Algebra Readiness

Chapter 4 Section 1

4.1: Compare and Order Integers

The numbers . . . . -4, -3, -2, -1, 0, 1, 2, 3, 4, . . . are called integers. Negative integers are less than 0. They lie to the left of 0 on a number line. Positive integers are greater than 0. They lie to the right of 0 on a number line.

Two numbers that are the same distance from 0 on a number line but are on opposite sides of 0 are called opposites. For example, -3 and 3 are opposites. The opposite of a number a is written –a.

The absolute value of a number a, written |a|, is the distance between a and 0 on a number line.

Graphing and Ordering IntegersExample 1

Below are the temperatures at which various substances freeze. To find which substance has the lowest freezing temperature, graph each integer ona number line.

SubstanceFreezing

temperature ( )°F

Water

Antifreeze and water

Sea water

Gasoline

32

32

28

36

–

–

Graphing and Ordering IntegersExample 1

SOLUTION

Order the numbers from least to greatest: 36, 32, 28, 32.– –

ANSWER

Gasoline has the lowest freezing temperature at .36°F–

Order the integers from least to greatest.1. 8, 5,– 2, 0, 6– ANSWER 8,– 2, 0, 5, 6–

2. 12, 15, 3, 9,– 6– ANSWER 12,– 6, 3, 9, 15–

3. 4, 4, 0, 16,– 7– ANSWER 7,– 4, 0, 4, 16–

Practice for Example 1

Finding the Opposite of a NumberExample 2

a. If a 6, then a 6.= – = – The opposite of a positive is a negative.

a = 5,– a– = –( )5– = 5.b. If then The opposite of a negative is a positive.

Finding the Absolute Value of a NumberExample 3

a = 3,a. If then a 3 3.= = The absolute value of a positive is a positive.

b. If thena = 8,– a 8.= =8– The absolute value of a negative is a positive.

Write the opposite and the absolute value of the number.

4. 14 ANSWER 14; 14–

ANSWER 8; 8–

6. 10– ANSWER 10; 10

5. 8

7. 2– ANSWER 2; 2

Practice for Examples 2 and 3

Using Absolute ValueExample 4

An elevation above sea level is a positive number, while an elevation below sea level is a negative number. The table gives the elevation of a whale at different times. Based on the table, what is the greatest depth the whale reached? How many seconds after diving did the whale return to the surface?

Time (secondsafter diving)

Elevation(m)

01234

04840

–

––

Using Absolute ValueExample 4

SOLUTION

Depth indicates a distance from the surface of water,so depth is a positive number. The table shows the whale’s lowest elevation to be 8 meters. Because 8 8, the greatest depth the whale reached was8 meters.

–– =

Because the table shows an elevation of 0 meters after 4 seconds, the whale returned to the surface 4 seconds after diving.

8. A fish is swimming 7 feet below the surface of a pond. At what elevation relative to the surface is the

fish? At what depth is the fish?

ANSWER 7 ft, 7 ft–

Practice for Example 4