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