Percent Increase and Decrease

Understanding Percent Change

Percent change tells you how much something increased or decreased compared to the original amount.

Percent Increase

Percent increase = when a value goes up.

Formula:

Percent Increase = (Amount of Increase ÷ Original Amount) × 100%

Example: A shirt costs $20, then goes up to $25.

Step 1: Find the increase

• Increase = New - Original
• $25 - $20 = $5

Step 2: Divide by original

• $5 ÷ $20 = 0.25

Step 3: Convert to percent

• 0.25 × 100% = 25%

Answer: 25% increase

Percent Decrease

Percent decrease = when a value goes down.

Formula:

Percent Decrease = (Amount of Decrease ÷ Original Amount) × 100%

Example: A price drops from $80 to $60.

Step 1: Find the decrease

• Decrease = Original - New
• $80 - $60 = $20

Step 2: Divide by original

• $20 ÷ $80 = 0.25

Step 3: Convert to percent

• 0.25 × 100% = 25%

Answer: 25% decrease

Finding New Amount After Percent Increase

Method 1: Two steps

Example: Increase $40 by 15%

Step 1: Find the increase

• 15% of $40 = 0.15 × 40 = $6

Step 2: Add to original

• $40 + $6 = $46

Method 2: Shortcut

Multiply by (1 + percent as decimal)

Example: Increase $40 by 15%

• $40 × 1.15 = $46

Why it works: $40 × 1.15 = $40 × (1 + 0.15) = $40 + ($40 × 0.15) = $40 + $6 = $46

Finding New Amount After Percent Decrease

Method 1: Two steps

Example: Decrease $60 by 20%

Step 1: Find the decrease

• 20% of $60 = 0.20 × 60 = $12

Step 2: Subtract from original

• $60 - $12 = $48

Method 2: Shortcut

Multiply by (1 - percent as decimal)

Example: Decrease $60 by 20%

• $60 × 0.80 = $48

Why it works: If you decrease by 20%, you keep 80%. So multiply by 0.80.

Common Percent Changes

Markup

Markup is how much a store adds to the cost to set the selling price.

Example: A store buys a toy for $30 and marks it up 40%. What's the selling price?

Markup = $30 × 0.40 = $12 Selling price = $30 + $12 = $42

Or shortcut: $30 × 1.40 = $42

Markdown (Discount)

Markdown or discount is the amount reduced from the original price.

Example: A $75 jacket is marked down 30%. What's the sale price?

Markdown = $75 × 0.30 = $22.50 Sale price = $75 - $22.50 = $52.50

Or shortcut: $75 × 0.70 = $52.50 (paying 70% since it's 30% off)

Multiple Percent Changes

Be careful! Percent changes don't simply add.

Example: A price increases 20%, then increases another 10%. Is that a 30% increase total?

NO! Let's see:

Starting price: $100

• After 20% increase: $100 × 1.20 = $120
• After 10% increase: $120 × 1.10 = $132

Total increase: $132 - $100 = $32 = 32% (not 30%!)

Why? The second 10% is calculated on the new amount ($120), not the original ($100).

Finding Original Price

Problem: After a 25% discount, the sale price is $60. What was the original price?

Think: $60 is 75% of the original (100% - 25% = 75%)

Set up: Original × 0.75 = $60

Solve: Original = $60 ÷ 0.75 = $80

Answer: $80

Real-World Applications

Population growth: "The town grew from 5,000 to 6,000 people"

• Increase: 6,000 - 5,000 = 1,000
• Percent: (1,000 ÷ 5,000) × 100% = 20% growth

Grade improvement: "Test score went from 70% to 84%"

• Increase: 84 - 70 = 14 percentage points
• Percent increase: (14 ÷ 70) × 100% = 20% improvement

Stock market: "Stock price dropped from $50 to $40"

• Decrease: $50 - $40 = $10
• Percent: ($10 ÷ $50) × 100% = 20% loss

Inflation: "Prices increased 3% this year"

• $100 item now costs: $100 × 1.03 = $103

Practice