Key points
The area method of multiplication is also known as the grid or box method. To use this method successfully you need to be able to:
- understand that the area of a rectangle is the result of a multiplication
- partition (break apart) a number using your understanding of place value
- recall times-tables up to 9 x 9 and multiply by multiples of powers of ten
How to use the area method of multiplication
Set up the grid by labelling the dimensions of a rectangle with the numbers to be multiplied.
To split a number into component parts. Eg, the two-digit number 38 can be partitioned into 30 + 8 or 19 + 19 each side by the The value of a digit that relates to its position or place in a number. Eg, in 1482 the digits represent 1 thousand, 4 hundreds, 8 tens and 2 units. of the One of the symbols of a number system, most commonly the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9 to simplify the calculation.
Add up the areas of all the rectangles inside the grid.
The total area of the rectangle gives the The result of multiplying one number by another, eg the product of 4 and 5 is 20 since 4 × 5 = 20 (answer to the multiplication).
Example: calculate 725 x 4
Image caption, Use the area method to calculate 725 x 4
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Use the area method to multiply a 2-digit number by a 2-digit number
To split a number into component parts. Eg, the two-digit number 38 can be partitioned into 30 + 8 or 19 + 19 each number into tens and units.
Set up a 2 by 2 grid.
For each rectangle on the grid multiply the numbers at the edge of the grid.
Add up the areas of all the rectangles inside the grid.
This gives the answer to the multiplication.
Example: calculate 83 x 37
Image caption, Use the area method to calculate 83 x 37
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How to multiply a multi-digit number by a 2-digit number
To split a number into component parts. Eg, the two-digit number 38 can be partitioned into 30 + 8 or 19 + 19 each number using The value of a digit that relates to its position or place in a number. Eg, in 1482 the digits represent 1 thousand, 4 hundreds, 8 tens and 2 units..
Where there is a zero digit, partitioning is not necessary. Remember this when setting up a grid.
For each rectangle on the grid multiply the numbers at the edge of the grid.
Add up the areas of all the rectangles inside the grid.
This gives the answer to the multiplication.
Multiplication is An operation is commutative if the order does not matter. Multiplication and addition are commutative, eg 4 × 3 = 3 × 4 and 4 + 3 = 3 + 4 so 2064 x 19 = 19 x 2064
Example: calculate 2064 x 19
Image caption, Use the area method to calculate 2064 x 19
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Question: spot the mistake
This example of multiplication using the area method is incorrect.
What mistakes have been made?
2 x 3 is 6 not 9
The total is 2226 not 2229
53 × 42 = 2226
Practise using the area method
Try this quiz to practise multiplication using the area method.
Real-world maths
The area method for multiplication is one way of calculating an answer when you don't have a calculator. It helps to organise the working out.
It is a skill used across many sectors and businesses such as gardening and farming.
- A landscape gardener might use multiplication to work out the total area of turf needed for a new lawn.
- A farmer might use this method to calculate the quantities of feed needed on a farm so that the sheep and cows have enough food through the winter.
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