Skill: Calculate percent increase and percent decrease

To find a percent increase or decrease:

1. Find the change:

$$\text{change}=\text{new amount}-\text{original amount}$$

2. Divide the change by the original amount.
3. Multiply by $(100\%)$.

The original amount is always the comparison base.

Example: A backpack’s price increases from 40$to$$46$. What is the percent increase?

Step 1: Find the change.

$$46-40=6$$

The price increased by 6$.

Step 2: Compare the change with the original price.

$$\frac{6}{40}$$

Step 3: Convert to a percent.

$$\frac{6}{40}\times 100\%=15\%$$

The price increased by $(15\%)$.

For a decrease, use the same steps: find how much the amount went down, divide by the original amount, and multiply by $(100\%)$. An increase of $(r\%)$ multiplies the original by $(1+r)$, while a decrease of $(r\%)$ multiplies it by $(1-r)$, using $r$ as a decimal.