Whole Numbers

A number whose value is 0 or greater (negative numbers are not considered whole numbers) and can be represented without a fractional or a decimal component.

Integers

A number (positive, negative, or zero) that can be represented without a fractional or a decimal component.

rational number

Any number that can be represented as a fraction of two integers. Equivalently, any number which has a decimal that either terminates or repeats.

real numbers

Any numbers on the number line. Real numbers include zero, negative and positive integers, rational numbers, and even numbers that are not rational (such as π).

set

In Mathematics: a set is a collection of things, usually numbers. You'll see some sets that aren't numbers later in the text.

Discrete data

A collection of numbers whose values are distinct, separate, and unconnected.

Continuous

A collection of numbers whose values are not divisible into distinct units.

interval

A set of numbers between two specified values.

identity property

The property that 0 can be added to any number without changing the value of the number. Likewise, 1 can be multiplied by any number without changing the value of that number.

additive inverse

Two numbers equidistant from 0 on a number line whose sum is 0. 3 and -3 are additive inverses.

commutative

The property that the order of the numbers under the operation does not change the result. Addition and multiplication are commutative: a + b = b + a and ab = ba.

factor

An integer that evenly divides a larger number

Fundamental Theorem of Arithmetic

A concept which states that any integer greater than 1 is either prime, or is the product of a unique set of prime numbers.

PEMDAS

prime factorization

Determining the set of prime numbers whose product is the original integer.

greatest common factor (GCF)

The greatest common factor of any two integers a and b is the greatest number that is both a factor of a and a factor of b.

square root

A number that produces a specified number when it is multiplied by itself.

principal square root

negative square root

The positive square root of a perfect square. For example, the principal square root of 36 is 6.

The negative number that equals the given number when squared. For example, -6 is the negative square root of 36.

radical sign

radicand

The sign √ which indicates the square root of the number that follows.

The number under or after the radical sign √ which is having its square root taken. The radicand of √ 4 is 4.

Equivalent fractions

Different fractions that represent the same value

least common multiple (LCM)

The smallest number in value that is a multiple of two or more numbers.

repeating decimal

terminal decimal

A decimal number that has either a digit, or sequence of digits, that repeat forever. A bar written over the top of the part of the decimal that repeats.

A decimal number that has a finite number of digits.

Equations for Temperature Conversion

To convert to Fahrenheit:

Temperature in degrees Fahrenheit=Celsius×9/5+32

To convert to Celsius:

Temperature in degrees Celsius=(Fahrenheit−32)×5/9

variable

A symbol that represents a mathematical value.

coefficient

A number by which a variable is being multiplied.

inverse operations

Two operations that undo one another.

like terms

Terms that have the same variable(s) with the same exponent(s). These terms can be "combined" using addition or subtraction.

degree

the largest exponent in an expression

coordinate plane

A tool used for graphing that is a display of a two dimensional plane. It consists of an x-axis and a y-axis; the x-axis being a horizontal number line, the y-axis is a vertical number line, and the axes meet at the origin (0,0).

slope-intercept form

A common format that a linear equation can take that is helpful for graphing purposes. It is of the form y = mx + b, where m is the slope of the line and b is the y-intercept.