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

associative property Grouping of elements makes no difference in the outcome. This is only true for multiplication and addition.

braces Grouping symbols used after the use of brackets; signs { } 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.

circumference The distance around a circle; equals 2 × π × the radius or π × the diameter (C = 2πr or πd).

closure property When all answers fall into the original set.

combinations The total number of independent possible choices.

common denominator A number that can be divided evenly by all denominators in the problem.

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

common multiples Multiples that are the same for two or more numbers.

commutative property The order of elements does not make any difference in the outcome. This is 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.

cube The result when a number is multiplied by itself twice.

cube root A number that when multiplied by itself twice gives you the original number; its symbol is  3√.

decimal fraction Fraction with a denominator 10, 100, 1,000, and so on, written using a decimal point; for example, .3 and .275.

decimal point A point used to distinguish decimal fractions from whole numbers.

denominator The bottom symbol or number of a fraction.

dependent events When the outcome of one event has a bearing or effect on the outcome of another event.

difference The result of subtraction.

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

even number An integer (positive whole numbers, zero, and negative whole numbers) divisible by 2 (with no remainder).

expanded notation Pointing out the place value of a digit by writing a number as the digit × its place value. For example, 342 = (3 × 102 ) + (4 × 101) + (2 × 10).

exponent A small number placed above and to the right of a number; expresses the power to which the quantity is to be raised or lowered.

factor (noun) A number or symbol that divides evenly into a larger number. For example, 6 is a factor of 24.

factor (verb) To find two or more quantities whose product equals the original quantity.

fraction symbol that expresses part of a whole and consists of a numerator and a denominator; for example, 3/5.

greatest common factor The largest factor common to two or more numbers.

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.

improper fraction A fraction in which the numerator is greater than the denominator; for example, 3/2.

independent events When the outcome of one event has no bearing or effect on the outcome of another event.

integer A whole number, either positive, negative, or zero.

invert Turn upside down, as in "invert 2/3 = 3/2."

irrational number A number that is not rational (cannot be written as a fraction x/y, with x a natural number and y an integer); for example, √3 or π.

least common multiple The smallest multiple that is common to two or more numbers.

lowest common denominator The smallest number that can be divided evenly by all denominators in the problem.

mean (arithmetic) The average of a number of items in a group (the total items divided by the number of items).

median The middle item in an ordered group. If the group has an even number of items, the median is the average of the two middle terms.

mixed number A number containing both a whole number and a fraction; for example, 5½.

mode The number appearing most frequently in a group.

multiples Numbers found by multiplying a number by 2, by 3, by 4, and so on.

multiplicative inverse The reciprocal of a number. Any number multiplied by its multiplicative inverse equals 1.

natural number A counting number; 1, 2, 3, 4, and so on.

negative number A number less than 0.

number series A sequence of numbers with some pattern. One number follows another in some defined manner.

numerator The top symbol or number of a fraction.

odd number An integer not divisible by 2.

operation Multiplication, addition, subtraction, or division.

order of operations The priority given to an operation relative to other operations. For example, multiplication is performed before addition.

parentheses Grouping symbols ( ).

percent or percentage A common fraction with 100 as its denominator. For example, 37% is 37/100.

permutations The total number of dependent choices.

place value The value given a digit by the position of a digit in the number.

positive number A number greater than zero.

power A product of equal factors. 4 × 4 × 4 = 43, reads "four to the third power" or "the third power of four." Power and exponent are some× used interchangeably.

prime number A number that can be divided by only itself and one.

probability The numerical measure of the chance of an outcome or event occurring.

product The result of multiplication.

proper fraction A fraction in which the numerator is less than the denominator; for example, 2/3.

proportion Written as two equal ratios. For example, 5 is to 4 as 10 is to 8, or 5/4 = 10/8.

quotient The result of division.

range The difference between the largest and the smallest number in a set of numbers.

ratio A comparison between two numbers or symbols; may be written x:y, x/y, or x is to y.

rational number An integer or fraction such as 7/8 or 9/4 or 5/1. Any number that can be written as a fraction x/y with x a natural number and y an integer.

real number Any rational or irrational number.

reciprocal The multiplicative inverse of a number. For example, 2/3 is the reciprocal of 3/2.

reducing Changing a fraction into its lowest terms. For example, 2/4 is reduced to 1/2.

rounding off Changing a number to the nearest place value as specified; a method of approximating.

scientific notation A number between 1 and 10 and multiplied by a power of 10, used for writing very large or very small numbers; for example, 2.5 × 104.

square The result when a number is multiplied by itself.

square root A number that when multiplied by itself gives you the original number; its symbol is √. For example, 5 is the square root of 25; √25 = 5.