Learn how to multiply using the area method – KS3 Maths

Key points

There are different ways to complete a calculation using long multiplication.
The method is also known as the grid method.
The area method can be useful when multiplying large numbers together.
Using an or grid model can help to see the relationship between multiplication and division.

For example:
5 x 8 = 40
8 x 5 = 40
40 ÷ 5 = 8
40 ÷ 8 = 5

Visual representations of multiplication

An is a rectangular arrangement to represent multiplication. This can be drawn as a rectangle made up of squares or dots in rows and columns.
The number in each row multiplied by the number in each column equals the total number.
An array can help to illustrate different involving multiplication and division. It can also help to demonstrate that multiplication is .
The means that more complicated multiplication calculations can be broken down into smaller chunks by bigger numbers. Eg, 15 x 3 is the same as 10 x 3 + 5 x 3. Both equal 45. 15 has been partitioned into 10 and 5
Using a visual representation of multiplication can be useful to look at before moving onto the area method for multiplication.

Example: visual representation

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What does this representation show?
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This array model provides a lot of information. Count the squares – there are 15 in total. The array is 5 by 3 which shows that 5 x 3 = 15
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The array can be shown as 5 groups of 3 showing that 5 x 3 = 15. Or it could be shown as 3 groups of 5 showing that 3 x 5 = 15. This demonstrates that multiplication is commutative.
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Representing the array as a grid can be helpful when dealing with large integer values. This means each array square does not have to be drawn. This area model representation highlights 4 multiplication and division facts.
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This grid representation shows that 15 x 3 = 45
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Partitioning numbers is useful when multiplying using the grid method. Larger numbers can be partitioned to make them easier to calculate. Eg, 15 can be partitioned into 10 and 5
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This grid has been highlighted to demonstrate the distributive law. The distributive law can help to break the calculation into more manageable chunks. 15 has been partitioned into 10 + 5. 15 x 3 is the same as 10 x 3 + 5 x 3. Both make 45

How to multiply using the area method

Draw a rectangle.
each number in the calculation.
Multiply the value in each column by the value in each row.
Add up all the totals within the grid.
The total is the answer to the multiplication.

Remember that multiplication and addition are both . The order in which you complete the grid or add up the totals does not matter. The outcome will be the same.

Example: 79 x 23

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Calculate 79 x 23 using the area method.
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Partition the numbers into tens and units. 79 is split into 70 and 9. 23 is split into 20 and 3. Draw a separate row and column for each partitioned number.
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Multiply each column and row with each other to get 4 numbers.
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This rectangle gives the answer to 20 x 70. 20 x 70 = 1400
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This rectangle gives the answer to 20 x 9. 20 x 9 = 180
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This rectangle gives the answer to 3 x 70. 3 x 70 = 210
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This rectangle gives the answer to 3 x 9. 3 x 9 = 27
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Add the 4 numbers in the grid together to get the total. 1400 + 180 + 210 + 27 = 1817
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Multiplication is commutative. This means that the four sections of the grid can be completed in any order. Addition is also commutative so the four values can be added together in any order. The outcome will be the same.

Question

What multiplication sum does the grid represent?

Practise multiplying using the area method

Try this quiz to practise multiplying using the area method. You may want to use a pen and paper to help with your workings out.

Quiz

Real-world maths

Long multiplication is used regularly in daily life. Using the area method breaks the stages into more manageable steps and is less likely to lead to place value errors.

A female Asian woman wearing blue dungarees is a painting a wall white with a roller. — Image caption,
A painter may use the area method to calculate how many tins of paint they need.

It is important that tradespeople have the right number of materials to complete the job they are working on. For example, a painter may use the area method to calculate the total surface area of a house they are decorating.
The same painter might use the area method to calculate the cost of the raw materials needed. Eg, 12 tins of paint are required which cost £14 per tin, so they would need to calculate 12 x 14