When you divide a by a percentage of a, you are essentially trying to find out what the percentage of a represents in terms of the value of a.
The percentage of a is represented by the formula (a * x%)/100, where x is the percentage. So if you divide a by (a * x%)/100, you get the following:
a / (a * x%)/100 = 100/x%
This is the equivalent of multiplying a by 100/x%. It's the representation of the percentage in terms of the value of a.
For example:
If a = 100 and x = 20, then a% of a is (10020)/100 = 20. So, a / (a20%) = 100/20 = 5
It means that 20% of 100 is 20 and dividing 100 by 20% of 100 is equal to 5.
Hopefully that helped and didn't make it more confusing.