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Equivalent Fractions

In one line: Equivalent fractions are different-looking fractions that show exactly the same amount, like 1/2 and 2/4.

Why it works

A fraction has a numerator (the top number, how many parts you have) and a denominator (the bottom number, how many equal parts the whole is split into). Knowing that fractions can look different but be worth the same helps you compare fractions, add and subtract them, and simplify answers. It is also the foundation for later topics like decimals, percentages and ratios.

Think of it like: Imagine two pizzas of the same size. One is cut into 2 equal slices and you eat 1 slice, so you eat 1/2. The other is cut into 4 equal slices and you eat 2 slices, so you eat 2/4. The slices are smaller, but you ate the same amount of pizza, so 1/2 and 2/4 are equivalent. (Where this breaks: The pizza picture only works if both pizzas are the same size and every slice is equal; half of a small pizza is not the same as half of a giant one. Also, real pizzas can only be cut so many times, but in maths you can keep making equivalent fractions forever, such as 50/100 or 500/1000.)

Worked example

Find the fraction equivalent to 3/4 that has a denominator of 12.

  1. Look at the denominators: we want to change 4 into 12.
  2. Ask what 4 is multiplied by to make 12: 4 × 3 = 12.
  3. Whatever you do to the bottom, you must do to the top, so multiply the numerator by 3 too: 3 × 3 = 9.
  4. Write the new fraction: 9/12.
  5. Check by dividing: 9 ÷ 3 = 3 and 12 ÷ 3 = 4, which takes you back to 3/4.

Answer: 3/4 = 9/12

Common mistakes

  • Adding the same number to the top and bottom (thinking 2/3 equals 3/4) is wrong; you must multiply or divide both numbers by the same number instead.
  • Changing only the denominator (turning 1/2 into 1/6) changes the amount, so always change the numerator by the same factor too.
  • Thinking a fraction with bigger numbers, like 4/8, must be bigger than 1/2 is a mistake; draw or picture both fractions to see they cover the same amount.
  • Dividing by a number that does not go exactly into both the top and the bottom gives messy results, so only divide when both numbers share that factor.

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Which fraction is equivalent to 1/2?

Questions parents ask

What year do kids learn equivalent fractions?

In the UK, children start recognising equivalent fractions with diagrams in Year 3 and work with families of equivalent fractions in Year 4 and Year 5. In Australia it is mainly taught in Years 3 to 5, and in the US it begins in Grade 3 and is extended in Grade 4.

How can I help my child with equivalent fractions at home?

Use real objects: fold paper strips into halves, quarters and eighths, or cut a pizza or cake into different numbers of equal slices and compare. Ask your child to explain why 1/2 and 4/8 cover the same amount before moving on to the multiply-top-and-bottom rule.

Is there an easy rule for finding equivalent fractions?

Yes: multiply or divide the numerator and the denominator by the same number. For example, 2/5 × 2/2 gives 4/10. This works because multiplying by 2/2 is the same as multiplying by 1, so the amount does not change.

What does simplifying a fraction mean?

Simplifying means finding the equivalent fraction with the smallest possible numbers by dividing the top and bottom by the same number. For example, 6/8 simplifies to 3/4 by dividing both by 2. A fraction is in its simplest form when no whole number bigger than 1 divides into both.