Rational Number

Section 1.3-p.24

The quotient of two integers. Therefore, a rational number is a number that can be written in the form a/b, where a and b are integers, and b is not zero.

Example: 2/3, -4/9, 18/-5, 4/1

Terminating Decimal

Section 1.3-p. 24

A decimal that is formed when dividing the numerator of its fractional counterpart by the denominator results in a remainder of zero.

Example:

Repeating Decimal

Section 1.3-p. 25

A decimal formed when dividing the numerator of a fraction by its denominator, in which a digit or a sequence of digits in the decimal repeats infinitely.

Example:

Irrational Numbers

Section 1.3-p. 25

A number that cannot be written in the form a/b, where a and b are integers and b is not equal to zero. A number that cannot be written as a repeating decimal or a terminating decimal

Example: 2.45445444544445...

Lowest Common Denominator

Section 1.3-p. 27

The smallest number that is a multiple of each denominator in question.

Example:

Percent

Section 1.3-p. 29

"Parts of 100"

Example: 27% means 27 parts of 100

Exponent

Section 1.4-p. 38

Indicates how many times the factor occurs in the multiplication.

Example: 2⁵⁼ 2•2•2•2•2

Base

Section 1.4-p.38

In exponential notation, the factor that is multiplied the number of times shown by the exponent.

Example: a⁴

Factored Form

Section 1.4-p. 38

The expression 2•2•2•2 is in factored form.

Exponential Form

Section 1.4-p.38

The expression 2⁵ is in exponential form.

Example: 2⁵ is read as "the fifth power of two"

The Order of Operations Agreement

Section 1.4-p.40

A set of rules that tells us in what order to perform the operations that occur in a numerical expression.

P - Parenthases or grouping symbols

Example:     E- exponents

M-multiplication

D- division

A- addition

S- subtraction

Variable

Section 2.1-p.67

A letter of the alphabet used to stand for a number that is unknown or that can change.

Example: a, b, x, y, etc.

Variable Expression

Section 2.1-p.67

Am expression that contains one or more variables.

Example: 3x²+2xy-x-7

Term(s)

Section 2.1-p.67

The addends of the expression.

Example: 3x or 7xy

Constant Term

Section 2.1-p.67

A term that includes no variable part.

Example: 1, 2, -3, -4

Numerical Coefficient

Section 2.1-p.67

The number part of a variable term. When the numerical coefficient is 1 or -1, the 1 is usually not written.

Example: 3x -5x 6x -1x

Variable Part

Section 2.1-p.67

In a variable term, the variable or variables and their exponents.

Example: 3x² or 2xy

Evaluating the Variable Expression

Section 2.1-p.68

Replace each variable by its value and then simplify the resulting numerical expression.

Example: Evaluate ab-b² when a=2 and b=-3

The Commutative Property of Addition

Section 2.2-p.74

Two terms can be added in either order; the sum is the same.

Example: a+b=b+a

             4+3=3+4

The Commutative Property of Multiplication

Section 2.2-p.74

Two factors can be multiplied in either order; the product is the same.

Example: a•b=b•a

                    (5)(-2)=(-2)(5)

The Associative Property of Addition

Section 2.2-p.74

When three or more terms are added, the terms can be grouped (with parenthses, for example) in any order; the sum is the same.

Example: (a+b)+c=a+(b+c)

              2+(3+4)=(2+3)+4

The Associative Property of Multiplication

Section 2.2-p.74

When three or more factors are multiplied, the factors can be grouped in any order; the product is the same.

Example: (a•b)•c=a•(b•c)

The Addition Property of Zero

Section 2.2-p.74

The sum of a term and zero is the term.

Example: a+0=0+a

The Multiplication Property of Zero

Section 2.2-p.74

The product of a term and zero is zero.

Example: a•0=0•a

The Multiplication Property of One

Section 2.2-p.74

The product of a term and 1 is the term.

Example: a•1=1•a

The Inverse Property of Addition

Section 2.2-p.74

The sum of a number and its oppisite is zero. The oppisite of a number is called its additive inverse.

Example: a+(-a)=(-a)+a

The Inverse Property of Multiplication

Section 2.2-p.74

The product of a number and its reciprocal is 1. 1/a is the reciprocal or the multiplicative inverse.

Example: a•1/a=1/a•a

The Distributive Property

Section 2.2-p.75

By the distributive property, the term outside the parentheses is multiplied by each term inside the parentheses.

Example: a(b+c)=ab+ac OR

        (b+c)a=ba+ca

Like Terms

Section 2.2-p.76

Terms of a variable expression that have the same variable part.

Example: 3x, 7x, 9x

Combine Like Terms

Section 2.2-p.74

Use the distributive property to add the coefficients of like variable terms; add like terms of a variable expression.

Example: -2y+3y=1y