Maths Trick: Multiplication by 25

Welcome to the new year 2018. I promise inasmuch as possible to keep you busy with mathematics this year.
Let's learn some new tricks of multiplication. Particularly multiplication by 25.
You have only 3 simple steps to take.
1. First divide the number by2
2. Divide it again by 2 ( If you are a big boy divide straight by 4)
3. Now multiply the result by 100

Now let's go and give it a trial:
1. Multiply 25 by 72

72/2=36

36/2 =18

Then multiply by 100 =1800

That is the answer

2. Multiply 87 by 25

87/2 =43.5

43.5/2= 21.75

Now multiply by 100 gives 2175

Amazing that is your answer!

Can you reason why these are so?

Try as many numbers as possible following the rules.