8th Grade Properties and Law Vocabulary

Addition Property of Equality

If you add the same number to each side of an equation, the two sides remain equal.

Additive Inverse Property

The sum of a number and its opposite is zero.

Additive Identity Property

The sum of any number and zero is the number

Associative Property of Addition

Changing the grouping of three or more addends does not change the sum.

Associative Property of Multiplication

the grouping of the factors does not change the product

Closure Property of Addition

the sum of two real numbers is a real number

Closure Property of Multiplication

the product of two real numbers is a real number

Combine like Terms

Adding or subtracting terms that have the same variable(s) and exponent(s).

Commutative Property of Multiplication

Changing the order of the factors does not change the product.

Communitive property of multiplication

The order of the numbers in the expression does not change the product. (Property)

completeness property of points on the number line

Every non-empty set of real numbers bounded above has a least upper bound (supremum)

Distributive Property of Multiplication over Addition

when a number is multiplied by the sum of two or more addends, the result is the same as multiplying each addend individually by the number and then adding the products together

distributive property of multiplication over subtraction

when a number is multiplied by the difference of the products of the numbers and each of the two numbers

division property of equality

If you divide each side of an equation by the same nonzero number, the two sides remain equal.

law of exponents for division

same base subtract the exponents (A^m/A^n = A^m-n

law of exponents for multiplication

keep the same base and add the exponents (A^m x A^n = A^m+n)

law of negative exponents

A negative exponent indicates the reciprocal of the base raised to the positive exponent

Law of Zero exponent

a^0 = 1 When multiplying expressions with the same base, the exponents are added. This law simplifies the multiplication of like terms by adding their exponents.

multiplication property of equality

If you multiply each side of an equation by the same nonzero number, the two sides remain equal.

multiplicative identity property

The product of any number and one is the number

multiplicative Inverse Property

the product of a nonzero number and its reciprocal is 1

Order of Operations

the order in which operations in an expression to be evaluated are carried out. 1. parentheses 2. exponets 3. multiplication and divison 4. addition and subtraction

Scientific Notation

A method of writing or displaying numbers in terms of a decimal number between 1 and 10 multiplied by a power of 10.

Order of Operations

the order in which operations in an expression to be evaluated are carried out. 1. parentheses 2. exponets 3. multiplication and divison 4. addition and subtraction

Substitution Principle

In industry, the tendency to substitute one factor of production for another in order to achieve optimum plant location.

Subtraction Property of Equality

If you subtract the same number from each side of an equation, the two sides remain equal.