Percentage Change (increase or decrease) is comparing old to new values. Learn how to find the percent of increase and decrease using the formula.

## Step by step guide to finding the percent of increase and decrease

To find the percentage of increase or decrease:

- New Number \(– \) Original Number
- The result \(÷\) Original Number \(× \ 100\)
- If your answer is a negative number, then this is a percentage decrease. If it is positive, then this is a percent of increase.

### Example 1:

Increased by \(20\%\), the number \(30\) becomes:

**Solution:**

First find \(20\%\) of \(30 → \frac{20}{100} \ × \ 30=\frac{20 \ × \ 30}{100}=6\)

Then: \(30 \ + \ 6=36\)

### Example 2:

The price of a shirt increases from \($10\) to \($15\). What is the percent increase?

**Solution:**

First find the difference: \(15 \ – \ 10=5\)

\(5\) is the result. Then: \(5 \ ÷ \ 10=\frac{5}{10}=0.5=50\% \)

### Example 3:

Increased by \(50\%\), the number \(84\) becomes:

**Solution:**

First find \(50\%\) of \(84 → \frac{50}{100} ×84=\frac{50 × 84}{100}=42\)

Then: \(84+42=126\)

### Example 4:

The price of a shirt increases from \($20\) to \($28\). What is the percent increase?

**Solution:**

First find the difference: \(28 –20=8\)

\(8\) is the result. Then: \(8÷20=\frac{8}{20}=0.4=40\%\)

## Exercises

### Solve each percent of change word problem.

- Bob got a raise, and his hourly wage increased from \($20\) to \($25\). What is the percent increase?
- The price of a pair of shoes increases from \($18\) to \($27\). What is the percent increase?
- At a coffee shop, the price of a cup of coffee increased from \($1.50\) to \($1.80\). What is the percent increase in the cost of the coffee?
- \(4\) cm are cut from a \(20\) cm board. What is the percent decrease in length?
- In a class, the number of students has been increased from \(25\) to \(29\). What is the percent increase?
- The price of gasoline rose from \($2.60\) to \($2.86\) in one month. By what percent did the gas price rise?

## Answers

- \(\color{blue}{25\%}\)
- \(\color{blue}{50\%}\)
- \(\color{blue}{20\%}\)
- \(\color{blue}{20\%}\)
- \(\color{blue}{16\%}\)
- \(\color{blue}{10\%}\)