# 3 Techniques to Improve Commutative Property

Commutative Property, Associative Property, and Distributive Property are three basic properties in math that will help you to increase your speed of computation.

## Commutative Property:

If you solve any expression and you get the same result irrespective of the order of operation then the property is commutative.

### Commutative Property of : Addition

Say if I give you 2 chocolates and then I give you 1 chocolate now in total you have 3 chocolates. Instead, if I give you 1 chocolate first and then I give you 2 chocolates later still you have 3 chocolates.

This means though the order of adding chocolates was different, you always had 3 chocolates

Conclusion: a + b = b + a

This is called the commutative property of addition.

## Subtraction:

Let’s take the same example of chocolates if you have 5 chocolates and you give away 3 chocolates then you have 2 chocolates left with you but if you have 3 chocolates and you give 5 chocolates, it means you had none left with you and had to borrow two chocolates.

This means in case of subtraction order matters,

Here 5 -3 =2 and 3 – 5 = -2

Conclusion: a-b is not equal to b – a

## Multiplication:

The commutative property of multiplication states that changing the order of the factors does not change the resulting product,

Say you have 3 sets of boxes have 5 chocolates in each box. This means you have a total of 3 X 5 = 15 chocolates.

Let’s do it the other way, if you have 5 sets of boxes with 3 chocolates in each box then in total you have 5 X 3 = 15 chocolates

So, in multiplication order doesn’t matter. Hence it is commutative.

Conclusion: a x b = b x a

## Division:

Division doesn’t satisfy the commutative property.

If I have 6 chocolates and want to divide it between 2 friends, each o them will get 6/2 = 3 chocolates but if I have 2 chocolates and have to divide it between 6 friends then each will get 2/6 = 1/3 = 0.33. Each chocolate has to be shared between 3 friends.

Conclusion: a/b is not equal to b/a

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