The properties of multiplication and division are an easier way when making calculations.
Let's see an example for each one.
Mutiplication:
Suppose we are going to multiply:

It is easier to make the product using the distributive property:

Division:
Suppose we have the following division:

By properties of the division, we know that this division is not defined.
Therefore, when we see a division between 0, we know that the answer is that it is not defined.
Answer:
The rules of multiplication and division help to divide and multiply in a faster way.