I have a set of percents, as decimals, like this:
$0.07, 0.12, 0.01, 0.20, 0.30, 0.10, 0.15, 0.05$
Now, if I, say, increase the first one from $0.07$ to $0.17$, and leave the other values alone, it obviously all does not add up to $1$. My question is, after I’ve increased the first percent, how can I get the others to add up to one without manually setting each one to a different value to make them add to $1$?
I’ve tried: Subtracting $0.17$ from $1$ to get $0.83$, then proportioning every other percentage based on $0.83$. For example, I would do: $12 \cdot {0.83\over 100}$ to get the new percent as a decimal (from $0.12$) to be $0.0996$. This would be done for every percent in my list except for the first one. The problem is, after I’ve done this for every percent except the first one and I add them all together (first one included), it does not add to $1$. Sorry if the question is hard to understand, I couldn’t really think of a clear way to explain my problem.
The other terms (i.e. excluding the first $0.07$) add up to $1-0.07=0.93$.
After increasing the first term to $0.17$, you want those other terms to add up to $1-0.17=0.83$ instead.
Therefore you could multiply all those other terms by $\frac{0.83}{0.93}$.