Percent, Ratio, and Proportion
What you must know
Percent means "per hundred": 45% = 45/100 = 0.45. You should convert among fractions, decimals, and percents, find a percent of a number, find what percent one number is of another, and solve proportions of the form a/b = c/d by cross-multiplying.
Common traps
- Percent increase vs. of: "20% of 50" is 10, but "50 increased by 20%" is 60. Read the wording carefully.
- Percent change: Change = (new − old)/old × 100. A price going from 40 to 50 is a 25% increase, not 10%.
- Reverse percent: If 30 is 60% of a number, the number is 30 ÷ 0.6 = 50, not 30 × 0.6.
- Ratio order: In a ratio of boys to girls of 3:2, the boys' share is 3 parts out of 5 total, not 3 out of 2.
- Proportion setup: Match units in the same positions on both sides before cross-multiplying.
Worked example
A jacket costs $80 and is discounted 15%. Find the sale price. Discount = 0.15 × 80 = $12, so the price is 80 − 12 = $68. Equivalently, pay 85% of the price: 0.85 × 80 = $68.
Rule of thumb
Translate percent problems into an equation: part = percent × whole. Then solve for whichever quantity is missing.