Percentage Increase and Decrease
Prices change, populations grow, and discounts reduce costs. Learn how to calculate a percentage increase or decrease, find the amount of change, and work out a new value step by step.
Learning time: approximately 25–30 minutes · Beginner to intermediate
What You Will Learn
- Find a percentage increase or decrease.
- Calculate the amount of change.
- Work out a new value after a percentage change.
- Solve discount, price-rise and everyday problems.
- Explain the difference between a percentage change and a percentage-point change.
1. What Is Percentage Change?
A percentage change compares how much a value has changed with its original value. The original value is the starting amount. Always use the original value as the base when calculating the percentage change.
First find the difference between the new value and the original value.
If the new value is greater, it is an increase. If the new value is smaller, it is a decrease.
2. Percentage Increase
A percentage increase happens when a value becomes larger.
Write the percentage as a decimal before multiplying.
Worked example: A price rises by 10%
A school bag originally costs $40. Its price increases by 10%. Find the increase and the new price.
- Convert 10% to a decimal: 0.10.
- Find the increase: 40 × 0.10 = $4.
- Add the increase to the original price: 40 + 4 = $44.
Increase: $4. New price: $44.
3. Percentage Decrease
A percentage decrease happens when a value becomes smaller. Discounts and reductions are common examples.
Worked example: A discount of 20%
A jacket costs $80. The shop offers a 20% discount. Find the discount and sale price.
- Convert 20% to 0.20.
- Find the discount: 80 × 0.20 = $16.
- Subtract the discount: 80 − 16 = $64.
Discount: $16. Sale price: $64.
4. Find the Percentage Change
Sometimes you know the old and new values but need to calculate the percentage change.
Worked example: A plant grows
A plant was 30 cm tall. It later measures 36 cm. What is the percentage increase?
- Find the change: 36 − 30 = 6 cm.
- Divide by the original value: 6 ÷ 30 = 0.2.
- Convert to a percentage: 0.2 × 100% = 20%.
The plant's height increased by 20%.
Worked example: A price falls
A game originally costs $50 and is now $40. Change = 50 − 40 = $10. Percentage decrease = 10 ÷ 50 × 100% = 20%.
5. Compare the Two Methods
| Change | New-value multiplier | Example from 100 |
|---|---|---|
| Increase by 10% | 1.10 | 110 |
| Increase by 25% | 1.25 | 125 |
| Decrease by 10% | 0.90 | 90 |
| Decrease by 25% | 0.75 | 75 |
| Decrease by 40% | 0.60 | 60 |
For an increase, add the rate to 100% to get the multiplier. For a decrease, subtract the rate from 100%.
6. Real-Life Problems
Example 1: A monthly bill increases
A monthly bill of $60 increases by 5%. Increase = 60 × 0.05 = $3. New bill = $63.
Example 2: A sale discount
A bicycle costs $240 and is reduced by 15%. Discount = 240 × 0.15 = $36. Sale price = 240 − 36 = $204.
Example 3: Attendance increases
A club had 80 members and now has 100. Increase = 20. Percentage increase = 20 ÷ 80 × 100% = 25%.
7. Common Mistakes
8. Practice Exercises
- A $50 item increases in price by 10%. Find the increase and new price.
- A $120 pair of shoes is discounted by 25%. Find the discount and sale price.
- A value rises from 40 to 50. Find the percentage increase.
- A quantity falls from 200 to 170. Find the percentage decrease.
- Write the multiplier for a 12% increase.
- Write the multiplier for a 35% decrease.
Show practice answers and working
- Increase = 50 × 0.10 = $5; new price = $55.
- Discount = 120 × 0.25 = $30; sale price = $90.
- Change = 10; 10 ÷ 40 × 100% = 25% increase.
- Change = 30; 30 ÷ 200 × 100% = 15% decrease.
- 1 + 0.12 = 1.12.
- 1 − 0.35 = 0.65.
9. Test Your Understanding
Choose one answer for each question, then select Check Answers.
10. Free Printable Worksheet
Print this worksheet or save it as a PDF.
Learnora — Grades 6–7 Mathematics
Percentage Increase and Decrease Worksheet
Name: __________________________ Date: _______________
Instructions: Show your calculations and label each answer.
- A $70 item increases by 20%. Find the increase and new price.
- A $150 tablet is discounted by 10%. Find the discount and sale price.
- A town's population rises from 500 to 550. Find the percentage increase.
- A number falls from 160 to 120. Find the percentage decrease.
- Write the multiplier for a 7% increase and a 7% decrease.
Teacher / Parent Answer Key
- Increase = 70 × 0.20 = $14; new price = $84.
- Discount = 150 × 0.10 = $15; sale price = $135.
- Change = 50; 50 ÷ 500 × 100% = 10% increase.
- Change = 40; 40 ÷ 160 × 100% = 25% decrease.
- Increase multiplier = 1.07; decrease multiplier = 0.93.
11. Lesson Summary
- Percentage change compares the change with the original value.
- Percentage change = (change ÷ original value) × 100%.
- For an increase, add the calculated change to the original value.
- For a decrease, subtract the calculated change from the original value.
- Multipliers make new-value calculations quicker: 1 + rate for an increase and 1 − rate for a decrease.
Before this lesson, review Understanding Percentages. You can also practise decimal place value.
Educational note: This is a curriculum-neutral lesson for Grades 6–7. Check your school's syllabus for the expected depth and order of percentage topics.