Unit 3 Summary

Pre-Algebra · Axiom Academy

SUMMARY Unit 3 Summary: Integers and Rational Numbers Extending numbers to include negatives doubles our vocabulary — letting us describe quantities below zero, losses, and positions in every direction. Integers add the negatives to the whole numbers: , extending the number line infinitely in both directions. Absolute value |x| is a number's distance from zero, so it is never negative — and two opposites like 5 and -5 share the same absolute value. Sign rules govern every operation: same signs add (keep the sign) or multiply to a positive; different signs subtract or multiply to a negative; subtraction means add the opposite . Rational numbers extend integers to every fraction and terminating/repeating decimal, filling in the number line completely. The coordinate plane uses ordered pairs (x, y) and four quadrants to pin down position in two dimensions. Core Concept Integers & the Number Line Integers are the whole numbers together with their negatives. The number line runs forever in both directions: negatives sit to the left of zero, positives to the right. Opposites: same distance from zero, opposite directions — e.g. 5 and -5 . Where it shows up: temperatures below zero, elevations below sea level, debts and losses. The absolute value |x| is the distance a number sits from zero. Distance is never negative, so an absolute value is always positive or zero. When to use: to measure size or distance, ignoring direction.

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