# Percent of Increase and Decrease 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?

• $$\color{blue}{25\%}$$
• $$\color{blue}{50\%}$$
• $$\color{blue}{20\%}$$
• $$\color{blue}{20\%}$$
• $$\color{blue}{16\%}$$
• $$\color{blue}{10\%}$$ 