Out of a Hundred: Percentages
Percentages express a number as a fraction of 100, making it easy to compare parts of different-sized wholes on the same scale. From test scores and sales tax to discounts and tips, percentages are one of the most frequently used math concepts in everyday life and a stepping stone to proportional reasoning in algebra.
Components of Percentages
This section covers the main percentage skills:
- Finding a Percent of a Number: Multiply the number by the percent written as a decimal (e.g., 25% of 80 = 0.25 × 80).
- Finding What Percent One Number Is of Another: Divide the part by the whole and multiply by 100.
- Percent Increase & Decrease: Calculate how much a value has grown or shrunk, expressed as a percentage of the original.
- Applications of Percentages: Tips, taxes, discounts, commissions, and interest calculations.
Examples of Percentages
Finding a Percent of a Number Examples
- Find 30% of 150: Convert 30% to 0.30, then 0.30 × 150 = 45.
- Find 8% of 250: Convert 8% to 0.08, then 0.08 × 250 = 20.
- A student scores 85% on a 40-question test. The number correct is 0.85 × 40 = 34 questions.
Finding What Percent Examples
- 15 out of 60 students play sports. Divide 15 ÷ 60 = 0.25, then 0.25 × 100 = 25%.
- A team wins 9 of 12 games. Divide 9 ÷ 12 = 0.75, so the win rate is 75%.
- You answered 42 out of 50 questions correctly. Divide 42 ÷ 50 = 0.84, so your score is 84%.
Percent Increase & Decrease Examples
- A shirt's price rises from $40 to $50. The increase is $10, so the percent increase is 10 ÷ 40 × 100 = 25%.
- A town's population drops from 8,000 to 7,200. The decrease is 800, so the percent decrease is 800 ÷ 8,000 × 100 = 10%.
- A stock price rises from $25 to $31.25. The increase is $6.25, so the percent increase is 6.25 ÷ 25 × 100 = 25%.
Applications Examples
- A meal costs $48.00 and you leave a 20% tip: 0.20 × 48 = $9.60 tip, for a total of $57.60.
- A jacket is marked $80 with a 15% discount: 0.15 × 80 = $12 off, so the sale price is $68.
- Sales tax is 7.5% on a $120 purchase: 0.075 × 120 = $9.00 in tax, for a total of $129.00.