Intermediate Algebra (11th edition)

The graph shows egg production in mil-

lions of eggs in selected states for 2005

and 2006. Use this graph to work Exer-

cises 113 –116.

113.In 2006, which states had produc-

tion greater than 6000 million eggs?

114.In which of the states was 2006 egg

production less than 2005 egg

production?

115.If xrepresents 2006 egg production

for Texas (TX) and y represents

2006 egg production for Ohio (OH),

which is true, or?

116.If xrepresents 2005 egg production

for Iowa (IA) and yrepresents 2005 egg production for Pennsylvania (PA), write two

inequalities that compare the production in these two states.

x 6 y x 7 y

14 CHAPTER 1 Review of the Real Number System

OBJECTIVES OBJECTIVE 1 Add real numbers.Recall that the answer to an addition prob-

lem is called the sum.The rules for adding real numbers follow.

Operations on Real Numbers

1.2

1 Add real numbers.

2 Subtract real

numbers.

3 Find the distance

between two points

on a number line.

4 Multiply real

numbers.

5 Find reciprocals and

divide real numbers.

Adding Real Numbers

Same sign To add two numbers with the samesign, add their absolute values.

The sum has the same sign as the given numbers.

Different signs To add two numbers with differentsigns, find the absolute

values of the numbers, and subtract the lesser absolute value from the greater.

The sum has the same sign as the number with the greater absolute value.

Millions of Eggs

U.S. Egg Production

State

IA

OH

PA

CA

TX

FL

Source: U.S. Department of Agriculture.

0 3000 6000 9000 12,000 15,000

12,978

13,811

2005

2006

7506

7507

6608

6687

5082

4962

4760

5039

2985

2940

Adding Two Negative Real Numbers

Find each sum.

(a)

First find the absolute values: and.

Because and have the samesign, add their absolute values.

Add the absolute values.

= - 20

= - 1202

- 12 + 1 - 82 = - 112 + 82

- 12 - 8

|- 12 |= 12 |- 8 |= 8

- 12 + 1 - 82

EXAMPLE 1

Both numbers are

negative, so the sum

will be negative.

(b) Add the absolute values.

= - 16 + 32 , or - 9

- 6 + 1 - 32 = - 1 |- 6 |+ |- 3 | 2

107. 108. 109.

110. 5 x | 3 ...x 666 111. 5 x | 06 x... 36 112. 5 x |- 1 ...x 666

5 x | 2 ...x... 76 5 x |- 3 ...x...- 26 5 x |- 46 x... 36