Order simple fractions

Part ofMathsFractionsYear 3

Ordering fractions

A girl sat at a table writing on a piece of paper. She is surrounded by fractions two ninths, four ninths, five ninths and eight ninths.

Fractions can be ordered, just like whole numbers.

These rules can help you order fractions.

When ordering unit fractions:

  • if the whole is the same, then the smaller the number of equal parts, the bigger each equal part is

This means that, with unit fractions, the greater the denominator, the smaller the fraction.

When ordering fractions with the same denominator:

  • the greater the numerator, the larger the fraction is.
A girl sat at a table writing on a piece of paper. She is surrounded by fractions two ninths, four ninths, five ninths and eight ninths.
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Activity: Ordering fractions

Complete this interactive activity to understand how to order fractions, then put your knowledge to the test.

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Comparing fractions of a whole

A fraction shows you how many equal parts of one whole you have. So in order to compare fractions, the whole needs to be the same.

Look at these two circles.

Two circles. One circle is much larger than the other circle. The larger circle is split into 4 parts with 1 part shaded. The much smaller circle is split into 2 parts with 1 part shaded.

\(\frac {1} {4}\) of the blue circle is larger than \(\frac {1} {2}\) of the green circle.

But this doesn't mean that \(\frac {1} {4}\) is larger than \(\frac {1} {2}\) because the two circles, or wholes, are not the same size.

As one circle is bigger than the other, you cannot compare the two fractions, just the size of the shapes.

When the circles are the same size, you can see that \(\frac {1} {4}\) is smaller than \(\frac {1} {2}\).

Two circles which are the same size. One circle is slit into 4 equal parts with 1 part shaded is labelled 1 fourth. The other circle is split into 2 parts with 1 part shaded is labelled 1 half.
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Ordering unit fractions

In unit fractions, the numerator is always 1.

In this bar model, the whole is the same amount, but each bar has been divided into a different number of parts. This means the denominators are different.

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.

Each bar represents a different unit fraction.

The unit fractions in this model have been ordered. You can see that the higher the denominator is, the smaller the fraction is.

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Ordering fractions with the same denominator

When fractions have the same denominator, you only need to look at the numerator to order the fractions.

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

This is because you are looking at more parts of the whole.

There are 4 row which are each split into 5 equal parts. In the first row, one of five parts are highlighted, to the left the fraction one fifth is written. In the second row, two of five parts are highlighted, to the left the fraction two fifths is written. In the third row, three of five parts are highlighted, to the left the fraction three fifths is written. In the fourth row, four of five parts are highlighted, to the left the fraction four fifths is written.
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Example 1

Four circles, each split into a number of different parts with 1 part shaded and a fraction written underneath. From left to right: the first circle is split into 5 parts with 1 part shaded and is labelled 1 fifth. The next is split into 2 parts with 1 part shaded and is labelled 1 half. The next 4 parts with 1 part shaded labelled 1 quarter. The next 6 parts with 1 part shaded and labelled 1 sixth.

Order these unit fractions from largest to smallest.

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Example 2

There are three measuring jugs from left to right labelled A, B and C. Jug A is half full of liquid, jug B is a quarter full of liquid and jug C is about one third full of liquid.

Use unit fractions to describe how full these containers are.

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Example 3

There are four rows that have each been split into eight equal parts. Some of those parts are shaded. The first row has 3 of 8 parts shaded with the fraction three eighths to the right of it. The second row has 5 of 8 parts shaded with the fraction five eighths to the side of it. The third row has 1 of 8 parts shaded with the fraction one eighth to the side of it. The fourth row has 7 of 8 parts shaded with the fraction seven eighths to the side of it.

Order these fractions with the same denominators from smallest to largest.

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