For Commutative Property of Addition
Let us take a decimal number
and a fraction 
Now, according to the Commutative property of Addition:
For any two numbers
and
:

So, for
and 
Let us add


Also,


Therefore, 
Hence, Commutative Property of Addition is satisfied.
For Associated Property of Addition
Let us take two same decimal numbers
,
and a fraction 
Now, according to the Associated property of Addition:
For any three numbers
,
and 

So, for
,
and 
The Left hand side:







The Right hand side:






Thus,

Therefore, 
Hence, Associative Property of Addition is satisfied.