Percent Increase and Decrease

The idea of determining the percent of increase or percent of decrease might sound a bit intimidating. But, in actuality, you're just finding out what percent of the original quantity was added or removed.

Calculating the percent of increase

When looking for the percent of increase of a number, you'll first want to find the increase by subtracting the original number from the new number.

$\mathrm{Increase}=\mathrm{New\; Number}-\mathrm{Original\; Number}$

Then create the following proportion.

Percentage of increase $=\frac{\mathrm{Increase}}{\mathrm{Original\; Number}}=\frac{x}{100}$

Example of percent of increase

Celia has been given a raise on her job from $3000 per month to $3750 per month. What percent raise did she receive?

First, find the increase.

$3750-3000=750$

Next, create a proportion.

$\frac{750}{3000}=\frac{x}{100}$

Equate the cross-products.

$3000x=75000$

Divide both sides by 3000.

$x=25$

Celia received a 25% raise.

Calculating the percent of decrease

When looking for the percent of decrease, first find the decrease by subtracting the new number from the original number.

$\mathrm{Decrease}=\mathrm{Original\; Number}-\mathrm{New\; Number}$

Then create the proportion.

Percentage of decrease $=\mathrm{Original\; Number}-\mathrm{New\; Number}$ $=\frac{\mathrm{Decrease}}{\mathrm{Original\; Number}}=\frac{x}{100}$

Example of percent of decrease

James wants to buy a used car that costs $17500, but when he arrives at the dealership he works out a deal for $16275. What is his percent of decrease?

First, find the decrease.

$17500-16275=1225$

Next, create a proportion.

$\frac{1225}{17500}=\frac{x}{100}$

Equate the cross-products.

$17500x=122500$

Divide both sides by 17500.

$x=7$

James paid 7% less for his used car.

Using increase or decrease as the numerator

Another way to calculate the percentage of increase or decrease is to find the difference between the original and new number, use the increase or decrease as the numerator over the original number, then convert the fraction into a decimal.

For example, if Sarah walked 2.75 miles on Day 1 and then 3.25 miles on Day 2, what was her percent of increase?

First, find the difference of increase.

$3.25-2.75=0.5$

Write the increase as the numerator of a fraction over the original miles walked.

$\frac{0.5}{2.75}$

Using a calculator, convert the fraction into a decimal.

$\frac{0.5}{2.75}\approx 0.18$

Sarah increased her miles walked by about 18%.

Practice questions on percent of increase and decrease

a. If Beth paid $50 to fill her car's gas tank last week and $75 this week, what is the percentage of increase?

$\mathrm{Percent}\mathrm{increase}=\frac{\mathrm{New\; value}-\mathrm{Old\; value}}{\mathrm{Old\; value}}\times 100$

$\mathrm{Percent}\mathrm{increase}=\frac{75-50}{50}\times 100=\frac{25}{50}\times 100=50\%$

b. During long jump practice, Karen's first jump was 4.0 meters. Her second jump was 3.6 meters. What was her percent of decrease?

$\mathrm{Percent}\mathrm{decrease}=\frac{\mathrm{Old\; value}-\mathrm{New\; value}}{\mathrm{Old\; value}}\times 100$

$\mathrm{Percent}\mathrm{decrease}=\frac{4.0-3.6}{4.0}\times 100=\frac{0.4}{4.0}\times 100=10\%$

c. John drove 400 miles on Monday and 330 miles on Tuesday. What was the percentage of decrease?

$\mathrm{Percent}\mathrm{decrease}=\frac{\mathrm{Old\; value}-\mathrm{New\; value}}{\mathrm{Old\; value}}\times 100$

$\mathrm{Percent}\mathrm{decrease}=\frac{400-330}{400}\times 100=\frac{70}{400}\times 100=17.5\%$

d. Jarrett slept 5 hours on Saturday night and 9 hours on Sunday night. What was the percentage of increase?

$\mathrm{Percent}\mathrm{decrease}=\frac{\mathrm{New\; value}-\mathrm{Old\; value}}{\mathrm{Old\; value}}\times 100$

$\mathrm{Percent}\mathrm{increase}=\frac{9-5}{5}\times 100=\frac{4}{5}\times 100=80\%$

e. Cassandra climbed a rock wall 12 feet on her first attempt and 15 feet on her second attempt. What was her percent of increase?

$\mathrm{Percent}\mathrm{decrease}=\frac{\mathrm{New\; value}-\mathrm{Old\; value}}{\mathrm{Old\; value}}\times 100$

$\mathrm{Percent}\mathrm{increase}=\frac{15-12}{12}\times 100=\frac{3}{12}\times 100=25\%$

f. Doug made a business profit of $20,000 in Year 1 and $17,500 in Year 2. What was his percent of decrease?

$\mathrm{Percent}\mathrm{decrease}=\frac{\mathrm{Old\; value}-\mathrm{New\; value}}{\mathrm{Old\; value}}\times 100$

$\mathrm{Percent}\mathrm{decrease}=\frac{20000-17500}{20000}\times 100=\frac{2500}{20000}\times 100=12.5\%$

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