Percent of a Number

To find a percent of something, turn the percent into a decimal and multiply. 18% of 45 is 0.18 × 45 = 8.1.

Mental shortcuts that pay off constantly:

• 10% is moving the decimal one place left. 10% of 68 is 6.8.
• 5% is half of 10%.
• 1% is moving the decimal two places left.
• 20% is double 10%.

So a 15% tip on $42: 10% is $4.20, half of that is $2.10, add them for $6.30.

The percent relationship has three quantities and one equation:

part = rate × whole

Every percent question is one of these three unknown. Finding the part is direct multiplication. Finding the rate is rate = part/whole. Finding the whole — the type most often set up wrong — is whole = part/rate: if 30 is 24% of a number, that number is 30/0.24 = 125.

Combined percents multiply rather than add, and the multiplier form makes this obvious. A 20% discount followed by 8% tax is 0.80 × 1.08 = 0.864 of the original, not 12% off. Multipliers also commute, which is the honest answer to whether the shop applies the discount or the tax first: it does not change the total.