Equivalent Fractions
Equivalent fractions are different fractions that describe the same amount. In Year 4 (ACARA v9), students learn that 1/2, 2/4 and 5/10 all mean the same thing — half. The key idea: if you multiply (or divide) the top and bottom of a fraction by the same number, its value doesn't change, because you're splitting the whole into more (or fewer) equal parts without changing how much you have. Recognising equivalent fractions is the foundation for comparing, adding and simplifying fractions later.
Worked examples
Making an equivalent fraction.
Start with 1/2. Multiply top and bottom by 3: (1×3)/(2×3) = 3/6. So 1/2 = 3/6 — half a pizza is the same whether it's cut into 2 pieces (take 1) or 6 pieces (take 3).
Answer: 1/2 = 3/6
Spotting equivalence with a picture.
Two identical chocolate bars: one split into 4 with 2 shaded, one split into 8 with 4 shaded. Both show the same amount shaded — so 2/4 = 4/8.
Answer: 2/4 = 4/8
Simplifying (dividing down).
6/8 can be made simpler. Divide top and bottom by 2: (6÷2)/(8÷2) = 3/4. So 6/8 = 3/4 — the same amount, written with smaller numbers.
Answer: 6/8 = 3/4
Checking with a number line.
Mark 1/2 on a line from 0 to 1. Now split the same line into quarters — 2/4 lands on the exact same spot. Same position = equivalent.
Answer: Same position = equivalent
Tips
- •The rule: same operation, top and bottom. Whatever you do to the numerator, do to the denominator. Multiply both by 2, or both by 3 — never just one.
- •Multiplying makes more, smaller pieces; the amount stays the same. 1/2 = 4/8 doesn't mean you have more — you've just cut the same half into more slices.
- •Common mistake to watch for: children sometimes add instead of multiply (thinking 1/2 = 2/3 because they added 1 to top and bottom). Adding changes the value; only multiplying/dividing keeps it equal.
- •Use real objects first. Fold a strip of paper in half, then in half again — the same crease line shows 1/2 and 2/4 at once. Seeing it beats being told it.