Distributive
property of multiplication over addition
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The
distributive property of multiplication over addition explains how
multiplication and addition interact. It simplifies many multiplication
questions. The formal algorithm and many informal algorithms are
based on this property.
The
distributive property of multiplication over addition is illustrated
by the following examples.
Example
1
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
i.e.
(3 x 4) + (3 x 2) = 3
x (4 + 2)
Example
2
4
x 13 is 4 groups of 13
Since
13 = 10 + 3, 4 groups of 13 will be 4 groups of 10 + 4 groups of
3
4
groups of 13
4
groups of 10 and 4 groups of 3
We
can use this to calculate 4 x 13 from tables up to ten tens:
4
x 13 = (4 x 10) + (4 x 3) = 40 + 12 =
52
General
statement
For
any three numbers a, b and m,
m
x (a + b) = (m x a ) + (m x b)
This
is called the distributive property of multiplication over addition.
Because
multiplication is commutative (the order doesn't matter), the distributive property also says that:
(a
+ b) x m = (a x m ) + (b x m)
