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Teacher Guide: Percent Increase and Decrease

Learn how to calculate percent increase and percent decrease to measure changes in quantities.

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10 questions on Percentages. Students join with a name, you see everyone's score.

For Teachers

Learning Objectives
  • Calculate percent increase given original and new values
  • Calculate percent decrease given original and new values
  • Find a new value after a percent increase or decrease
  • Find the original value when given the new value and percent change
  • Apply percent change to real-world contexts like shopping, wages, and growth
Prerequisites
  • • Converting between decimals and percentages
  • • Finding a percent of a number
  • • Basic fraction and decimal operations
Discussion Starters
  • 1. If a store has a 50% off sale, then takes an additional 20% off, is that the same as 70% off? Why or why not?
  • 2. Why do companies prefer to advertise '25% more free!' instead of '20% off'?
  • 3. A stock drops 20% one day and rises 20% the next. Are you back where you started?
  • 4. If inflation is 3% per year, what does that mean for the cost of things you buy?
Common Misconceptions

Percent increase and decrease are inverse operations

Remediation: Use concrete examples: Start with 100. Add 50% to get 150. Subtract 50% from 150 to get 75, not 100. The base changes!

The percent change is the same regardless of which value is 'original'

Remediation: Show that going from 100 to 150 is a 50% increase, but going from 150 to 100 is only a 33.3% decrease.

Differentiation Ideas

For Struggling Students:

  • • Use visual models like bar diagrams to show percent change
  • • Start with simple numbers (multiples of 10 and 100)
  • • Focus on one type (increase only) before mixing with decrease

For On-Level Students:

  • • Calculate percent changes with various real-world scenarios
  • • Work backwards to find original values
  • • Compare successive percent changes

For Advanced Students:

  • • Explore compound percent changes (multiple increases/decreases)
  • • Calculate what single percent change equals two successive changes
  • • Investigate percent change in exponential growth contexts
Standards Alignment
  • 7.RP.A.3 (CCSS.MATH.CONTENT.7.RP.A.3)

    Use proportional relationships to solve multi-step ratio and percent problems

  • 7.EE.B.3 (CCSS.MATH.CONTENT.7.EE.B.3)

    Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers

Lesson Resources
  • visualPercent Change Calculator

    Interactive tool to visualize percent increases and decreases

  • activitySale Shopping Simulation

    Calculate final prices with various discounts

  • worksheetReal-World Percent Change

    Problems involving salaries, prices, and populations

Lesson Content

Everything students see: definition, examples, common mistakes, applications. Tap to open.

Definition

Percent increase measures how much a value has grown, while percent decrease measures how much it has shrunk. Both are expressed as a percentage of the original value.
Percent Change Formula:
Percent Change=New Value−Original ValueOriginal Value×100%\text{Percent Change} = \frac{\text{New Value} - \text{Original Value}}{\text{Original Value}} \times 100\%
  • If the result is positive, it's a percent increase
  • If the result is negative, it's a percent decrease
Alternative Method - Using Multipliers:
  • For a 20% increase: multiply by 1.201.20 (which is 1+0.201 + 0.20)
  • For a 20% decrease: multiply by 0.800.80 (which is 1−0.201 - 0.20)

Worked Examples

A pair of sneakers was 80 dollars last year. This year it costs 100 dollars. What is the percent increase?
1

Identify the values

Original = 80 dollars, New = 100 dollars → Original: 80, New: 100
2

Find the change

100−80=20100 - 80 = 20 dollars → Change = 20
3

Divide by original

2080=0.25\frac{20}{80} = 0.25
4

Convert to percent

0.25×100%=25%0.25 \times 100\% = 25\% → 25% increase

Common Mistakes

Using the new value instead of the original value in the denominator

Why it's wrong: Percent change is always relative to where you started, not where you ended up.

Correct: Always divide by the ORIGINAL value: ChangeOriginal×100%\frac{\text{Change}}{\text{Original}} \times 100\%

Thinking a 50% increase followed by a 50% decrease returns to the original

Why it's wrong: After a 50% increase, the new base is larger. A 50% decrease of a larger number takes away more.

Correct: Example: 100 increases by 50% to 150. Then 150 decreases by 50% to 75, not back to 100!

Confusing percent increase with the new total

Why it's wrong: A 20% increase doesn't mean the new value is 20% - it means you ADD 20% to 100%.

Correct: For 20% increase, multiply by 1.20 (not 0.20). The new value is 120% of the original.

Forgetting to convert the decimal to a percent

Why it's wrong: 0.15 and 15% look different but represent the same amount. Forgetting to multiply by 100 gives the wrong answer format.

Correct: After dividing, multiply by 100 to express as a percent: 0.15×100%=15%0.15 \times 100\% = 15\%

Why It Matters

Percent change is everywhere in daily life:
  • Shopping: A shirt originally 40 dollars is now 25% off. What's the sale price?
  • Salary: Your hourly wage increases from 15 to 18 dollars. What percent raise is that?
  • Investments: A stock rises from 50 to 65 dollars. What's the percent gain?
  • Population: A town grows from 10,000 to 12,500 people. What's the growth rate?
  • Grades: Your test score improved from 70 to 84. How much did you improve?
Understanding percent change helps you make smart financial decisions and interpret data in news reports!

Real World Applications

Shopping and Discounts

Stores use percent decrease to show how much you save during sales.

Example:

A 40% off sale on a 90 dollar item means you pay 90×0.60=5490 \times 0.60 = 54 dollars.

1Try It Yourself

A store advertises '30% off everything!' You want to buy headphones originally priced at 80 dollars.

How much will you pay?

Step 1: Write the mathematical expression

Calculate the sale price:

Salary and Wages

Employers and employees use percent increase to discuss raises and cost-of-living adjustments.

Example:

A 5% raise on a 50,000 dollar salary means a new salary of 50,000×1.05=52,50050,000 \times 1.05 = 52,500 dollars.

2Try It Yourself

Your monthly salary is 3,000 dollars. You receive an 8% raise.

What is your new monthly salary?

Step 1: Write the mathematical expression

Calculate the new salary:

Population Growth

Demographers use percent change to track how populations grow or shrink over time.

Example:

A city with 500,000 people that grows by 4% will have 500,000×1.04=520,000500,000 \times 1.04 = 520,000 people.

3Try It Yourself

A town had 25,000 residents last year. This year it has 27,500 residents.

What is the percent increase in population?

Step 1: Write the mathematical expression

Calculate the percent change:

Key Takeaways

  • 1Percent change = New−OriginalOriginal×100%\frac{\text{New} - \text{Original}}{\text{Original}} \times 100\%
  • 2Positive result = percent increase; Negative result = percent decrease
  • 3For X% increase, multiply by (1+X/100)(1 + X/100). Example: 15% increase uses multiplier 1.15
  • 4For X% decrease, multiply by (1−X/100)(1 - X/100). Example: 15% decrease uses multiplier 0.85
  • 5Always use the ORIGINAL value as the base for calculations

Frequently Asked Questions

What's the difference between percent increase and percent of?

Percent OF finds a part of something (e.g., 20% of 50 = 10). Percent INCREASE adds that amount to the original (e.g., 50 increased by 20% = 50 + 10 = 60).

Can percent decrease be more than 100%?

No, a percent decrease cannot exceed 100% because you cannot lose more than you have. A 100% decrease means the value becomes zero.

Why doesn't a 25% increase followed by a 25% decrease give back the original?

Because the 25% decrease applies to the INCREASED value, not the original. Example: 100 increased by 25% is 100×1.25=125100 \times 1.25 = 125. Then 125 decreased by 25% is 125×0.75=93.75125 \times 0.75 = 93.75, not 100.

Glossary

Percent increase
A positive percent change indicating growth from the original value
Percent decrease
A negative percent change indicating reduction from the original value
Multiplier
A decimal used to calculate the new value directly (e.g., 1.20 for 20% increase)
Original value
The starting value before any percent change is applied
Markup
A percent increase added to cost to determine selling price
Discount
A percent decrease from the regular price

Formula Card

Percent Change

Percent Change=New−OriginalOriginal×100%\text{Percent Change} = \frac{\text{New} - \text{Original}}{\text{Original}} \times 100\%

Calculates the percent increase (positive) or decrease (negative)

Increase Multiplier

New Value=Original×(1+Percent100)\text{New Value} = \text{Original} \times (1 + \frac{\text{Percent}}{100})

Find new value after percent increase

Decrease Multiplier

New Value=Original×(1−Percent100)\text{New Value} = \text{Original} \times (1 - \frac{\text{Percent}}{100})

Find new value after percent decrease

Find Original

Original=New ValueMultiplier\text{Original} = \frac{\text{New Value}}{\text{Multiplier}}

Work backwards from new value to find original

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