Percent Increase and Decrease

Lesson 1 of 4: Real-World Applications

Learning Objectives:

• Calculate percent increase and decrease
• Find new amounts using multipliers
• Find original amounts from changed values
• Solve percent error problems

What is Percent Change?

Percent Change describes how much a value has gone up or down compared to where it started.

• Increase: Price rises, population grows (+)
• Decrease: Discount, weight loss, depreciation (-)

The key is that we always compare the change to the Original Amount.

The Formula

Example: Percent Increase

Problem: A video game price rose from $40 to $50. What is the percent increase?

1. Find Change:
2. Divide by Original:
3. Convert to %:

Answer: 25% Increase

Example: Percent Decrease

Problem: A phone battery dropped from 80% to 60%. What is the percent decrease?

1. Find Change: (percent points)
2. Divide by Original:
3. Convert to %:

Answer: 25% Decrease

Practice: Calculate the Change

Find the percent change. Round to the nearest percent.

1. From 20 to 30
2. From 50 to 40
3. From 200 to 250

Pause and solve.

Answers

1. 20 to 30: Change = 10.
2. 50 to 40: Change = 10.
3. 200 to 250: Change = 50.

Concept 2: Finding New Amounts

How do we find the new price after a percent change?

Method A: Two Steps

1. Calculate the change amount.
2. Add to (or subtract from) the original.

Method B: One Step (Multipliers)
Multiply by .

Understanding Multipliers

• 20% Increase: . Multiply by 1.20.
• 20% Decrease: . Multiply by 0.80.

Example: Using Multipliers

Increase: A $80 jacket is marked up 15%.

• Multiplier:
• New Price:

Decrease: A $80 jacket is 15% off.

• Multiplier:
• New Price:

Practice: Finding New Amounts

Use multipliers to find the new value.

1. Increase 40 by 10%
2. Decrease 40 by 10%
3. Increase 200 by 5%

Pause and solve.

Answers

1. Increase 40 by 10%:

   • Multiplier: 1.10

2. Decrease 40 by 10%:

   • Multiplier: 0.90

3. Increase 200 by 5%:

   • Multiplier: 1.05

Concept 3: Working Backwards

Finding the Original Amount when you know the New Amount.

Key Idea:

So using inverse operations:

Example: Working Backwards

Problem: After a 20% discount, a shirt costs $32. What was the original price?

1. Determine Multiplier: 20% discount means we pay 80%.
   • Multiplier = 0.80
2. Set up Equation: Original 0.80 = 32
3. Solve: Original =

Check:

Misconception Alert: Reversibility

Does a +10% increase followed by a -10% decrease bring you back to the start?

NO! Because the "original" changes for the second step.

Concept 4: Percent Error 3

Percent error tells us how accurate a measurement is.

Example: Percent Error

Problem: You estimated a crowd of 200 people. The actual count was 250.

1. Difference:
2. Divide by Actual:
3. Convert:

Answer: 20% Error

Summary: Key Takeaways

• Percent Change:
• Multipliers:
  • Increase: (e.g., 1.25)
  • Decrease: (e.g., 0.75)
• Working Backwards: Divide the new amount by the multiplier.
• Trap: Percents don't simply add or subtract across steps ().

Next Steps

You've mastered the basics of Percent Change!

Practice:

• Complete the worksheet problems.
• Try the "Percent Change Detective" activity with real news headlines.

Coming Up:

• Simple Interest
• Tax, Tips, and Markups in depth