Algebra Foundations
Properties of Multiplication
Objective:
Investigate the ordering and grouping properties of multiplication and division.
Investigate the identity property of multiplication.
Investigate the inverse property of multiplication.
Investigate the property of zero for multiplication.
Review:
Properties of addition
Commutative property:
Associative property:
Identity property:
Inverse property:
Order doesn’t matter
Grouping symbols can be moved.
Adding zero does not change the value.
Operation that “undoes” another operation
Question:
How does changing the order of numbers or the grouping of numbers affect the value of
an expression?
Commutative Property
True or False?
Multiplication
5·6=6·5
Division
10 ÷ 5 = 5 ÷ 10
1
1
· 16 = 16 ·
2
2
3÷
1 1
= ÷3
3 3
4.1 · 3.5 = 3.5 · 4.1
5.8 ÷ 2 = 2 ÷ 5.8
Does the order matter when you are multiplying two numbers?
Does the order matter when you are dividing two numbers?
Associative Property
True or False?
5 ( 6 · 2) = (5 · 6) · 2
50 ÷ (10 ÷ 2) = (50 ÷ 10) ÷ 2
(3.1 · 6.8) · 4 = 3.1 ( 6.8 · 4)
(10.4 ÷ 5.2) ÷ 4.5 = 10.4 ÷ (5.2 ÷ 4.5)
(
3 4
7
3
4 7
· )·
= ·( · )
4 7
9
4
7 9
7
3
3
7 3
3
÷(
÷ )=( ÷ )÷
10 10 4
10 10
4
Do the grouping symbols affect the answer to a multiplication problem?
Do the grouping symbols affect the answer to a division problem?
Identity Property
True or False?
5·3=5
5·1=5
5 · -1 = 5
5·0=5
What number is multiplied in the Multiplicative Identity Property?
Inverse Property
True or False?
3 3
·
=1
4 4
3 3
·- =1
4 4
3 4
·
=1
4 3
How do you find the multiplicative inverse of a number?
Property of Zero
True or False?
5·0=0
-5 · 0 = 0
15 · 0 = 0
306 · 0 = 0
What affect does multiplying by zero have on a number?
Name: _____________________________________ Hour: _____ Date: __________
Identify the property illustrated.
6 7
1.
- (- ) = 1
7 6
2.
1.4 (-3.7) = -3.7(1.4)
3.
0·4=0
4.
-4 · -
5.
15
15
·1=
16
16
6.
1
- · (-5) = 1
5
7.
-
8.
5 · (12 · 10) = (5 · 12) · 10
9.
3 · (5 · 6) = 3 · (6 · 5)
10.
2·
11.
17.1 · 1 = 17.1
12.
3 5
3 5
( · 6) = ( · ) · 6
5 9
5 9
13.
1 · 5.8 = 5.8
1
=1
4
5
·0=0
4
1
=1
2