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Using a fraction wall

How can we make a fraction that is equivalent to 陆?

A fraction with the top number labelled as the numerator and the bottom number labelled as the denominator

Fractions have a numerator and a denominator.

In the fraction 陆 the denominator tells us that the whole is split into 2 equal parts.

A fraction with the top number labelled as the numerator and the bottom number labelled as the denominator

If you look on a fraction wall, you can see that 1/2 is the same as 2/4 and the same as 3/6.

A fraction wall showing one whole, halves, quarters, thirds and sixths.
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Using multiplication

You can check if fractions are equivalent by using multiplication.

Look at the following calculations and see if you can spot a pattern.

One half = three sixths, one third = two sixths, two thirds = four sixths

To find the equivalent fraction, we multiply the numerator and denominator by the same number and the new fraction will be equivalent to the first fraction.

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Using multiplication and division

Six tenths equals ?

You can also use division to find equivalent fractions. What about this fraction? Can you work it out?

Six tenths equals ?

We have divided the denominator 10 by 2, to get 5, so we also need to divide the numerator 6 by 2, to get 3.

Each time we multiply or divide the denominator and the numerator by the same number to work out the equivalent fraction.

Sixth tenths equals three fifths
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Using a numberline

We can check this on a numberline. Here you can see that 2/10 equals 1/5 or 1/5 equals 2/10.

Two numberlines. One divided into fifths and one divided into tenths.
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Activity

Quiz

In this quiz you will look at the numerator and denominator to find equivalent fractions.

Think carefully about whether you are using multiplication or division!

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NEW! Play Guardians: Defenders of Mathematica - the winter update
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More on Fractions

Find out more by working through a topic