How to divide using the area method

Key points

The method treats a division as an area problem. It is sometimes known as the array method or the grid method.
The area method for division is similar to the method for multiplication.
To make the calculation simpler the number to be divided, for example 85 could be partitioned as 40 + 40 + 5
To use the area method for division, you need to be able to recall your times-tables, as each partition should have an area that is a of the .

To solve a division problem using the area method:

Draw a rectangle.
The area of the rectangle is the number being divided.
The length of one side of the rectangle is the number being divided by. This length is the .
The other side-length must be worked out. This length is the answer to the division.
the rectangle into smaller parts which are easier to work with. Each partition should have an area that is a of the divisor. Use numbers from the times tables that you know.

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Use the area division method to calculate 85 ÷ 5
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The area of the rectangle is 85. The rectangle has one side-length of 5. The other side-length is the answer to 85 ÷ 5
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Partition the area of the rectangle into smaller parts. The partitions must add up to 85 and each partition should have an area that is a multiple of 5 (because 5 is the divisor). Choose numbers that you can easily divide by 5. There are several ways this could be done.
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Partition the rectangle into smaller parts to make it easier to work out the calculation. 50 and 35 are both multiples of 5 that you should recognise from the 5 times table. Now that there are smaller numbers to work with, each rectangle will be divided by 5.
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Divide the area of each smaller rectangle by 5. 50 ÷ 5 = 10 and 35 ÷ 5 = 7
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Add up each side-length to get the total length of the original rectangle. 10 + 7 = 17. This is the answer to the division. Write the answer clearly. 85 ÷ 5 = 17

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Use the area division method to calculate 654 ÷ 6. The area of the rectangle is 654. The rectangle has one side-length of 6. The other side-length is the answer to 654 ÷ 6
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Partition the area of the rectangle into smaller parts. Choose numbers that can easily be divided by 6 and add up to 654. 600 can easily be divided by 6, so that is a good first partition. 54 is then left. 54 can be used as a partition because it is a multiple of 6, but can be split further into multiples of 6. 6 × 5 = 30, so in this example 30 is the next partition, leaving 24 as the last partition.
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Work out the missing side-lengths. 600 ÷ 6 = 100. 30 ÷ 6 = 5. 24 ÷ 6 = 4
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Add up each side-length to get the total length of the original rectangle.100 + 5 + 4 = 109. This is the answer to the division. Write the answer clearly. 654 ÷ 6 = 109
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The rectangle can be partitioned in different ways. The outcome of the division is the same.

Which two of these diagrams are correct for the area division of 728 ÷ 4? You may want to use a pen and paper to work out the answer.

Practise what you've learned about using the area method. You may want to use a pen and paper to help with your workings out.

Area division (the grid method) is useful as a visual way of breaking up a calculation.

A barista at a coffee shop may need to use division to work out how many cups of coffee they can make out of a 10kg bag of coffee beans.
A group of four friends going to a concert need to work out how much each ticket cost. The total amount is £264. They will need to divide the amount by the number of people to calculate the cost per ticket.