**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 × 10^{2} ) + (4 × 10^{1}) + (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 = 4^{3}, 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.

**sum** The result of addition.

**tenth** The first decimal place to the right of the decimal point. For example, .7 is seven-tenths.

**weighted mean** The mean of a set of numbers that have been weighted (multiplied by their relative importance or × of occurrence).

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