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# Integers

## Associative, commutative, identity, and inverse properties with positive and negative numbers

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Practice Integers
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Identify and Apply Number Properties in Integer Operations

### Vocabulary Language: English

The sum of any number and zero is the number itself.

The additive inverse or opposite of a number x is -1(x). A number and its additive inverse always sum to zero.
Associative Property

Associative Property

The associative property states that you can change the groupings of numbers being added or multiplied without changing the sum. For example: (2+3) + 4 = 2 + (3+4), and (2 X 3) X 4 = 2 X (3 X 4).
Commutative Property

Commutative Property

The commutative property states that the order in which two numbers are added or multiplied does not affect the sum or product. For example $a+b=b+a \text{ and\,} (a)(b)=(b)(a)$.
distributive property

distributive property

The distributive property states that the product of an expression and a sum is equal to the sum of the products of the expression and each term in the sum. For example, $a(b + c) = ab + ac$.
Multiplicative Identity

Multiplicative Identity

The multiplicative identity for multiplication of real numbers is one.
Zero Property

Zero Property

The zero property of multiplication says that the product of any number and zero is zero. The zero property of addition states that the sum of any number and zero is the number.