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Chapter 2 Definitions Numbers such as 3 and -3 that are the same distance from 0 but on the opposite side of 0 are called opposites. The set of integers consists of the whole numbers and their opposites. Positive/Negative numbers on the number line:

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Defs Inequality Absolute Value Any number that can be expressed as the ratio of two integers is called a rational number There is a point on the number line for every rational number. The number is called the coordinate of the point; the point is the graph of the number.

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Rational numbers are a part of a larger set of numbers called the real numbers. Adding and subtracting positive and negative numbers Using the number line Examples Two rational numbers whose sum is 0 are called additive inverses of each other. a+(-a) = 0 Multiplying positive and negative numbers Examples

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Multiplicative Property of Zero For any rational number n, n*0 = 0 Definition: Quotient Two rational numbers whose product is 1 are called multiplicative inverses or reciprocals of each other. Property of multiplicative inverses A rational number can be expressed as either a : –Terminating decimal –Repeating decimal A decimal that neither terminates or repeats is called a irrational number.

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The Distributive Property of Mulitiplication over Addition For any rational numbers a, b, and c a(b+c) = (b+c)a = The Distributive Property of Mulitiplication over Subtraction a(b-c) = (b-c)a = The property of -1: For any rational number a, -1(a) =

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The inverse of a sum property For any rational numbers –(a+b) = -a +(-b) Grouping symbols used in Algebra: (){}[] ParenthesisBracesBrackets Properties of Equality Reflexive: a = a is always true Symmetric: If a = b, then b = a Transitive: If a = b and b = c then a = c

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