Percentage Calculations in Everyday Life: Tips, Tricks, and Common Mistakes

Percentage Fundamentals

A percentage is a fraction expressed as a part of 100. The word comes from the Latin per centum, meaning "by the hundred." When you say "25%," you mean 25 out of every 100, or the fraction 25/100, or the decimal 0.25.

The three basic percentage calculations are:

• Finding a percentage of a number: What is 15% of 200? Multiply 200 x 0.15 = 30.
• Finding what percentage one number is of another: 30 is what percent of 200? Divide 30 / 200 = 0.15 = 15%.
• Finding the original number when you know a percentage: 30 is 15% of what number? Divide 30 / 0.15 = 200.

Common Percentage Problems

Tipping

To calculate a 15% tip, move the decimal point one place left (that gives 10%) and add half of that amount. For a $48 bill: 10% is $4.80, half of that is $2.40, so 15% is $7.20. For 20%, just double the 10% figure: $9.60.

Discounts

A 30% discount on an $80 item: multiply 80 x 0.30 = $24 off, so you pay $56. For quick mental math, if the discount is a round number, calculate 1% and multiply. 1% of $80 is $0.80, so 30% is $24.

Sales Tax

Tax is calculated on the pre-tax price, then added. For a 7.5% tax rate on a $40 purchase: 40 x 0.075 = $3.00 in tax, total is $43.00.

Markup vs. Margin

These are frequently confused. Markup is the percentage added to cost to get the selling price. If you buy for $100 and sell for $150, the markup is 50%. Margin is the profit as a percentage of the selling price: $50 / $150 = 33.3%. A 50% markup does not mean a 50% profit margin.

Mental Math Tricks

• 10% is just moving the decimal. 10% of $65 = $6.50. From there, 5% is half of 10%, and 20% is double 10%.
• To find 1%, move the decimal two places. 1% of $250 = $2.50. Now you can find any percentage: 3% = 3 x $2.50 = $7.50.
• Percentages work both ways. 8% of 25 is the same as 25% of 8. Both equal 2. This trick is useful when one calculation is clearly easier than the other.
• Approximate with friendly numbers. Need 18%? Calculate 20% and subtract 10% of that result. Need 16%? Use 15% (10% + half of 10%) and add a little.

Percentage Change vs. Percentage Of

This is one of the most common sources of confusion. If a price goes from $100 to $120, that is a 20% increase ($20 is 20% of the original $100). If it then drops from $120 back to $100, that is a 16.67% decrease ($20 is 16.67% of $120). The dollar amount is the same, but the percentages differ because the base (denominator) changed.

Common Mistake: Adding Percentages

You cannot simply add percentages that have different bases. If your salary increases by 10% one year and 10% the next, the total increase is not 20%. It is 21%, because the second 10% is applied to the already-increased amount. Similarly, a 20% discount followed by another 20% discount is not a 40% discount. The combined discount is 36%.