Properties of
Multiplication & Addition

Numbers can be added or multiplied in
any order and still yield the same result
a+b=b+a
4n = n x 4
3(6) = 6(3)
Commutative Property

When adding or multiplying, numbers can
be grouped in any way and still yield the
same result
(4 + 3) + 2 = (2 + 3) + 4



(7 x n) x 3 = (7 x 3) x n
(a + b) + c = (c + a) + b
Associative Property

When a number is multiplied by a group
of numbers nested in parentheses, you
can use the product of that number and
each part inside the parentheses and still
yield the same result. This also removes
the parentheses from the problem.


7(4 + 1) = (7 x 4) + (7 x 1)
5(n – 12) = (5 x n) – (5 x 12)
Distributive Property
When you add zero
to any number,
the result is
always that
number.
When you multiply
any number by 1,
the result is that
number.
5+0=5
14 x 1 = 14
0+n=n
1xb=b
Identity Property of Addition &
Multiplication

5 x (4 x 4) = (5 x 4) x 4
Which property is it?

6( n – 13) = (6 x n) – (6 x 13)
Which property is it?

7x1=7
Which property is it?

ab = ba
Which property is it?

38 + 0 = 38
Which property is it?

5(n + 5)
Simplify using the distributive
property

-8(n + 12)
Simplify using the distributive
property

-6(n – 4)
Simplify using the distributive
property
Challenge!
 -b(b + 12)

Simplify using the distributive
property

Play rags to riches!
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