Associative, Commutative, Distributive Properties

Associative Law for Addition states that:
For any 3 numbers a, b, and c:
(a + b) + c = a + (b + c)

Associative Law for Multiplication states that:
For any 3 numbers a, b, and c:
(a x b) x c = a x (b x c)

The Associative Law does not hold for Subtraction and Division

Commutative Law for Addition :

If a and b are any two integers, then

a + b = b + a

Commutative Law for Multiplication :

For any two integers a and b, we have

(a x b) = (b x a)

The Commutative Law does not hold good for Subtraction and Division

Subtraction: 5- 3 = 2

But 3 – 5 = -2

Or, a – b ≠ b – a

Division: 15 ÷ 5 = 3

But 5 ÷ 15 = 1/3

Or, a ÷ b ≠ b ÷ a

Distributive Law of Multiplication over Addition states that for any integers a, b, c, we have

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

OR

 (a x b) + (a x c) = a(b +c)

Distributive Law of Multiplication over Subtraction states that for any integers a, b, c, we have

a x (b – c) = (a x b) – (a x c)

 OR

 (a x b) - (a x c) = a(b – c)

a x (b + c) = (a x b) + (a x b) is called expanding

To solve any mathematical expression involving numerous additions and multiplications, following points will prove to be useful:

Try and rearrange the numbers in the expression such that their sum / product is a multiple of 10

After rearrangement, use the Commutative Law to group the compatible numbers

Add/multiply the numbers to get the desired results