Lesson 2: Percentages
Percent means 'per hundred.' Percentages describe parts of a whole, changes over time, and comparisons. They're essential for test scores, discounts, tips, taxes, and statistics.
Key Concepts
Converting Between Forms
Percent ↔ Decimal: divide by 100 (move decimal 2 left). 75% = 0.75. Decimal ↔ Fraction: 0.75 = 75/100 = 3/4. To find a percent: (part/whole) × 100.
Finding the Percent
What percent of 80 is 20? (20/80) × 100 = 25%. What is 30% of 150? 0.30 × 150 = 45. Finding the whole: 24 is 40% of what? 24/0.40 = 60.
Percent Change
(new − old) / old × 100. Increase: new > old → positive %. Decrease: new < old → negative %. Example: price went from $50 to $65. Change = (65-50)/50 × 100 = 30% increase.
Real Applications
Sales tax: price × tax rate. Discount: price × (1 − discount rate). Tip: bill × tip rate. Grade: (points earned / total points) × 100.
🔬 Interactive Lab: Percentages Lab
✅ Check Your Understanding
1. What is 35% of 200?
2. A shirt costs $40 and goes on sale for $30. What is the percent decrease?
3. To convert a decimal to a percent, you: