Opposite Numbers and Absolute Value

Pre-Algebra · Axiom Academy

LESSON Opposite Numbers and Absolute Value Every number has a mirror twin across zero, and absolute value is just the distance between them and zero — direction stripped away. 1. Opposites Reflect Across Zero Two numbers are opposites when they sit the same distance from zero but on opposite sides. Press play: the point at 5 swings across the zero-mirror and lands exactly on -5 — same distance, flipped direction. The opposite of a number flips its sign Flip the sign twice and you are back where you started The absolute value of a number is its distance from zero — and distance is just a length . Watch the bar grow from 0 out to -5 , then watch its sign get stripped off so only the length, 5 , remains. Now measure both directions at once. Two bars grow outward from zero — one left to -5 , one right to 5 . They reach the same length because both points sit five units from the mirror. Five units of distance. |-5| = 5 . Five units of distance. |5| = 5 . 4. Opposites Always Share an Absolute Value This isn't special to 5 . Watch the pair of points slide together — from out to — and the two distance bars stay perfectly matched the whole way. Whatever the number, it and its opposite are always the same distance from zero. A number and its opposite are equally far from zero, by definition. Equal distance means |n| and |-n| give the same answer. |7| = 7 and |-7| = 7 . |12| = 12 and |-12| = 12 . The number and its opposite always tie. 5. Above and Below Zero in the Real World

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