Intermediate Algebra (11th edition)

1.3 Exponents, Roots, and Order

of Operations

The product of an even number of negative factors is
positive. The product of an odd number of negative
factors is negative.

Order of Operations
1.Work separately above and below any fraction
bar.

2.If parentheses, brackets, or absolute value bars are
present, start with the innermost set and work
outward.

3.Evaluate all exponents, roots, and absolute values.

4.Multiply or divide in order from left to right.

5.Add or subtract in order from left to right.

is positive:

is negative:

= 21

= 18 + 3

= 1 - 623 - 34 + 3

= 1 - 6234 - 74 + 3

= 1 - 62322 - 74 + 3

1 - 62322 - 13 + 424 + 3

12 + 3

5 # 2

=

15

10

=

3

2

1 - 523 1 - 523 = 1 - 521 - 521 - 52 =- 125

1 - 522 1 - 522 = 1 - 521 - 52 = 25

CONCEPTS EXAMPLES

1.4 Properties of Real Numbers

For real numbers a,b, and c, the following are true.

Distributive Property

and

Identity Properties

and

Inverse Properties

and

and

Commutative Properties

and

Associative Properties

and

Multiplication Property of 0

a# 0  0 and 0 #a 0

a 1 bc 2  1 ab 2 c a 1 bc 2  1 ab 2 c

abba abba

1

a

a#^1 #a 1
a

 1

a 1 a 2  0 aa 0

a 0  0 aa a# 1  1 #aa

a 1 bc 2 abac 1 bc 2 abaca

4 # 0 = 0 01 - 32 = 0

7 + 15 + 32 = 17 + 52 + 3 - 416 # 32 = 1 - 4 # 623

9 + 1 - 32 = - 3 + 9 61 - 42 = 1 - 426

-

1

3

5 # 1 - 32 = 1

1

5

= 1

5 + 1 - 52 = 0 - 12 + 12 = 0

• 32 + 0 =- 32 17.5# 1 =17.5

1214 + 22 = 12 # 4 + 12 # 2

CHAPTER 1 Summary 41