percent

A percent is a fraction whose denominator is 100. 15% means 15 out of 100, which as a decimal is 0.15, and taking 15% of 200 is 0.15 × 200 = 30. Converting between the three forms — percent, decimal, fraction — is the arithmetic that sits under almost every word problem on this subtest, so it is worth being able to do in either direction without stopping to think.

The moves to know: percent to decimal, divide by 100; decimal to percent, multiply by 100; percent of a number, multiply by the decimal. A discount is the percent of the price subtracted from it, a tip is the percent amount added on, and sales tax is the same move again on a subtotal.

The two changes that catch people out: a percent change is measured against the value you started from, so it is (new − old) ÷ old, and two percent changes in a row are multiplied rather than added — a 40% rise followed by a 25% fall is × 1.40 × 0.75, which is 1.05, not the 1.15 that adding them would give.