Lesson 4: Solve Percent Change and Percent Error Problems

Property

To determine the type of percent change:

• If new amount $>$ original amount, then percent increase
• If new amount $<$ original amount, then percent decrease
• If new amount $=$ original amount, then no change (0%)

Examples

Property

To find the percent increase, first we find the amount of increase, which is the difference between the new amount and the original amount. Then we find what percent the amount of increase is of the original amount.
Find Percent Increase.
Step 1. Find the amount of increase.
increase = new amount − original amount
Step 2. Find the percent increase as a percent of the original amount.

Examples

• A company's workforce grew from 200 to 250 employees. The increase is $250 - 200 = 50$. The percent increase is the increase (50) divided by the original (200), so $\frac{50}{200} = 0.25$, or a 25% increase.
• The price of a concert ticket rose from 60 dollars to 75 dollars. The increase is $75 - 60 = 15$ dollars. The percent increase is $\frac{15}{60} = 0.25$, or 25%.
• In a decade, a town's population grew from 10,000 to 11,500. The increase is $11,500 - 10,000 = 1,500$. The percent increase is $\frac{1,500}{10,000} = 0.15$, a 15% increase.

Explanation

Percent increase shows how much a value has grown relative to its starting point. First, find the simple difference (the 'increase'). Then, divide that increase by the original amount to see how big the change is proportionally.

Property

Finding the percent decrease is very similar to finding the percent increase, but now the amount of decrease is the difference between the original amount and the final amount. Then we find what percent the amount of decrease is of the original amount.
Find percent decrease.
Step 1. Find the amount of decrease.
decrease = original amount − new amount
Step 2. Find the percent decrease as a percent of the original amount.

Examples

• The price of a laptop dropped from 800 dollars to 600 dollars. The decrease is $800 - 600 = 200$ dollars. The percent decrease is $\frac{200}{800} = 0.25$, or 25%.
• A runner's time to complete a mile improved from 8 minutes to 7 minutes. The decrease is $8 - 7 = 1$ minute. The percent decrease is $\frac{1}{8} = 0.125$, or 12.5%.
• A store reduced its inventory from 500 items to 450 items. The decrease is $500 - 450 = 50$ items. The percent decrease is $\frac{50}{500} = 0.10$, or 10%.

Explanation

Percent decrease measures how much a value has shrunk compared to its original size. Calculate the amount of the drop, then divide that drop by the original value to find the percentage of value that was lost.