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Integers and Absolute Value Integers Integers are the whole numbers (0, 1, 2, 3, …) (-1, -2, -3, …) and their opposites Integers are modeled on a number line: Negative Integers -3 -2 -1 Positive Integers 0 1 2 3 •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 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 │0│ =0 │5│ =5 │-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: 8 -11 -8 11 121 -121 0 0