# Properties Of Integers

## About:

## Properties of Integer

1.Commutative property of addition

2.Commutative property of multiplication

3.Associative property of addition

4.Associative property of multiplication

5.Distributive property

## Commutative property of addition

The commutative property of addition says that we can add numbers in any order.

The example shows us that "negative three plus positive four" is the same as "positive four plus negative three."

**-3 + 4 = 4 + (-3)**

## Commutative property of multiplication

The commutative property of multiplication is very similar. It says that we can multiply numbers in any order we want without changing the result.

The example shows us that "negative three times positive four" is the same as "positive four times negative three."

**-3(4) = 4(-3)**

## Associative property of addition

The associative property of addition tells us that we can group numbers in a sum in any way we want and still get the same answer.

You can remember the associative property by thinking of two numbers associating with each other, and then one leaves to associate with another number.

The example shows us that we can either add "negative 5 and positive four" together and then add that sum to positive three to get the final answer, or we can add "positive four and positive three" together first and then add that sum to negative five to get the final answer. The answer will be the same no matter which way we do it.

**(-5 + 4) + 3 = -5 + (4 + 3)**

## Associative property of multiplication

We can group numbers in a product in any way we want and still get the same answer.

The example shows us that we can either multiply "negative five and positive four" together and then multiply that product times positive three to get the final answer, or we can multiply "positive four and positive three" together first and then multiply that product times negative five to get the final answer. The answer will be the same no matter which way we do it.

**-5(4) x 3 = -5(4 x 3)**

## Distributive property

When an expression involving addition is then multiplied by something, it tells us that we can add first and then multiply, or multiply first and then add. Either way, the multiplication is "distributed" over all the terms inside the parentheses.

In the example, we can either add the numbers inside the parentheses first ( **4+3** ) and then multiply the result by **-5**; or, we can multiply the -5 and each term separately and then add the two products together. The answer is the same in both cases.

**-5(4 + 3) = (-5 x 4) + (-5 x 3)**

Subtraction is neither commutative nor associative.

Division is neither commutative nor associative.