Integers andAbsolute Value

IntegersIntegers are the whole numbers

(0, 1, 2, 3, …)

and their opposites

Integers are modeled on a number line:

-3 -2 -1 0 1 23

• As you move to the right on a number line, the integers increase in value

• As you move to the left on a number line, the integers decrease in value

Negative Integers Positive Integers

(-1, -2, -3, …)

Integers• -5 is read “negative five” NOT minus five!• You do not need to include a + sign in front of a

positive integer.• 2 is still just 2, not +2!

• Plotting a number on a number line means to draw a dot at the point that represents that number– Be sure to label your points!

• Draw a number line and plot the integers -6, -2, and 3.

-6 -2 0 3

Absolute Value

• Absolute value is the distance from zero on a number line.

• Because AV is a distance, it is always positive.– There is no such thing as a negative distance.– If I drive 11 miles to school, I drive 11 miles

home, not -11 miles!

Absolute Value

• AV is written with two vertical lines called absolute value signs– Ex: │7│ or │-3│

• The absolute value of 7 (│7│) is 7, because it is seven spaces away from zero on a number line

• The absolute value of -3 (│-3│) is 3, because it is three spaces away from zero on a number line

Evaluating Absolute Value

│-17│

=17

│5│

=5

│0│

=0

│-121│

=121

Opposites

• Opposites are numbers that are the same distance from, but on opposing sides of, zero

• Opposites have the same absolute value• Find the opposites of the following:

-118

-8 11

121

-121

0

0

Ordering Integers

• Plot the numbers on a number line.• Order the numbers from left to right

• Example: -3, 4, 1, -1, 2, -4, -5

Homework

•Page

78-79•#2-58 even