Percent Increase and Decrease
Understanding how quantities grow or shrink, expressed as a percentage of the original value.
1. What is Percent Change?
Percent Increase
When a quantity gets larger, we have a percent increase. The value grows by some percentage of the original.
Examples: Price goes up, population grows, salary raises
Percent Decrease
When a quantity gets smaller, we have a percent decrease. The value shrinks by some percentage of the original.
Examples: Discounts, depreciation, weight loss
The chart below shows how a 50% increase and a 50% decrease affect an original value of 50 — shown as colored columns.
2. Finding New Value After Increase
Method 1: Two Steps
Step 1: Find the increase amount
$$\color{#e67e22}{\text{Increase}} = \color{#2980b9}{\text{Original Value}} \times \frac{\color{#27ae60}{\text{Percent}}}{100}$$
Step 2: Add to original
$$\color{#8e44ad}{\text{New Value}} = \color{#2980b9}{\text{Original}} + \color{#e67e22}{\text{Increase}}$$
Method 2: One Step (Multiplier)
$$\color{#8e44ad}{\text{New Value}} = \color{#2980b9}{\text{Original}} \times \left(1 + \frac{\color{#27ae60}{\text{Percent}}}{100}\right)$$
This is the multiplier method - faster and easier!
Example: 200 increased by 25%
Method 1: Increase = 200 × 0.25 = 50, so New = 200 + 50 = 250
Method 2: New = 200 × 1.25 = 250