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:

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.

• Rational numbers are a part of a larger set of numbers called the real numbers.

• Adding and subtracting positive and negative numbersUsing the number lineExamples

• Two rational numbers whose sum is 0 are called additive inverses of each other. a+(-a) = 0

Multiplying positive and negative numbers Examples

• 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.

• 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) =

• The inverse of a sum property

For any rational numbers –(a+b) = -a +(-b)

• Grouping symbols used in Algebra:

() {} []

Parenthesis Braces Brackets

• 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