Properties of integers

1.  Commutative Property of Addition


Adding integers will have the same result regardless of the arrangement of the integers.


Commutative Property of Addition

Example 1
 Yes

Explanation:

2 + 6 = 8

6 + 2 = 8

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

Example 2
 4 + 3

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..


Commutative Property of Multiplication

The sum will not change even if the integers are grouped differently.


Example 1
 Yes

Explanation:

3 x 5 = 15

5 x 3 = 15

By Commutative Property of Multiplication:

3 x 5 = 5 x 3

Example 2
 6 x 4

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.


Associative Property of Addition

The sum will not change even if the integers are grouped differently.
Example 1
 Yes

Explanation:

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

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

By Associative Property of Addition:

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

Example 2
 (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.


Associative Property of Multiplication

The product will not change even if the integers are grouped differently.


Example 1
 Yes

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

Example 2
 (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.


Integer

Each integer inside the parenthesis is multiplied by the integer outside the parenthesis, then the resulting products are added together.


Example 1
 Yes

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)

Example 2
 (4 x 2) + (4 x 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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