Download Ch1-Section 1.7

§ 1.7
Multiplying and
Dividing Real Numbers
Multiplying Real Numbers
The product of two numbers with the same sign is a
positive number.
Example:
Multiply. –75 × (– 3)
–75 × (– 3) = 225
Example:
5  2 
Multiply.  12
 3 
The result will always be positive.

 
5
 5  2   5  2
 12  3  2  2  3  3 
18

 
Martin-Gay, Beginning and Intermediate Algebra, 4ed
2
Multiplying Real Numbers
The product of two numbers with different signs is a
negative number.
Example:
Multiply. – 6(4)
– 6(4) = – 24
Example:
Multiply. 12(– 9)
12(– 9) = – 108
The result will always be negative.
Martin-Gay, Beginning and Intermediate Algebra, 4ed
3
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
Martin-Gay, Beginning and Intermediate Algebra, 4ed
4
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
Martin-Gay, Beginning and Intermediate Algebra, 4ed
5
Quotient of Two Real Numbers
If a and b are real numbers and b is not 0, then
a
1
a b   a
b
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.
Martin-Gay, Beginning and Intermediate Algebra, 4ed
6
Multiplying or Dividing Real Numbers
Example:
36
Find the quotient.
12
36
 36  (12)  3
12
Example:
Find the quotient. 3  1
2 6
3 5 3 6 3 6 33 2 9
   


2 6 2 5 25
25
5
Martin-Gay, Beginning and Intermediate Algebra, 4ed
7
Zero as a Divisor or Dividend
1. The quotient of any nonzero real number and 0 is
undefined. In symbols, if
a
a  0,
0 is undefined.
2. The quotient of 0 and any real number except 0 is 0.
In symbols, if
0
a  0,  0.
a
Example:
Divide. – 6 ÷ 0
There is no answer because division by 0 is undefined.
Martin-Gay, Beginning and Intermediate Algebra, 4ed
8
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
Work inside the parentheses.
= 4 + 81 – 3
Evaluate the exponent.
= 85 – 3
Add.
= 82
Subtract.
Martin-Gay, Beginning and Intermediate Algebra, 4ed
9