The Distributive property of integers

The Distributive property of integers affects when multiplication and summation operations are performed together. 
The Distributive property of integers indicates distribution of operations means the answer of multiplication operation performed after the summations and the answer of multiplication operation performed before the summations are equal. 
The Distributive property of integers can be represented as following

a (b + c) = ab + ac

OR

a x (b + c) = (a x b) + (a x c)

For example,

If a = 5, b = 3 and c = 7

Then 5 x (3 + 7) = 50 and (5 x 3) + (5 x 7) = 50

So, 5 x (3 + 7) = (5 x 3) + (5 x 7) as 50 = 50

Another example,

If a = 5, b = -3 and c = 7

Then 5 x ((-3) + 7) = 20 and (5 x (-3)) + (5 x 7) = 20

So, 5 x ((-3) + 7) = (5 x (-3)) + (5 x 7) as 20 = 20

Associative property of mathematical multiplication of integers

The associative property of mathematical multiplication of integers says that any order of grouping of numbers in multiplication results into same answer. 
The associative property of mathematical multiplication of integers can be represented as following

(ab)c = a(bc)

OR

(a x b) x c = a x (b x c)

To understand associative property of mathematical multiplication of integers we can try multiplying numbers in different orders and note the results. 
For example,

If a = 5, b = 3 and c = 7

Then (5 x 3) x 7 = 105 and 5 x (3 x 7) = 105

So, (5 x 3) x 7 = 5 x (3 x 7) as 105 = 105

 
Another example,

If a = 5, b = -3 and c = 7

Then (5 x (-3)) x 7 = -105 and 5 x ((-3) x 7) = -105

So, (5 x (-3)) x 7 = 5 x ((-3) x 7) as -105 = -105

Associative property of mathematical addition of integers

The associative property of mathematical addition of integers says that any order of grouping of numbers in addition/summation results into same answer. 
The associative property of mathematical addition of integers can be represented as following

(a + b) + c = a + (b + c)

To understand associative property of mathematical addition of integers we can try adding numbers in different orders and note the results. 
For example,

If a = 5, b = 3 and c = 7

Then (5 + 3) + 7 = 15 and 5 + (3 + 7) = 15

So, (5 + 3) + 7 = 5 + (3 + 7) as 15 = 15

 
Another example,

If a = 5, b = -3 and c = 7

Then (5 + (-3)) + 7 = 9 and 5 + ((-3) + 7) = 9

So, (5 + (-3)) + 7 = 5 + ((-3) + 7) as 9 = 9

Commutative property of mathematical multiplication of integers

The commutative property of mathematical multiplication of integers says that multiplication of numbers in any order results into same answer.
In other words we can multiply numbers in any order without changing the result. 
The commutative property of mathematical multiplication of integers can be represented as following

ab = ba

OR

a x b = b x a

To understand commutative property of mathematical multiplication of integers we can try multiplying numbers in different orders and note the results. 
For example,

If a = 5 and b = 3

Then 5 x 3 = 15 and 3 x 5 = 15

So, 5 x 3 = 3 x 5 as 15 = 15

Another example,

If a = 9 and b = (-5)

Then 9 x (-5) = (-45) and (-5) x 9 = (-45)

So, 9 x (-5) = (-5) x 9 as (-45) = (-45)

Commutative property of mathematical addition of integers

The commutative property of mathematical addition of integers says that addition/summation of numbers in any order results into same answer. 
The commutative property of mathematical addition of integers can be represented as following

            a + b = b + a

To understand commutative property of mathematical addition of integers we can try adding numbers in different orders and note the results. 
For example,

If a = 5 and b = 3

Then 5 + 3 = 8 and 3 + 5 = 8

So, 5 + 3 = 3 + 5 as 8 = 8

           

Another example,

If a = 9 and b = (-5)

Then 9 + (-5) = 4 and (-5) + 9 = 4

So, 9 + (-5) = (-5) + 9 as 4 = 4