# Properties of integers

## 1.  Commutative Property of Addition

Adding integers will have the same result regardless of the arrangement of the integers. ## Is 2 + 6 = 6 + 2 ?

#### Explanation:

2 + 6 = 8

6 + 2 = 8

By Commutative Property of Addition: 2 + 6 = 6 + 2

## By Commutative Property of Addition, 3 + 4 = ?

#### Explanation:

In Commutative Property of Addition, the integers on the other side are interchanged.

3 + 4 = 4 + 3

## 2.  Commutative Property of Multiplication

Multiplying integers will have the same result regardless of the arrangement of the integers.. The sum will not change even if the integers are grouped differently.

## Is 3 x 5 = 5 x 3?

#### Explanation:

3 x 5 = 15

5 x 3 = 15

By Commutative Property of Multiplication:

3 x 5 = 5 x 3

## By Commutative Property of Multiplication, 4 x 6 = ?

#### Explanation:

In Commutative Property of Multiplication, the integers on the other side are interchanged.

4 x 6 = 6 x 4

## 3.  Associative Property of Addition

Adding integers will have the same result regardless of the grouping. The sum will not change even if the integers are grouped differently.

## Is 1 + (4 + 6) = (1 + 4) + 6?

#### Explanation:

1 + (4 + 6) = 1 + 10 = 11

(1 + 4) + 6 = 5 + 6 = 11

1 + (4 + 6) = (1 + 4) + 6

## By Associative Property of Addition, 3 + (5 + 4) = ?

#### Explanation:

In Associative Property of Addition, the integers on the other side can be grouped differently.

3 + (5 + 4) = (3 + 5) + 4

## 4.  Associative Property of Multiplication

Multiplying integers will have the same result regardless of the grouping. The product will not change even if the integers are grouped differently.

## Is 3 x (5 x 6) = (3 x 5) x 6?

#### Explanation:

3 x (5 x 6) = 3 x 30 = 90

(3 x 5) x 6 = 15 x 6 = 90

By Associative Property of Multiplication:

3 x (5 x 6) = (3 x 5) x 6

## By Associative Property of Multiplication, 4 x (5 x 2) = ?

#### Explanation:

In Associative Property of Multiplication, the integers on the other side can be grouped differently.

4 x (5 x 2) = (4 x 5) x 2

## 5.  Distributive Property of Addition and Multiplication

Distributive property involves the addition of integers being multiplied by another integer. Each integer inside the parenthesis is multiplied by the integer outside the parenthesis, then the resulting products are added together.

## Is 2 x (1 + 3) = (2 x 1) + (2 x 3) ?

#### Explanation:

2 x (1 + 3) = 2 x 4 = 8

(2 x 1) + (2 x 3) = 2 + 6 = 8

By Distributive Property of Multiplication and Addition:

2 x (1 + 3) = (2 x 1) + (2 x 3)

## By Distributive Property of Addition and Multiplication, 4 x (2 + 3) = ?

#### Explanation:

In Distributive Property of Addition and Multiplication, each integer inside the parenthesis is multiplied by the integer outside the parenthesis, then the resulting products are added together.

4 x (2 + 3) = (4 x 2) + (4 x 3)

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