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Distributive law

The distributive law simplifies many multiplication questions.

The formal algorithms and many of the informal algorithms are based on this property.

The distributive property of multiplication over addition is illustrated by the following examples.

Example 1

3 x 6 is 3 groups of 6

That is the same as 3 groups of 4 and 3 groups of 2.

The diagram shows that 3 groups of 4 yellow stars and 3 groups of 2 blue stars can be considered as 3 groups of 6 stars.

3 groups of 4 + 3 groups of 2 = 3 groups of 6

ie. 3 x 6

= 3 x (4 + 2)

= 3 x 4 + 3 x 2

= 12 + 6 = 18

Example 2

13 x 4 is 4 groups of 13

13 = 10 + 3

4 groups of 13 will be

4 groups of 10 + 4 groups of 3

= 40 + 12

= 52