Percent of Change
Percent change measures how much something increases or decreases compared to the original value. Master this essential skill for understanding sales, price changes, population growth, discounts, and statistics!
Concept
Percent of change helps you compare changes in a meaningful way! **WHAT IS PERCENT OF CHANGE?** Percent of change tells you how much a quantity increased or decreased as a percentage of the original amount. **THE FORMULA:** Percent of Change = (Amount of Change / Original Amount) × 100% OR Percent of Change = ((New Value - Original Value) / Original Value) × 100% **TWO TYPES:** **1. PERCENT INCREASE** When the new value is GREATER than the original: - Formula: ((New - Original) / Original) × 100% - Result is POSITIVE - Example: Price rises from $20 to $25 - Change: $25 - $20 = $5 - Percent increase: (5/20) × 100% = 25% **2. PERCENT DECREASE** When the new value is LESS than the original: - Formula: ((Original - New) / Original) × 100% - Often expressed as positive percentage - Example: Price drops from $80 to $60 - Change: $80 - $60 = $20 - Percent decrease: (20/80) × 100% = 25% **STEP-BY-STEP PROCESS:** **Step 1:** Identify original and new values **Step 2:** Find the amount of change - Increase: New - Original - Decrease: Original - New **Step 3:** Divide change by ORIGINAL **Step 4:** Multiply by 100 to get percent **Step 5:** Label as increase or decrease **DETAILED EXAMPLES:** **Example 1: Store Discount** Original price: $60 Sale price: $45 Change: $60 - $45 = $15 (decrease) Percent decrease: (15/60) × 100% = 0.25 × 100% = 25% Answer: 25% decrease **Example 2: Population Growth** Original population: 8,000 New population: 10,400 Change: 10,400 - 8,000 = 2,400 (increase) Percent increase: (2,400/8,000) × 100% = 0.30 × 100% = 30% Answer: 30% increase **Example 3: Test Scores** Original score: 75 New score: 90 Change: 90 - 75 = 15 (increase) Percent increase: (15/75) × 100% = 0.20 × 100% = 20% Answer: 20% improvement **FINDING NEW VALUE FROM PERCENT CHANGE:** If you know the percent increase: New Value = Original × (1 + percent as decimal) Example: Increase $200 by 15% New Value = 200 × (1 + 0.15) = 200 × 1.15 = $230 If you know the percent decrease: New Value = Original × (1 - percent as decimal) Example: Decrease 80 by 25% New Value = 80 × (1 - 0.25) = 80 × 0.75 = 60 **FINDING ORIGINAL VALUE:** If New Value = Original × (1 + rate): Original = New Value / (1 + rate) Example: After 20% increase, price is $144. Find original. Original = 144 / 1.20 = $120 **COMMON APPLICATIONS:** - Sales/Discounts: 30% off original price - Tips/Gratuity: 20% increase on bill - Taxes: 8% increase on price - Sports: Scoring average increased 15% - Economics: Inflation rate, GDP growth - Science: Population change, experimental results
Try it
Apply percent of change to real-world scenarios! **FIND PERCENT OF CHANGE:** Identify if it's an increase or decrease, then calculate. 1. Original: 40, New: 50 2. Original: 80, New: 64 3. Original: 25, New: 30 4. Original: 120, New: 90 **WORD PROBLEMS - PERCENT INCREASE:** 5. A plant grew from 8 inches to 10 inches. What is the percent increase in height? 6. The price of a video game increased from $40 to $50. What is the percent increase? 7. School enrollment rose from 450 students to 540 students. Find the percent increase. **WORD PROBLEMS - PERCENT DECREASE:** 8. A jacket originally priced at $80 is on sale for $60. What is the percent decrease? 9. The number of errors on a test decreased from 15 to 9. What is the percent decrease? 10. A phone's price dropped from $600 to $480. Find the percent decrease. **FIND THE NEW VALUE:** 11. Increase 200 by 35% 12. Decrease 150 by 20% 13. A $75 item increases by 12%. What's the new price? 14. A 60-pound dog loses 15% of its weight. What's the new weight? **FIND THE ORIGINAL VALUE:** 15. After a 25% increase, a population is 1,500. What was the original population? 16. After a 20% discount, a TV costs $400. What was the original price? **MULTI-STEP PROBLEMS:** 17. A store marks up a $50 item by 40%, then offers a 25% discount on the marked price. What's the final price? 18. A stock price increases 20% on Monday, then decreases 20% on Tuesday. Is the final price the same as the starting price? Explain. **CHALLENGE:** 19. The population of a town increased from 12,000 to 15,600. By what percent did it increase? If it increases by the same percent next year, what will the population be? 20. A shirt is marked down 25% to $30. What was the original price? Show your work using the formula: New = Original × (1 - rate).