Equivalent fractions — Mathematics, 7–10 years
Learn why different-looking fractions can name exactly the same amount. Mathematics, 7–10 years.
Different names, same amount
A fraction can be written in more than one way without changing the amount. One half and two fourths look different, but they cover the same part of a sandwich. If every piece is split into the same number of smaller pieces, the numerator and denominator change together.
Why we need matching names
People often need to compare or combine amounts cut into different-sized pieces. Saying one half is the same as two fourths lets us compare them fairly, instead of trusting how many pieces we see. This way of renaming amounts grew from sharing food, measuring land and trading goods.
Changing three fifths
Start with 3/5. To make smaller pieces, split each fifth into 2 equal parts, so the denominator becomes 10. Each of the original 3 pieces also splits into 2, so the numerator becomes 6. Therefore 3/5 = 6/10. Both fractions describe the same shaded amount.
Changing only one number
A common mistake is to change the denominator but leave the numerator alone: 3/5 becomes 3/10. This feels natural because the pieces have become smaller, but it keeps only three pieces instead of splitting all three original pieces. The whole amount must be changed evenly, so both numbers are multiplied by 2.
Where equivalent fractions help
A recipe may ask for 1/2 litre of milk, while your measuring jug shows only quarters. You can pour 2/4 of a litre because 1/2 and 2/4 are equal. Equivalent fractions also help compare prices, distances or scores when each is recorded using different-sized parts.
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