1. Copyright 2013, 2010, 2007, 2005, Pearson, Education, Inc.

2. Multiplying and Dividing Real Numbers
1.7
Multiplying and Dividing Real Numbers

3. 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.

4. Examples
Multiply.
a. 4(–2) = –8
b. ‒7(‒5) = 35
c. 9(‒6.2) = ‒55.8 d.

5. 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

6. 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

7. Example Evaluate. a. (–2)4 = (–2)(–2)(–2)(–2) = 16
b. ‒72 = ‒(7 ·7) = ‒49

8. 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.

9. Example
Find the reciprocal.
a The reciprocal is b.

10. Quotient of Two Real Numbers
If a and b are real numbers and b is not 0, then
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.

11. Example
Divide. a. b. c.

12. Examples
a. Find the quotient.
b. Find the quotient.

13. Division Involving Zero
If a is a nonzero number, then
If a and b are real numbers, and b  0, then

14. Evaluating Expressions
Example: Evaluate the expression (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.
= – 3
Evaluate the exponent.
= 85 – 3
Add.
Subtract.
= 82

15. Example
Use order of operations to evaluate each expression. a. b.