How 100/96 became 25/24?

Tim, by dividing by 4 to reduce both the denominator and numerator. 100/4 = 25, and 96/4 = 24.
Hence, ¹⁰⁰⁄₉₆ = ²⁵⁄₂₄

What is the rule when 1/(96/100) changes to 1*(100/96)?

Can you give another example?

BM, I suppose there is some Latin derived name, but I just call it the "flip it upstairs" rule. If you divide something by a fraction, flip the fraction and multiply instead of dividing by it. An example is: divide by 2 is the same as multiplying by 1/2. But, divide by half or 1/2 is the same as multiplying by 2. It's something worth keeping in mind.

I think we can simplify the mathematical fomura.

.2 is 0.2 so it means 1/5.

1/5^2 is 1/25.

1-1/25=25/25-1/25=24/25

and reverse the denominator and numerator.

It will be 25/24.