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Adding and multiplying percents

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Adding and Multiplying Percentages

Adding and multiplying percentages: add percents when they are parts of the same whole, and multiply a percent of a percent by changing each to a decimal first. Includes worked examples and the successive-discount trap.

Adding percentages

You can add percentages when they are parts of the same whole. For example, if a bill has 13% tax and you add a 15% tip on the same amount, together that is 13% + 15% = 28% of the bill. The rule is simple: as long as every percent refers to the same total, you just add the numbers. Adding is common with taxes and tips — see taxes, discounts and tips.

You multiply percentages when you take a percent of another percent. The trick is to change each percent to a decimal first, then multiply:

Multiplying percentages 50% of 20%the question 0.5 × 0.2as decimals = 10%0.10 = 10%
How to multiply percentages: change each percent to a decimal and multiply.

So 50% of 20% is 0.5 × 0.2 = 0.10, which is 10%. If you can already find a percent of a number, this is the same idea applied to a percent. Converting fluently between forms helps — review percents, fractions and decimals.

  • Add: 8% + 6% of the same price = 14% of that price.
  • Multiply: 25% of 40% = 0.25 × 0.40 = 0.10 = 10%.
  • Multiply: 30% of 30% = 0.30 × 0.30 = 0.09 = 9%.

A store offers 20% off, then another 10% off at the register. That is not 30% off. The second discount applies to the already-reduced price, so you multiply: after 20% off you pay 80% (0.80), then 10% off leaves 90% (0.90), and 0.80 × 0.90 = 0.72. You pay 72% of the original, which is only 28% off — not 30%.

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