Percentages without the confusion
Percentages are the math people use most outside school and get wrong most often. Nearly all the mistakes are four mistakes, and all four take a minute to explain.
Removing a percentage isn't subtracting it
This is the expensive one. If a total already includes eleven and a half percent and you want the pre-tax price, you don't subtract eleven and a half percent from the total: you divide the total by one point one one five.
The reason is that the percentage was computed on the base price, not on the total. Subtracting it from the total computes it against a larger base and gives you a number lower than the right one. It's the same mistake small businesses make when they break out a tax-inclusive sale.
Stacked discounts don't add
Twenty percent off plus a ten percent coupon is not thirty percent off. The second discount applies to the already-reduced price, so what you save in total is less.
It works the other way too: a fifty percent increase followed by a fifty percent cut doesn't return you to the original price, it leaves you below it. The base changed between the two steps.
Percent versus percentage point
If a rate goes from four percent to six, it rose two percentage points — but it rose fifty percent. Both statements are correct and describe the same thing with very different numbers.
It's the favorite ambiguity of headlines and advertising. When someone tells you something “went up two percent,” it's worth asking two percent of what.
The three questions you actually ask
Almost everything you need fits in three questions: what is X percent of Y, what percent of Y is X, and how much did something change from X to Y. The percentage calculator has a mode for each, plus one for stripping out an included percentage.
If sales tax is involved, the IVU calculator already has the combined rate loaded and works in both directions, which is faster than doing it by hand and won't let you forget which base goes on the bottom.