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Maths · Fractions

Equivalent fractions

Recognise fractions that name the same amount, like 1/2 = 2/4.

Not startedCAMBRIDGE · 4CBSE · IVIB · PYP-4

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What are equivalent fractions?

Equivalent fractions are fractions that show the same amount. They look different but mean the same thing. Imagine a chocolate bar split into 2 pieces. You eat 1 piece, so you ate 1/2. Now imagine the same bar split into 4 pieces. You eat 2 pieces, so you ate 2/4. Both times you ate the same amount! So 1/2 and 2/4 are equivalent.

Making equivalent fractions

To make an equivalent fraction, multiply the top and bottom by the same number. The top number is the numerator. The bottom number is the denominator. If you start with 1/3 and multiply both by 2, you get 2/6. These fractions are equivalent because they show the same amount.

Spotting equivalent fractions

You can check if fractions are equivalent by simplifying them. Divide the top and bottom by the same number. Keep going until you cannot divide any more. If two fractions simplify to the same fraction, they are equivalent. For example, 4/8 and 2/4 both simplify to 1/2.

Why do equivalent fractions work?

When you multiply or divide both the numerator and denominator by the same number, you are really multiplying or dividing by 1. That does not change the value. Think of 2/2 or 3/3. They both equal 1. So 1/2 times 2/2 gives 2/4, which is still the same amount.

Worked examples

  1. 1. Are 2/5 and 4/10 equivalent?

    1. Look at 2/5. Multiply the top and bottom by 2.
    2. 2 times 2 equals 4. 5 times 2 equals 10.
    3. So 2/5 equals 4/10. Yes, they are equivalent!

  2. 2. Simplify 6/9 to find an equivalent fraction.

    1. Find a number that divides into both 6 and 9. Try 3.
    2. 6 divided by 3 equals 2. 9 divided by 3 equals 3.
    3. So 6/9 equals 2/3. These fractions are equivalent.

  3. 3. Which fraction is equivalent to 3/4?

    1. Multiply both 3 and 4 by the same number. Let's try 3.
    2. 3 times 3 equals 9. 4 times 3 equals 12.
    3. So 3/4 equals 9/12. They are equivalent fractions.

Try it yourself

Find a fraction equivalent to 1/2 by multiplying both numbers by 4.

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