absolute value A number’s distance from zero on the number line.

addition property of equality Adding the same number or term to both sides of a true equality creates a new equation that is also true.

associative property Terms can be grouped in any order for addition or multiplication.

base The number or variable in an exponential expression that is raised to a power or exponent (in x³, x is the base and 3 is the power or exponent).

binomial A polynomial with two terms. Examples are x + y; 2a - 5; x² + 7.

coefficient The number in front of the variable. For example, in 3x, 3 is the coefficient.

common denominator The number or variable(s) that are the same denominator in two or more fractions, so that the fractions can be added or subtracted.

common factors Numbers or variables that are divisible into another number or variable. For example, 4 is a common factor of 12 and 16; 3 is not a common factor of 12 and 16; x is a common factor of xy and xz; and x is not a common factor of xy and yz.

commutative property Two numbers or terms can be added or multiplied in either order. For example, 2 + 3 = 3 + 2; x · y = y · x.

completing the square One of four processes used to solve some quadratic equations by making the quadratic trinomial factorable into a squared binomial.

consecutive integers Integers that are next to each other on the real number line. For example, 2 and 3 are consecutive integers, as are -8 and -7.

denominator The part of a fraction under the fraction line.

direct variation A relationship shown by y = kx, where k is the constant rate of change and, as x increases, y also increases, or as x decreases, y also decreases (it is the same as directly proportional).

discriminant The radicand from the quadratic formula: b ² - 4ac.

distributive property Multiplying a sum by a number or variable is equal to the sum of the product of the numbers. For example, 2 (x + y) = 2x + 2y.

division property of equality Both sides of an equation can be divided by the same nonzero number or variable, and the new equation will be true.

equation An expression that includes an equal sign. For example, 2 + 3 = 5 and x + 2y = -4.

evaluate To substitute numbers for variables in an expression and calculate a numerical answer.

expanded form A monomial written with no exponents. For example, x · x · x is the expanded form of x³.

exponent The number (power) that is above and to the right of the base. For example, in x³, 3 is the exponent and indicates how many times to use the base x as a factor.

factoring Showing the numbers or variables that multiply to form another number or monomial term. For example, factoring 9x gives 3 · 3 · x.

factors Numbers or variables that can be multiplied to give a number or monomial term.

FOIL method A shortcut way to multiply two binomials.

graphing Putting points on a number line or ordered pairs on a coordinate system of x- and y-axes.

grouping symbols Parentheses or brackets used to separate or emphasize two or more numbers or variables.

identity property of addition Adding 0 to any number or variable does not change the number or the variable.

identity property of multiplication Multiplying a number or variable by 1 does not change the number or variable.

imaginary number A number that is the result of taking the square root of a negative number.

infinite Continuing without end; the integers are infinite because there is always another integer larger than or smaller than any integer.

integers The set of whole numbers and their opposites (…, -2, -1, 0, 1, 2, …).

inverse variation A relationship shown by xy = k, where k is the constant rate of change, and as x increases, y decreases, or as x decreases, y increases.

irrational numbers Numbers that are the result of taking the square root of a number that has a factor that is not a perfect square (√8 is irrational; √9 = 3 is rational).

isolate the variable To solve an equation for the variable.

monomial A polynomial with one term. Examples are 4ab, 4, ab, a, b, and b³.

multiplication property of equality Both sides of an equation can be multiplied by the same number or variable, and the new equation will be true.

numerator The part of a fraction above the fraction line.

open equations Equations that might not be true, depending on what value is given to the variable. For example, 2x + y = 6 and x + 7 = - 5 are open equations.

operations Adding, subtracting, multiplying, dividing, squaring, and taking the square root of numbers or variables.

opposites Numbers or variables that have different signs (2 and -2 are opposites; x and -x are opposites).

opposites property of addition When two opposites are added, the result is 0.

ordered pair Two numbers that represent a solution to a two-variable equation; (1,2) is not the same as (2,1) because the order of the numbers is different.

ordering numbers Comparing two or more numbers to list them in ascending or descending order.

origin On an (x,y) graph, the point (0,0); on a number line, the point 0.

parallel lines Lines in the same plane that never intersect.

parentheses Can be used as grouping symbols: 7 · (2 + 3x); to show multiplication: (7)(5) = 35; to show emphasis (-3) + 7 = 4; or to raise a power to a power: (2⁴)³ = 2 ¹².

percent From “per hundred”; for example, 6/100 = 6% = .06.

perfect squares Numbers that come from multiplying a number times itself (1, 4, 9, 16, 25, …).

plotting Graphing points on a number line or ordered pairs on an (x,y) axis graph. See also: monomials, binomials, trinomials.

polynomials Numbers or variables that are added or subtracted to form an expression. For example, 2c; 3x - 9; and 5abc + 8 are all polynomials. See also: monomials, binomials, trinomials.

power Exponent or the number that indicates how many times to use a base as a factor; for example, 4³ has a power of 3 and shows that 4 is to be multiplied times itself 3 times.

proportion Two ratios (or fractions) that are equal.

quadratic equation An equation with a variable with an exponent of 2.

quadratic formula A method of solving a quadratic equation of the form ax² + bx + c = 0, where

radical Square root.

radicand The number or variable(s) inside the square root symbol.

ratio A fraction.

rational number A number that can be written as the ratio of two integers.

real number line The horizontal line that contains marked intervals evenly spaced, with the negative numbers on the left and positive numbers on the right.

real numbers The numbers that can be plotted on the real number line (all numbers are real except the square root of a negative number).

reciprocal A number that, when multiplied by another number, gives a product of 1.

reciprocal property of multiplication Two reciprocals have a product of 1.

rise In slope, the rise is the change in the y values for two ordered pairs.

run In slope, the run is the change in the x values for two ordered pairs.

simplifying Reducing a fraction to its lowest terms or combining like terms in an expression.

simplifying radicals Removing all perfect square factors from the radicand.

slope The ratio of rise to run of a line.

slope-intercept formula The formula y = mx + b, where m is the slope and b is the y-intercept of the line on an (x,y) graph.

subtraction property of equality A number or variable can be subtracted from both sides of an equation, and the new equation will be true.

systems of equations Two equations with two of the same variables in each equation (x + y = 6 and 2x + y = -8 form a system of equations).

trinomial A polynomial with three monomials. For example, x + y - z and 2a + 4c + t.

variables Letters that represent numbers in an expression.

x-intercept The point where a graphed line crosses the x-axis of the (x,y) coordinate graph (the ordered pair where y = 0).

y-intercept The point where a graphed line crosses the y-axis of the (x,y) coordinate graph (the ordered pair where x = 0).