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Percentages are not symmetrical, and this catches out more people than any other bit of everyday arithmetic.

A price that rises by 50 percent has to fall by about 33 percent to get back where it started. A stock down 50 percent needs to gain 100 percent to recover. The reason is that each percentage is taken from a different base — the increase from the old price, the decrease from the new one.

The same trap sits inside discounts. Two successive 20 percent reductions are not 40 percent off. They are 36 percent, because the second comes off the already-reduced price. Retailers know this. Shoppers generally do not.

Removing tax

Divide, do not subtract. To strip 17 percent tax from a gross figure, divide by 1.17. Subtracting 17 percent of the total gives you the wrong answer, and it is wrong in the direction that costs you money.

Margin is not markup

A 50 percent markup on cost produces a 33 percent margin on the selling price. They are different numbers describing the same transaction, and quoting one while calculating the other is where a surprising amount of pricing goes quietly wrong.

Markup is measured against what you paid. Margin is measured against what you charged.

Percent versus percentage points

Going from 5 percent to 10 percent is a rise of five percentage points and a 100 percent increase. Both statements are true, and headlines routinely pick whichever sounds more dramatic. When someone quotes a percentage change without saying which they mean, it is worth asking.

Always name the base

A percentage change is meaningless without knowing what it is a percentage of. Comparing two percentages taken from different bases is the most common way statistics mislead honestly — nobody is lying, and the comparison is still wrong.