Integers and Absolute Value

1. Integers andAbsolute Value

2. Integers Integers are the whole numbers (0, 1, 2, 3, …) and their opposites Integers are modeled on a number line: -3 -2 -1 0 1 2 3 (-1, -2, -3, …) Negative Integers Positive Integers • 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

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

4. 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!

5. 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

6. │-17│ =17 │5│ =5 │0│ =0 │-121│ =121 Evaluating Absolute Value

7. 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: 8 -11 121 0 -121 0 -8 11