# Percent of Increase and Decrease

When some quantity gets bigger or smaller, we can talk about the
**
percent of increase
**
or
**
percent of decrease
**
. Basically we are asking "what percent of the original quantity was added (or taken away)?"

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Example 1
**
:

Fauzia had been earning a monthly salary of $\$2600$ . She got a raise to $\$2990$ per month. What percent raise did she get?

First find the actual amount of the raise by finding the difference between the original salary and the new salary.

$2990-2600=390$

Now find what percent the $\$390$ raise is of the original salary of $\$2600$ . Write a proportion.

$\frac{390}{2600}=\frac{x}{100}$

Equate the cross products.

$2600x=39000$

Divide both sides by $2600$ .

$x=15$

So, Fauzia got a $15\%$ raise.

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Example 2
**
:

A cell phone originally costs $\$200$ . It goes on sale for $\$135$ . What is the percent of decrease?

First, find the difference.

$200-135=65$

Now find what percent $65$ is of $200$ . Write a proportion.

$\frac{65}{200}=\frac{x}{100}$

Equate the cross products.

$6500=200x$

Divide both sides by $200$ .

$x=32.5$

So, the price was reduced by $32.5\%$ .

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Another method
**
is to find the amount of increase or decrease, write this as the numerator over the original amount, and then convert that fraction to a decimal.

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Example 3
**
:

A study showed that the average ice thickness in the Arctic Ocean in March $2011$ was $2.26$ meters. Two years later, in March $2013$ , the average ice thickness was $1.94$ meters. What is the percent of decrease?

First, find the difference.

$2.26-1.94=0.32$

Write this as the numerator of a fraction, over the original thickness.

$\frac{0.32}{2.26}$

Convert the fraction to a decimal. (Use a calculator.)

$\frac{0.32}{2.26}\approx 0.14$

So, the thickness decreased by about $14\%$ .