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ALGEBRA: CHAPTER 1 - FOUNDATIONS FOR ALGEBRA

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Section 1

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Algebra Math

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Date created

Mar 1, 2020

Cards (41)

Section 1

(41 cards)

Open sentence

Front

An equation that contains one or more variables and may be true or false depending on the value of its variables.

Back

Inequality

Front

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

Back

Subset

Front

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

Back

Solution of an equation (two variables)

Front

A solution of a two-variable equation with the variables and y is any ordered pair (x, y) that makes the equation true.

Back

Square root

Front

A number of such that a2=b. square root of b is the principle square root. -square root of b is the negative square root.

Back

Additive inverse

Front

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

Back

Perfect squares

Front

Numbers whose square roots are integers.

Back

Real numbers

Front

A number that is either rational or irrational.

Back

Simplify

Front

To replace an expression with its simplest name or form.

Back

Quantity

Front

Anything than can be measured or counted.

Back

Numerical expression

Front

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

Back

Base

Front

A number that is multiplied repeatedly.

Back

Counterexample

Front

An example showing that a statement is false.

Back

Opposite

Front

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

Back

Coefficient

Front

The numerical factor when a term has a variable.

Back

Algebraic expression

Front

A mathematical phrase that includes one or more variables.

Back

Exponent

Front

A number that shows repeated multiplication.

Back

Equivalent expressions

Front

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

Back

Deductive reasoning

Front

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

Back

Like terms

Front

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

Back

Term

Front

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

Back

Inductive reasoning

Front

Making conclusions based on observed patterns.

Back

Element of a set

Front

Members of a set.

Back

Distributive property

Front

For every real number a, b, and c: a(b + c) = ab + ac (b + c)a = ba + ca a(b - c) = ab - ac (b - c)a = ba - ca

Back

Integers

Front

Whole numbers and their opposites.

Back

Radicand

Front

The expression under the radical sign is the radicand.

Back

Set

Front

A well-defined collection of elements.

Back

Whole numbers

Front

The nonnegative integers.

Back

Irrational number

Front

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

Back

Power

Front

A power has two parts, a base and an exponent.

Back

Absolute value

Front

The distance that a number is from zero on a number line.

Back

Variable

Front

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

Back

Constant

Front

A term that has no variable factor.

Back

Solution of an equation (one variable)

Front

Any value or values that make an equation true.

Back

Natural numbers

Front

The counting numbers.

Back

Equation

Front

A mathematical sentence that uses an equal sign.

Back

Multiplicative inverse

Front

Given a nonzero rational number a/b, the multiplicative inverse, or reciprocal, is b/a. The product of a nonzero and its multiplicative inverse is 1.

Back

Radical

Front

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

Back

Reciprocal

Front

Given a nonzero rational number a/b, the reciprocal, or multiplicative inverse, is b/a. The product of a nonzero numbers and its reciprocal is 1.

Back

Evaluate

Front

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

Back

Rational numbers

Front

A real number that can be written as a ratio of two integers. Rational numbers in decimal form are terminating or repeating.

Back