**abscissa** the distance along the horizontal axis in a coordinate graph.

**absolute value** the numerical value when direction or sign is not considered. The symbol for absolute value is ∣ ∣.

**additive axiom of equality** if *a* = *b* and *c* = *d*, then *a* + *c* = *b* + *d*.

**additive axiom of inequality** if *a* > *b*, then *a* + *c* > *b* + *c*.

**additive inverse** the opposite (negative) of a number. Any number plus its additive inverse equals 0.

**algebra** arithmetic operations using letters and/or symbols in place of numbers.

**algebraic expressions** expressions composed of letters to stand for numbers.

**algebraic fractions** fractions using a variable in the numerator and/or denominator.

**ascending order** basically, when the power of a term increases for each succeeding term.

**associative property** grouping of elements does not make any difference in the outcome. Only true for multiplication and addition.

**axioms of equality** basic rules for using the equal sign.

**binomial** an algebraic expression consisting of two terms.

**braces** grouping symbols used after the use of brackets. Also used to represent a set. { }

**brackets** grouping symbols used after the use of parentheses. [ ]

**canceling** in multiplication of fractions, dividing the same number into both a numerator and a denominator.

**cartesian coordinates** a system of assigning ordered number pairs to points on a plane.

**closed half-plane** a half-plane that includes the boundary line and is graphed using a solid line and shading.

**closed interval** an interval that includes both endpoints or fixed boundaries.

**closure property** when all answers fall into the original set.

**coefficient** the number in front of a variable. For example, in 9*x*, 9 is the coefficient.

**common factors** factors that are the same for two or more numbers.

**commutative property** order of elements does not make any difference in the outcome. Only true for multiplication and addition.

**complex fraction** a fraction having a fraction or fractions in the numerator and/or denominator.

**composite number** a number divisible by more than just 1 and itself (such as 4, 6, 8, 9, . . . ). 0 and 1are *not* composite numbers.

**conjugate** the conjugate of a binomial contains the same terms, but the opposite sign between them. (*x* + *y*) and (*x* − *y*) are conjugates.

**coordinate axes** two perpendicular number lines used in a coordinate graph.

**coordinate graph** two perpendicular number lines, the *x* axis and the *y* axis, creating a plane on which each point is assigned a pair of numbers.

**coordinates** the numbers that correspond to a point on a coordinate graph.

**cube** the result when a number is multiplied by itself twice. Designated by the exponent 3 (such as *x*^{3}).

**cube root** the number that when multiplied by itself twice gives you the original number. For example, 5 is the cube root of 125, which is symbolized as [img id:59962].

**denominator** everything below the fraction bar in a fraction.

**descending order** basically, when the power of a term decreases for each succeeding term.

**direct variation** when *y* varies directly as *x* or *y* is directly proportional to *x*.

**discriminant** the value under the radical sign in the quadratic formula. [*b*^{2} − 4*ac*]

**distributive property** the process of distributing the number on the outside of the parentheses to each number on the inside. *a*(*b* + *c*) = *ab* + *ac*

**domain** the set of all first coordinates from the ordered pairs in a relation.

**element** a member of a set.

**empty set** a set with no members (a null set).

**equal sets** sets that have exactly the same members.

**equation** a balanced relationship between numbers and/or symbols. A mathematical sentence.

**equivalent sets** sets that have the same number of members.

**Euler circles** a method of pictorially representing sets.

**evaluate** to determine the value or numerical amount.

**exponent** a numeral used to indicate the power of a number.

**extremes** outer terms.

**factor** to find two or more quantities whose product equals the original quantity.

**finite** countable. Having a definite ending.

**F.O.I.L. method** a method of multiplying binomials in which first terms, outside terms, inside terms, and last terms are multiplied.

**function** a relation in which each element in the domain is paired with exactly one element in the range.

**graphing method** a method of solving simultaneous equations by graphing each equation on a coordinate graph and finding the common point (intersection).

**half-open interval** an interval that includes one endpoint, or one boundary.

**half-plane** the region of a coordinate graph on one side of a boundary line.

**identity element for addition** 0. Any number added to 0 gives the original number.

**identity element for multiplication** 1. Any number multiplied by 1 gives the original number.

**imaginary numbers** square roots of negative numbers. The imaginary unit is *i*.

**incomplete quadratic equation** a quadratic equation with a term missing.

**indirect variation or inverse variation** when *y* varies indirectly as *x* or *y* is indirectly proportional to *x*. That is, as *x* increases, *y* decreases and as *y* increases, *x* decreases. Also referred to as *inverse* or *indirect proportion*.

**inequality** a statement in which the relationships are not equal. The opposite of an equation.

**infinite** uncountable. Continues forever.

**integer** a whole number, either positive, negative, or zero.

**intersection of sets** the members that overlap (are in both sets).

**interval** all the numbers that lie within two certain boundaries.

**inverse relations** relations where the domain and the range have been interchanged—switching the coordinates in each ordered pair.

**linear equation** an equation whose solution set forms a straight line when plotted on a coordinate graph.

**literal equation** an equation having mostly variables.

**means** inner terms.

**monomial** an algebraic expression consisting of only one term.

**multiplicative axiom of equality** if *a* = *b* and *c* = *d*, then *ac* = *bd*.

**multiplicative inverse** the reciprocal of the number. Any number multiplied by its multiplicative inverse equals 1.

**negative multiplication property of inequality** reverse the inequality sign when multiplying (or dividing) by a negative number. If *c* < 0, then *a* > *b* if, and only if, *ac* < *bc*.

**nonlinear equation** an equation whose solution set does not form a straight line when plotted on a coordinate graph.

**null set** a set with no members (an empty set).

**number line** a graphic representation of integers and real numbers. The point on this line associated with each number is called the graph of the number.

**numerator** everything above the fraction bar in a fraction.

**numerical coefficient** the number in front of the variable.

**open half-plane** a half-plane that does not include the boundary line. If the inequality is a ">" or "<", then the graph is an open half-plane.

**open interval** an interval that does not include endpoints or fixed boundaries.

**open ray** a ray that does include its endpoint (half line).

**ordered pair** any pair of elements (*x, y*) having a first element *x* and a second element *y*. Used to identify or plot points on a coordinate grid.

**ordinate** the distance along the vertical axis on a coordinate graph.

**origin** the point of intersection of the two number lines on a coordinate graph. Represented by the coordinates (0,0).

**polynomial** an algebraic expression consisting of two or more terms.

**positive multiplication property of inequality** if *c* > 0, then *a* > *b* if, and only if, *ac* > *bc*.

**proportion** two ratios equal to each other. For example, *a* is to *c* as *b* is to *d*.

**quadrants** four quarters or divisions of a coordinate graph.

**quadratic equation** an equation that could be written *Ax*^{2} + *Bx* + *C* = 0.

**quadratic formula** a method of solving quadratic equations using the formula

**radical sign** the symbol used to designate square root.

**range** the set of all second (or *y*) coordinates from the ordered pairs in a relation.

**ratio** a method of comparing two or more numbers. For example, *a*:*b*. Often written as a fraction, *a/b*.

**real numbers** the set consisting of all rational and irrational numbers.

**reducing** changing a numerical or algebraic fraction into its lowest terms. For example, 2/4 is reduced to 1/2, or *a*/*ab* is reduced to 1/*b*.

**reflexive axiom of equality** for any number *a*, *a* = *a*.

**relation** any set of ordered pairs.

**repeating decimal** a decimal fraction that continues forever repeating a number or block of numbers.

**roster** a method of naming a set by listing its members.

**rule** a method of naming a set by describing its elements.

**set** a group of objects, numbers, and so forth.

**set builder notation** a formal method of describing a set. Often used for inequalities. For example, {*x*: *x* > 1}, which is read "*x* such that all *x* is greater than 1."

**simplify** to combine several or many terms into fewer terms.

**simultaneous equations (system of equations)** a set of equations with the same unknowns (variables).

**slope of a line** the ratio of the change in *y* to the change in *x* in a linear equation (slope = rise/run).

**solution set (or solution)** all the answers that satisfy the equation.

**square** the result when a number is multiplied by itself. Designated by the exponent 2 (such as *x*^{2}).

**square root** the number that when multiplied by itself gives you the original number. For example, 5 is the square root of 25, which is symbolized as [img id:59963].

**subset** a set within a set.

**substitution method** a method of solving simultaneous equations that involves substituting one equation into another.

**symmetric axiom of equality** if *a* = *b*, then *b* = *a*.

**system of equations** simultaneous equations.

**term** a numerical or literal expression with its own sign.

**transitive axiom of equality** if *a* = *b* and *b* = *c*, then *a* = *c*.

**transitive axiom of inequality** if *a* > *b* and *b* > *c*, then *a* > *c*. Or if *a* < *b* and *b* < *c*, then *a* < *c*.

**trichotomy axiom of inequality** the only possible relationships between two numbers are: *a* > *b*, *a* = *b*, or *a* < *b*.

**trinomial** an algebraic expression consisting of three terms.

**union of sets** all the numbers in those sets.

**universal set** the general category set, or the set of all those elements under consideration.

**unknown** a letter or symbol whose value is not known.

**value** numerical amount.

**variable** a symbol used to stand for a number.

**variation** a relationship between a set of values of one variable and a set of values of other variables.

**Venn diagram** a pictorial description of sets.

**vinculum** a line placed over (sometimes under) a digit or group of digits in a repeating decimal fraction to show which digits are repeating.

**whole number** 0, 1, 2, 3, and so on.

**-axis** the horizontal axis in a coordinate graph.

**-coordinate** the first number in the ordered pair. Refers to the distance on the *x*-axis (the abscissa).

**-axis** the vertical axis in a coordinate graph.

**-coordinate** the second number in the ordered pair. Refers to the distance on the *y*-axis (the ordinate).