Equivalent fractions

Part ofMathsFractionsYear 4

What are equivalent fractions?

A boy and girl are beside a white board. On the left side of the white board the fraction 'one fifth' is next to an equals sign with the fraction two tenths on the right.

When two fractions have the same value, but have different denominators and numerators, they are called equivalent fractions.

Equivalent means they are equal. They have the same value.

When two different fractions are equivalent, the numerator and the denominator can be:

  • multiplied by the same number

  • divided by a common factor to simplify them

A boy and girl are beside a white board. On the left side of the white board the fraction 'one fifth' is next to an equals sign with the fraction two tenths on the right.
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Activity: What are equivalent fractions?

Complete this interactive activity to understand equivalent fractions. Then put your knowledge to the test.

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Finding equivalent fractions

This fraction chart shows \(\frac {1} {2}\). If you look down the chart you can see which fractions are equal to \(\frac {1} {2}\).

A tables with five rows. The first row has been split in two each representing 1 half. The second row has been split into four, each representing 1 quarter. The third row has been split into six, each representing 1 sixth. The fourth row has been split into eight, each representing 1 eighth. The fifth row is split into ten, each representing 1 tenth. Through shading of parts the table shows that one half is equivalent to two quarters, it is also equivalent to three sixths, four eighths and five tenths.

You can see that:

\(\frac {1} {2}\) = \(\frac {2} {4}\)

\(\frac {1} {2}\) = \(\frac {3} {6}\)

\(\frac {1} {2}\) = \(\frac {4} {8}\)

\(\frac {1} {2}\) = \(\frac {5} {10}\)

All these fractions take up the same space on the chart and represent the same value.

They are all equivalent fractions.

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Using multiplication to find equivalent fractions

You can use multiplication to find equivalent fractions, by multiplying both the denominator and the numerator by a number.

Here, \(\frac {1} {2}\) has been multiplied by 2. The equivalent fraction is \(\frac {2} {4}\).

The written fraction one half is next to an equals sign. To the right of it is the fraction two quarters. Connecting the two fractions at the numerators and denominators is an arrow with × 2 next to them.

You can multiply by any number to find an equivalent fraction.

Remember to multiply both the denominator and the numerator by the same number.

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Using division to find equivalent fractions

You can also find an equivalent fraction by dividing both the numerator and the denominator by a number.

Here, the fraction \(\frac {4} {8}\) has been divided by 2. The equivalent fraction is \(\frac {2} {4}\).

The fraction four eighths is written next to an equal sign. To the right of the sign is two quarters. Connecting the two fractions at their numerators and denominators are arrows with ÷ 2 next to them.

You can divide by any number that evenly divides both the numerator and the denominator to find an equivalent fraction.

Just make sure to divide both parts of the fraction by the same number.

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Example 1

There are four fractions written with numerators and denominators. One sixth, two twelfths, three eighteenths and four twenty fourths.

Complete this sentence to describe the proportional relationship between this set of equivalent fractions:

The value of the denominator is always ______ times the value the numerator.

Remember, the number of times the numerator has been multiplied to make the denominator in each equivalent fraction is always the same.

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Example 2

A number line from 0 to 1. Below the number line the numbers increase in increments of 'one twelfth'. Above the number line each fourth point on the number line is a quarter.

How many pairs of equivalent fractions are on this number line?

What are the equivalent fractions?

To find equivalent fractions on the number line, look for fractions that share a position with another fraction on the line.

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Example 3

There are three tables. The first table on the left has six equal parts with two being highlighted. The middle table has fifteen equal parts with five parts highlighted. The third table has three equal parts with one part highlighted.

Which 3 equivalent fractions are shown by these area models?

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