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Absolute Value Absolute Value -7 -10 -5 +7 0 5 10 A number line has many functions. Previously, we learned that numbers to the right of zero are positive and numbers to the left of zero are negative. By putting points on the number line, we can graph values. If one were to start at zero and move seven places to the right, this would represent a value of positive seven. If one were to start at zero and move seven places to the left, this would represent a value of negative seven. Absolute Value -7 -10 -5 +7 0 5 10 Both of these numbers, positive seven (+7) and negative seven (-7), represent a point that is seven units away from the origin. The absolute value of a number is the distance between that number and zero on a number line. Absolute value is shown by placing two vertical bars around the number as follows: | 5 | The absolute value of five is five. | -3 | The absolute value of negative three is three. 1 block 1 block You walk directly east from your house one block. How far from your house are you? You walk directly west from your house one block. How far from your house are you? It didn't matter which direction you walked, you were still 1 block from your house. This is like absolute value. It is the distance from zero. It doesn't matter whether we are in the positive direction or the negative direction, we just care about how far away we are. 4 4 4 units away from 0 4 units away from 0 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 4 4 Absolute Value What does absolute value look like? the absolute value of 7 |7|= 7 the absolute value of – 7 |–7 |= 7 Integers & Absolute Value What is absolute value? The distance of some number from zero on the number line What does absolute value look like? 7 units -8 -7 -6 -5 -4 -3 -2 -1 0 1 7 units 2 3 4 5 6 7 8 Opposites vs Absolute Value Given Number Opposite Absolute Value 8 -8 8 8 -24 +24 24 24 -3.5 +3.5 35 . 35 . Absolute Value Let’s Try Some… Ask yourself, how far is the number from zero? 1) | -4 | = 2) | 3 | = 3) | -9 | = 4) | 8 - 3 | + = -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6