Comparing fractions

Part ofMathsFractionsYear 4

Comparing unit fractions

Unit fractions can be compared by looking at the denominator, or the number of equal pieces the whole has been divided into.

The denominator is the number below the division bar.

Unit fractions always have the number 1 above the division bar.

This is an example of a unit fraction:

The fraction one quarter. Written as 1 with a horizontal bar under it and then under that bar the number 4. The word 'numerator' is next to the 1. The word 'denominator' is next to the 4.

Fractions with a numerator higher than 1 can also be compared.

Comparing fractions with the same denominator is much easier than comparing fractions with different denominators.

When you compare fractions with the same denominator look at the numerators (the numbers above the division bars). The larger the numerator is, the larger the fraction is.

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Activity: How to compare fractions

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

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How to compare unit fractions

Bar models can help you to compare unit fractions.

Look at this bar model.

Each bar represents a whole. They are both the same size, but they have been divided into a different number of equal parts.

Two tables with one row each. The first table has been split in two each representing 1 half. The second table has been split into 10, each representing 1 tenth. 1 half and 1 tenth have been highlighted.

You can see by looking at the bars that \(\frac {1} {10}\) is smaller than \(\frac {1} {2}\).

The greater the number of equal parts, the smaller each equal part is.

As this bar model shows, comparing unit fractions by looking at the denominator involves thinking in the opposite way to when you compare whole numbers.

As the denominator gets higher, the fraction becomes smaller.

A table which with ten rows. The first row represents 1 or a whole. The second is split into two each represent 1 half. The third row is split into 3 parts each representing 1 third. The fourth row is split into 4 parts each representing 1 fourth. The fifth row is split into 5 parts each representing 1 fifth. The sixth row is split into 6 parts each representing 1 sixth. The seventh row is split into 7 parts each representing 1 seventh. The eighth row is split into 8 parts each representing 1 eighth. The ninth row is split into 9 parts each representing 1 ninth. The tenth row is split into 10 parts each representing 1 tenth.
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How to compare fractions with the same denominator

When you compare fractions with the same denominator, you only have to focus on the numerator.

Here is a circle. It has been split into four equal parts. Each part is one quarter.

Look at the fractions when each part is shaded. Which fraction is the biggest?

There are three circles, each divided into 4 parts. The first circle on the left has one of four parts shaded with 1 quarter written underneath. The second circle in the middle has two of four parts shaded with 2 quarters written underneath. The circle on the right has three of four parts shaded with 3 quarters written underneath.

The fraction is larger if the numerator is a bigger number.

So, \(\frac {3} {4}\) is the biggest.

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Example 1

A table which with ten rows. The first row represents 1 or a whole. The second is split into two each represent 1 half. The third row is split into 3 parts each representing 1 third. The fourth row is split into 4 parts each representing 1 fourth. The fifth row is split into 5 parts each representing 1 fifth. The sixth row is split into 6 parts each representing 1 sixth. The seventh row is split into 7 parts each representing 1 seventh. The eighth row is split into 8 parts each representing 1 eighth. The ninth row is split into 9 parts each representing 1 ninth. The tenth row is split into 10 parts each representing 1 tenth.

Which fractions are larger than \(\frac {1} {5}\)?

You can use the bar models to help you.

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Example 2

There are two children and each child has some pizza slices. Dotted lines show where, for each child, six slices of each pizza should be to make a whole circular pizza. One child has only two slices remaining, below the fraction two sixths is written. The other child has 3 slices remaining, the fraction 3 sixths is written below.

James and Maya cut a pizza into 6 slices. James ate \(\frac {2} {6}\) of the pizza and Maya ate \(\frac {3} {6}\).

Who ate more pizza?

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