Adding and subtracting fractions

Part ofMathsFractionsYear 4

How to add and subtract fractions

A boy with a piece of chalk in his hand is writing the calculation 1 quarter plus 2 quarters on a board.

There are two rules to remember when adding or subtracting fractions.

  1. The fractions need to have a common denominator. This means the denominator has to be the same.

  2. You only need to add or subtract the numerators.

A boy with a piece of chalk in his hand is writing the calculation 1 quarter plus 2 quarters on a board.
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Activity: Adding and subtracting fractions

Complete this interactive activity to understand how to add and subtract fractions. Then put your knowledge to the test.

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How to add fractions

When adding fractions, make sure the denominator is the same.

The denominator is the number written below the division line on a fraction. It shows the total number of equal parts the whole is divided into.

Let's look at adding fractions first.

\(\frac {3} {6}\) + \(\frac {2} {6}\) = ?

This circle has been divided into 6 equal parts and \(\frac {3} {6}\) and \(\frac {2} {6}\) shaded.

A circle with 5 sixths coloured in, three sixths are green and two are purple and one sixth is left blank.

To add \(\frac {3} {6}\) and \(\frac {2} {6}\), count the number of one sixths that have been shaded in total. The answer is \(\frac {5} {6}\).

You only add the numerators together. The denominator always stays the same, because that is the number of parts the circle is divided into, and this has not changed.

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How to subtract fractions

When subtracting fractions, the denominators still needs to be the same before you start the calculation.

This time, subtract one numerator from the other.

Let's look at a subtraction calculation:

\(\frac {6} {8}\) - \(\frac {2} {8}\) = ?

This bar model has been divided into 8 equal parts and \(\frac {6} {8}\) has been shaded.

bar model showing 6 eighths

If you take away \(\frac {2} {8}\) from \(\frac {6} {8}\) that are shaded, you can see that there are \(\frac {4} {8}\) left.

bar model showing 4 eights

Looking at the calculation, you can see that you only need to subtract one numerator from the other. The denominator stays the same.

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Example 1

A circle divided into fractions of 1 tenths. Each part is outlined in orange.

An orange has been cut into 10 equal pieces.

James eats two pieces, Lucas eats two pieces and John eats five pieces.

What fraction of the orange has been eaten?

You can use the diagram to help you work out the answer.

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Example 2

A jug of orange with a line split into five parts going down its centre. The orange juice goes up to the fourth part of the line.

Here is some juice in a jug. There is \(\frac {4} {5}\) of it left.

If you drank \(\frac {2} {5}\) of it, how much would be left?

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Example 3

A number line from 0 to 1 increasing in steps of one tenth.

Use the numberline to work out this calculation:

\(\frac {9} {10}\) - \(\frac {7} {10}\) =

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Play our fun maths game Guardians: Defenders of Mathematica. game

Use your times tables and more maths skills to defeat monsters and reclaim the Kingdom of Mathematica

Play our fun maths game Guardians: Defenders of Mathematica
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More on Fractions

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