross-multiplying: 3×20=60 and 5×12=60, so they are equal.

Answer: 12/20

Concept mastery

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Practice

Practice happens on its own screen, one question at a time. Answers stay hidden until you submit yours, and you can stop and pick up at the same question later.

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Common mistake. Pupils sometimes multiply only the numerator or only the denominator, turning 1/2 into the wrong fraction 2/2 instead of 2/4. Always apply the same multiplier to both parts.

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