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expanded form

A number written as the sum of the place values of its digits.

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exponential form

A way of writing repeated multiplication of a number using exponents.

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base (in numeration)

A number multiplied by itself the number of times shown by an exponent.

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exponent

The number that tells how many times the base is being multiplied by itself.

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power

The number of times a number is multiplied by itself.

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squared

A number that is multiplied by itself two times.

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cubed

A number that is multiplied by itself three times.

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expanded form using exponents

A number written in expanded form with the place values written in exponential form.

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round

To give an approximation for a number to the nearest one, ten, hundred, thousand, and so on.

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estimate

To find a number that is close to an exact answer.

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front-end estimation

A method of estimation using the first digits of each addend that have the same place value.

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front-end estimation with adjusting

A method of front-end estimation that adjusts the result based on the remaining digits of each addend.

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front-end estimation

An estimation method where numbers that are approximately equal are treated as if they were equal.

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compatible numbers

Numbers that are easy to compute mentally.

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range

The difference between the greatest and the least numbers in a set of data.

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order of operations

A set of rules mathematicians use to determine the order in which operations are performed.

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Commutative Properties

The properties that state the order of the addends or factors does not affect the sum of the products.

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Associative Properties

Properties that state the way in which addends or factors are grouped does not affect the sum or product.

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Identity Properties

The properties that state the sum of any number and zero is that number and the product of any number and one is that number.

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Multiplication Property of Zero

Property that states the product of any number and zero is zero.

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Distributive Property

Multiplying a sum by a number produces the same result as multiplying each addend by the number and adding the products.

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break apart

Using the Distributive Property to compute mentally.

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compensation

Choosing numbers close to the numbers in a problem, and then adjusting the answer to compensate for the numbers chosen.

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equal additions

Adding the same number to two numbers in a subtraction problem does not affect the difference.

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variable

A quantity that can change or vary, often represented by a letter.

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evaluate

To find the number that an algebraic expression names by replacing a variable with a given number.

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properties of equality

Properties that state performing the same operation to both sides of an equation keeps the equation balanced.

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inverse operations

Operations that "undo" each other, such as addition and subtraction, or multiplication and division (except multiplication by zero).

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equation

A mathematical sentence stating that two expressions are equal.

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