Unit 2: Foundations for Algebra

Subset

A _______ of a set consists of elements from the given set.

Reciprocal

A mathematical expression or function so related to another that their product is one; the quantity obtained by dividing the number one by a given quantity.

Numerical Expression

A mathematical phrase involving numbers and operation symbols, but no variables.

Algebraic Expression

A mathematical phrase that includes one or more variables.

Inequality

A mathematical sentence that compares the values of two expressions using an inequality symbol.

Irrational Numbers

A number that cannot be written as a ratio of two integers. When in decimal form they are nonterminating and nonrepeating.

Real Numbers

A number that is either rational or irrational.

Base

A number that is multiplied repeatedly.

Opposites

A number that is the same distance from zero on the number line as a given number, but lies in the opposite direction.

Square Root

A number that produces a specified quantity when multiplied by itself.

Exponent

A number that shows repeated multiplication.

Term

A number, variable, or the product or quotient of a number and one or more variables.

Deductive Reasoning

A process of reasoning logically from given facts to a conclusion.

Rational Numbers

A real number that can be written as a ratio of two integers. When in decimal form they are terminating and repeating.

Variable

A symbol, usually a letter, that represents one or more numbers.

Constant

A term that has no variable factor.

Set

A well-defined collection of elements.

Equivalent Expressions

Algebraic expressions that have the same value for all values of the variable(s).

Distributive Property

An algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.

Counterexample

An example showing that a statement is false.

Radical

An expression made up of a radical symbol and a radicand.

Multiplicative Inverse

Another name for Reciprocal.

Quantity

Anything that can be measured or counted.

Identity Property

This property states that any time you multiply a number by 1, the result, or product, is that original number.

Commutative Property

This property states that order does not matter.

Simplify

To replace an expression with its simplest name or form.

Evaluate

To substitute a given number for each variable, then simplify.

Integers

Whole numbers and their opposites.

Radicand

The expression under the radical sign.

Whole Numbers

The nonnegative integers.

Coefficient

The numerical factor when a term has a variable.

Additive Inverses

The opposite or _______ _______ of any number a is -a. The sum of opposites is 0.

Power

It is represented with a base number and an exponent. The base number tells what number is being multiplied. The exponent, a small number written above and to the right of the base number, tells how many times the base number is being multiplied.

Element of a Set

Members of a set.

Perfect Square

Numbers whose square roots are integers.

Associative Property

States that you can add or multiply regardless of how the numbers are grouped.

Like Terms

Terms with exactly the same variable factors in a variable expression.

Natural Numbers

The counting numbers.

Absolute Value

The distance that a number is from zero.