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1.7
Multiplying and
Dividing Real
Numbers
Multiplying Real Numbers
Multiplying Real Numbers
1. The product of two numbers with the same
sign is a positive number.
2. The product of two numbers with different
signs is a negative number.
Examples
Multiply.
a.
4(–2) = –8
b.
‒7(‒5) = 35
c. 9(‒6.2) = ‒55.8
d.
3 1
3 1
3
  

4 7
47
28
Zero as a Factor
If b is a real number, then b · 0 = 0. Also 0 · b = 0.
Example:
Multiply. – 6 · 0
–6·0=0
Example:
Multiply. 0 · 125
0 · 125 = 0
Evaluating Exponents
Example:
Evaluate ( 3)3.
( 3)3 = ( 3)( 3)( 3) =  27
Odd exponent: Negative result
Example:
Evaluate ( 2)4.
( 2)4 = ( 2)( 2) ( 2) ( 2) = 16
Even exponent: Positive result
Example
Evaluate.
a.
(–2)4 = (–2)(–2)(–2)(–2) = 16
b.
‒72 = ‒(7 ·7) = ‒49
Finding Reciprocals
Reciprocal or Multiplicative Inverse
Two numbers whose product is 1 are called
reciprocals or multiplicative inverse of each
other.
Quotients Involving Zero
The number 0 does not have a reciprocal.
Example
Find the reciprocal.
a.
55 The reciprocal is
3
b. 
7
1
1
since 55   1.
55
55
7
3 7
The reciprocal is  since     1.
3
7 3
Quotient of Two Real Numbers
If a and b are real numbers and b is not 0,
then
a
1
a b 
b
 a
b
The product or quotient of two numbers with the
same sign is a positive number.
The product or quotient of two numbers with
different signs is a negative number.
Example
Divide.
a. 20  5
4
b. 36  12
3
56
c.
 70
0.8
Examples
36
a. Find the quotient.
12
36
 36  (12)  3
12
3
1
b. Find the quotient. 
2 6
3 5 3 6 3 6 33 2 9
   


2 6 2 5 25
25
5
Division Involving Zero
If a is a nonzero number, then
0
a
 0 and
is undefined.
a
0
5
is undefined
0
0
0
9
If a and b are real numbers, and b  0, then
a
a
a


b
b
b
Evaluating Expressions
Example: Evaluate the expression
4 + (42 – 13)4 – 3.
4 + (42 – 13)4 – 3
= 4 + (16 – 13)4 – 3 Evaluate the exponent
inside the parentheses.
= 4 + (3)4 – 3
= 4 + 81 – 3
Work inside the
parentheses.
Evaluate the exponent.
= 85 – 3
Add.
= 82
Subtract.
Example
Use order of operations to evaluate each
expression.
a. 7(9)  2(6)  63  12  75
86
14
14
8  3(2)
8  (6)

 


b.
96 3
3
 9  2(3)  9  (6)