addendA number added to one or more numbers to form a sum.
addition property of 0The sum of any number and 0 is equal to that number. The number 0 is often called the additive identity.
associative law of additionFor three or more numbers, the sum is the same regardless of how you group the numbers. For example, (6 + 2) + 1 = 6 + (2 + 1).
associative law of multiplication

For three or more numbers, the product is the same regardless of how you group the numbers. For example, 3 • (5 • 7) = 3 • (5 • 7).

base

In a percent problem, the base represents how much should be considered 100% (the whole); in exponents, the base is the value that is raised to a power when a number is written in exponential notation. In the example of 53, 5 is the base.

commutative law of additionTwo numbers can be added in any order without changing the sum. For example, 6 + 4 = 4 + 6.
commutative law of multiplication

Two numbers can be multiplied in any order without changing the product. For example, 8 • 9 = 9 • 8.

cubing

Raising a number to a power of 3. 23 is read “2 to the third power” or “2 cubed,” and means use 2 as a factor three times in the multiplication. 23 = 2 • 2 • 2 = 8.

differenceThe quantity that results from subtracting one number from another, or from subtracting the subtrahend from the minuend.
digitOne of the symbols 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.
distributeTo rewrite the product of the number and a sum or difference using the distributive property.
distributive property of multiplication over additionThe product of a number and a sum is the same as the sum of the product of the number and each of the addends making up the sum. For example, 3(4 + 2) = 3(4) + 3(2).
distributive property of multiplication over subtractionThe product of a number and a difference is the same as the difference of the product of the number and each of the numbers being subtracted. For example, 8(10 – 2) = 8(10) – 8(2).
dividend

The number to be  divided up in a division problem. In the problem 8 ÷ 2 = 4, 8 is the dividend.

divisor

The number that is being divided into the dividend in a division problem. In the problem 8 ÷ 2 = 4, 2 is the divisor.

estimateAn answer to a problem that is close to the exact number, but not necessarily exact.
expanded form

A way to write a number as a sum of the value of its digits. For example, thirty-two is written in expanded form as 30 + 2, or 3 tens + 2 ones, or (3 • 10) + (2 • 1).

exponent

The number that indicates how many times the base is used as a factor. In the example of 53, 3 is the exponent and means that 5 is used three times as a factor: 5 • 5 • 5.

exponential notation

A notation that represents repeated multiplication using a base and an exponent. For example, 24 is notation that means 2 • 2 • 2 • 2. This notation tells you that 2 is used as a factor 4 times. 24 = 16. (Also called exponential form.)

expression

A mathematical phrase. For example, 8 • 2 + 3 is an expression. It represents the quantity 19.

factor

A number that is multiplied by another number or numbers to get a product. For example, in the equation 4 • 5 = 20, 4 and 5 are factors.

grouping symbolsSymbols such as parentheses, braces, brackets, and fraction bars that indicate the numbers to be grouped together.
inequalityA mathematical sentence that compares two numbers that are not equal.
inverse operationA mathematical operation that can reverse or “undo” another operation. Addition and subtraction are inverse operations. Multiplication and division are inverse operations.
minuendThe number from which another number is subtracted.
multiplication property of 1The product of any number and 1 is equal to that number. The number 1 is often called the multiplicative identity.
operationA mathematical process; the four basic operations are addition, subtraction, multiplication, and division.
order of operationsThe rules that determine the sequence of calculations in an expression with more than one type of computation.
perfect square

A whole number that can be expressed as a whole number raised to a power of 2. For example, 25 is a perfect square because 25 = 5 • 5 = 52.

perimeterThe distance around a two-dimensional shape.
periodEach group of three digits in a number separated by a comma.
place valueThe value of a digit based on its position within a number.
place-value chartA chart that shows the value of each digit in a number.
polygonA closed plane figure bounded by three or more line segments.
product

The result when two numbers are multiplied. For example, the product of 4 • 5 is 20.

quotient

The result of a division problem. In the problem 8 ÷ 2 = 4, 4 is the quotient.

radical sign

The symbol used for square root and other roots. It looks like  and the number is written under it. For example, the square root of nine is written with the radical sign:

raised to the power

When a base has an exponent, it can be said that the base is “raised to the power” of the exponent. For example, 35 is read as “3 raised to the 5th power.”

regroupRewriting a number so you can subtract a greater digit from a lesser digit.
remainder

The amount left over after dividing a number. In the problem 11 ÷ 4 = 2 R3, 3 is the remainder.

roundingFinding a number that’s close to a given number, but is easier to think about.
square root

A value that can be multiplied by itself to give the original number. For example if the original number is 9, then 3 is its square root because 3 multiplied by itself (32, pronounced "3 squared") equals 9. The symbol used for a square root is called a radical sign and goes on top of the number. The square root of 9 is written as.

squaring

Multiplying a number by itself, or raising the number to a power of 2. 82 can be read as “8 to the second power,” “8 to a power of 2,” or “8 squared.”

standard formA way to write a number using digits. For example, thirty-two is written in standard form as 32.
subtrahendThe number that is subtracted from another number.
sumThe result when two or more numbers are added; the quantity that results from addition.
whole numberAny of the numbers 0, 1, 2, 3, and so on.