Integers and Absolute Value

{...-6, -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, 6, 7...}

Definition of Integer:

The set of whole numbers, their opposites and zero.

Define Integer

Examples of Integer:

X

-1 0-2-3-4-5 1 2 3 4 5

Integers on a Number Line

NegativeNumbers

PositiveNumbers

Numbers to the left of zero are less than zero

Numbers to the right of zero are greater than zero

Zero is neitherpositive or negative

Zero

10 2 3 4 5 6 7 8 9 10-1-2-3-4-5-6-7-8-9-10

The numbers -4 and 4 are shown on the number line.

Both numbers are 4 units from 0, but 4 is to the right of 0 and -4 is to the left of zero.

The numbers -4 and 4 are opposites.

Opposites are two numbers which are the same distance from zero.

Opposites

Absolute Value of Numbers

The absolute value is the distance a number is from zero on the number line, regardless of direction.

Distance and absolute value are always non-negative (positive or zero).

10 2 3 4 5 6 7 8 9 10-1-2

-3-4-5-6-7-8-9-10

What is the distance from 0 to 5?

10 2 3 4 5 6 7 8 9 10-1

-2-3-4-5-6-7-8-9-10

What is the distance from 0 to -5?

10 2 3 4 5 6 7 8 9 10

-1-2

-3

-4

-5-6-7

-8

-9

-10

Absolute value is symbolized by two vertical bars

|4|

What is the | 4 | ?

This is read, "the absolute value of 4"

Real life application

The freezing point is the temperature at which a liquid becomes a solid. a. Which substance in the table has the lowest freezing point? b. Is the freezing point of mercury or butter closer to the freezing point of water, 0°C?

• Is the freezing point of airplane fuel or candle wax closer to the freezing point of water? Explain your reasoning.