# How much of the total is percentage after a percentage?

Imagine we have a pie and let $p,q$ be ratios between 0 and 1 (non-inclusive). If I first take $p$ out of the pie, and then $q$ out of the remainder, how much is that of the whole pie?

I can easily visualize that if $p=0.5$ so I take half of the pie, and then take again $q=0.5$ of the remainder, I will have taken a total of 0.75 of the pie. But how do I compute this in general for any $p$ and $q$?

• After you take out $p$, how much is left? After you take $q$ of what's left, how much have you taken in total? – NickD Jul 26 '18 at 19:46

The rule you want is $$pq$$ when you take fraction $p$ and then fraction $q$ of what you just took.
In your problem you take $p$ of the pie and then $q$ from what's left over so your total is $$p + (1-p)q .$$