1.6 Multiplying and Dividing Real
Numbers; Multiplication and
Division Properties
Mult/Div
• If you mult/div 2 #s w/same sign, your answer is
positive
• If you mult/div 2#s w/different signs, your answer
is negative
Multiplication:
pos ∙ pos = pos
neg ∙ neg = pos
pos ∙ neg = neg
neg∙ pos = neg
Ex: Multiply.
-5(-7)
= 35
(-12)(-2)
= 24
(-3)(-1)(4)
= (3)(4)
= 12
(0.3)(-0.5)
= -0.15
0.3
x0.5
.15.
Properties
• Commutative Property of Multiplication:
changing order when we multiply doesn’t
change the answer.
ab = ba
Ex: 5 ∙ 7 = 7 ∙ 5
• Associative Property of Multiplication:
changing grouping when multiplying doesn’t
change the answer.
a(bc) = (ab)c
Ex: 2 ∙ (5 ∙ 9) = (2 ∙ 5) ∙ 9
More Properties
• Multiplication Property of 1 (Identity Property of
Multiplication): any # (other than 0) mult. by 1 is just
that #
Ex: a ∙ 1 = a
1∙a=a
7∙1=7
• Multiplicative Inverses (Inverse Property of
Multiplication): the product of reciprocals (multiplicative
inverses) is 1
1
3  1
Ex: a  1  1
3
5/4 is the multiplicative inverse of 4/5
a
1
a 1
a
4 5
 1
5 4
• Multiplication Property of -1: mult. by -1 gives
the additive inverse or opposite
Ex: -1(-3) = 3
-1(a) = -a
-1(5) = -5
-(x – y + 2)= -1(x – y + 2)
-x + y – 2
• Double Negative Property: the opposite of -a
is a
Ex: -(-2) = 2
• Multiplication Property of 0: the product of 0
and any real number is 0.
Ex: -1(0) = 0
0(a) = 0
Division Properties
• Division Properties: any # divided by 1 is just that #. Any
number (except 0) divided by itself is 1.
Ex: a  a
1
a
1
a
a≠0
• Division involving 0: 0 divided by a nonzero number is 0.
A number divided by 0 is undefined.
Ex:
0
0
a
a
is undefined
0
Division by Zero
10
 5 b/c
2
0
 0 b/c
2
4
 ? b/c
0
10  5(2)
0  0(2)
4  0(?)
Nothing works!
*Division by Zero is UNDEFINDED
Division
a
1
• Related to multiplication: a  b   a 
b
b
p os
 p os
p os
neg
 p os
neg
p os
 neg
neg
neg
 neg
p os
Ex: Divide.
Ex: Divide.
Rewritten using “mult. inv.” a.k.a. the “reciprocal”
12 ÷ 2
= 12 ∙ ½ = 6
-21 ÷ (-3)
=7
3 7
 
4 8
3 8
 
4 7
2
38

14  7
6

7
0 ÷ (-13)
 32
0
undefined
Group Work?
4
 (30)
5
2.7
 0.9
4 
1

3   2 
 15   10 