Percent of Increase and Decrease

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?

Answers

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

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