Introductory Algebra Glossary The Language of Math

natural numbers The numbers used for counting: {1, 2, 3, 4,...}.

whole numbers The set of whole numbers is: {0, 1, 2, 3, 4, 5,...}.

numerator The number above the fraction bar that shows how many equivalent parts are being considered.

denominator The number below the fraction bar in a fraction. It shows the number of equal parts in a whole.

factor Any number that divides evenly (without remainder) into the given number: 1, 2, 3 and 6 are factors of 6.

product The answer to a multiplication problem. 6 is the product of 2 times 3.

factored A number is factored by writing it as the product of two or more numbers. 6 is factored as 2 times 3.

prime number A natural number (except one) that has only one and itself as factors. 2, 3, 5, 7, 11, 13, and 17 are prime numbers.

composite number A composite number has at least one factor other than itself and one.

greatest common factor (GCF) The largest common factor of a list of integers or the largest term that is a factor of all terms in the polynomial.

lowest terms A fraction is in lowest terms when there are no common factors in the numerator and denominator (except 1).

reciprocals Pairs of numbers whose product is 1: 1/3 and 3 are reciprocals.

quotient The answer to a division problem.

sum The answer to an addition problem.

least common denominator (LCD) Given several denominators, the smallest expression that is divisible by all the denominators is called the least common denominator.

mixed number A whole number and a fraction written together and understood to be their sum.

difference The answer to a subtraction problem.

exponent (power) A number that indicates how many times a factor is repeated: Given 2 3 the exponent is three.

base The number that is a repeated factor when written with an exponent: Given 2 3 the base is two.

exponential expression A number or letter (variable) written with an exponent: Examples: 2 3 or x 6.

grouping symbols Parentheses, ( ), square brackets, [ ], or fraction bars.

variable A variable is a symbol used to represent an unknown number: In the term 3x the variable is x.

algebraic expression Any collection of numbers or variables joined by the basic operations of addition, subtraction, multiplication, or division (except by zero), or the operation of taking roots.

equation A statement that two algebraic expressions are equal: Example: 4x = 5y.

solution of an equation Any replacement for the variable that makes the equation true.

set A collection of objects.

elements (members) The objects that belong to a set.

number line A line with a scale that is used to show how numbers relate to each other.

negative number A number located to the left of zero on a number line.

positive number A number located to the right of zero on the number line.

signed numbers Numbers that can be written with a positive or negative sign.

integers The set of integers is: {...-3, -2, -1, 0, 1, 2, 3,...}.

graph of a number The point on a number line that corresponds to a number is its graph.

rational numbers Rational numbers can be written as the quotient of two integers, with denominator not zero.

irrational numbers Irrational numbers cannot be written as the quotient of two integers but can be represented by points on the number line.

real numbers All numbers that can be represented by points on the number line, that is, all rational and irrational numbers.

additive inverse Two numbers that are the same distance from zero on a number line but on opposite sides of zero. The sum of two additive inverses equals zero.

absolute value The distance between zero and a number on a number line.

multiplicative inverse (reciprocal) The multiplicative inverse of a nonzero real number a is 1/a. The product of multiplicative inverses is one.

commutative property of addition The order of numbers in an addition problem can be changed without changing the sum: =

commutative property of multiplication The product in a multiplication problem remains the same regardless of the order of the factors: 6 4 = 4 6

associative property of addition The way in which numbers being added are grouped does not change the sum: 6 + (3 + 2) = (6 + 3) + 2

associative property of multiplication The way in which numbers being multiplied are grouped does not change the product: 6 (2 3) = (6 2) 3

identity property The sum of zero and any number equals the number, and the product of one and any number equals the number: X + 0 = x x 1 = x

inverse property A number added to its opposite is zero and a number multiplied by its reciprocal is one: 1 + (-1) = 0 1 (1/2) = 1

distributive property For any real numbers a, b, and c, the distributive property states that: a (b + c) = ab + ac.

term A number, a variable, or the product or quotient of a number and one or more variables raised to powers.

numerical coefficient The numerical factor in a term. In the term 6x 2 the numerical coefficient is 6.

like terms The same variables raised to exactly the same powers. The terms 2x 2 and 7x 2 are like terms.

unlike terms Terms that do not have the same variable or the variables are not raised to the same powers. The terms 2x 2 and 7x 3 are unlike terms.

combining like terms A method of adding or subtracting like terms by using the properties of real numbers: 2x 2 + 7x 2 = 9x 2.

Return to Introductory Algebra Introductory Algebra Created by James Q. Jacobs