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ks2 Multiplication Methods

 

The Grid Method of Multiplication

The standard method for multiplying together two numbers with two or more digits is usually called long multiplication. 

However a simpler method, which is easier to understand, and which uses easier calculations, is now taught in schools. It is sometimes referred to as the Grid Method.

The Grid Method is based on the idea of splitting both numbers being multiplied, into their tens and units.   We will illustrate the method by calculating 23 x 42, the 23 becoming 20 + 3 and the 42 becoming 40 + 2.

Imagine a rectangular array of  counters, with dimensions 23 x 42.  The total number of counters laid out will equal the multiplication of the two numbers. 

We split the array into four segments, as shown below:

We then calculate the number of counters in each segment, and add the results together, as follows:

20

x

40

=

800

20

x

2

=

40

3

x

40

=

120

3

x

2

=

6

TOTAL

=

966

We don’t need to draw out each of the counters but can just use  rectangles as shown below:

The Grid Method for Three Digit Numbers

It uses the same principle but splits the numbers into hundreds, tens and units, and the rectangle is split into more parts.

The calculation of 26 x 145 is shown below.

20

x

100

=

2000

20

x

40

=

800

20

x

5

=

100

6

x

100

=

600

6

x

40

=

240

6
x
5
=
30
TOTAL
=
3770

 
The grid method is easier to understand than standard long multiplication, and so is taught first.  When children are confident with with this method and understand fully the concept of units, tens and hundreds etc (number place value), then they can move onto the method that you were probably taught at school, long multiplication.

Long Multiplication

We will illustrate the method using the same calculation as before, 23 x 42. The method uses the principle that 23 x 42 is the same as 23 x (40 + 2) and get the answer by multiplying 2 x 23 and then 40 x 23 and adding the two results as follows:

23

x

42

__

46

( = 2 x 23)

920

(= 40 x 23)

_____

TOTAL

966

step by step

Both methods will give the same answer, and ultimately long division is probably faster, but the grid method is easier to explain and to understand. If the long multiplication method is used without a thorough understanding of the principles behind it, the likelihood is the incorrect positioning of the digits of the second and subsequent rows of multiplication ( eg. Forgetting to put in the zero in the above example so that 40 x 23 is put down as 92 and not 920) and a nonsensical answer.