Tax difference on dollar amounts? Why is it that on all my calculators, when I subtract 12% from $56$, I get $49.28$, but when I add 12% to $50$, I get $56$?
 A: The difference is in what exactly you are calculating 12% of.
In the first case, you found 12% of 56 which is 6.72.
In the second case, you found 12% of 50 which is 6.
A: Because $12\%$ of $50$ is $\frac{12}{100}\cdot 50=6$, whereas $12\%$ of $56$ is $\frac{12}{100}\cdot 56=6.72$.
A: This is easier to understand with a more extreme example. Suppose you are earning \$100/hour and get a 50% raise. Then you're earning \$150/hour. If that's followed by a 50% pay cut you're only making \$75/hour.
It's just as bad if the pay cut comes first (down to \$50/hour) followed by the pay raise (up to \$75/hour, but not all the way to \$100/hour).
The best way to do these percentage problems is by multiplying rather than adding and subtracting. In your case 12% off means "multiply by 0.88" since there's 88% remaining. Then a 12% increase means "multiply by 1.12". Overall, your change is 0.88 * 1.12 = 0.9856, which is less than 1.
Edit: I seem to have answered this question once before, at
Finding total after percentage has been used?. I like that answer better than this one.
