# Basic Algebra/Proportions and Proportional Reasoning/Percent of Change

## Vocabulary[edit]

**percent** - a ratio that compares a number to 100

**percent of change** - the percent an amount changes from its original amount.

percent of change = (amount of change) / (original amount), where the amount of change is the new value minus the original value.

**percent of increase** - when a value increases from its original amount, you call the percent of change the percent of increase

**percent of decrease** - when a value decreases from its original amount, you call the percent of change the percent of decrease

## Lesson[edit]

Finding the percent of change is using the ratio of the amount of change to the original amount. If the amount increases then the percent of change is called the percent of increase and will result in a positive value. If the amount decreases then the percent of change is called the percent of decrease and will result in a negative value.

The first question to ask yourself when finding the percent of change is: Is it an increase or a decrease? Once you have determined what type of change you are dealing with then you can calculate what that percent of change is.

The percent of change is calculated by dividing the amount of change by the original amount. The amount of change is the new value minus the original value. An easy way to remember how to find percent of change is to consider the no over o method. In the no over o method, **n** stands for the **new amount** and the **o** stands for the **original amount**.

Here is how to use the no over o method.

(the new amount - the original amount) over the original amount.

(n-o)/o

## Example Problems[edit]

**A. Solve and describe the percent of change as a percent of increase or decrease. Round to the nearest percent.**

**1) $12 to $9**

new amount = $9

original amount = $12

(n-o)/o

(9-12)/12 = -3/12 = -1/4 = -0.25

no over o is negative which means it decreased so there is a 25% decrease

**2) 19 in to 25 in**

new amount = 25 in

original amount = 19 in

(n-o)/o

(25-19)/19 = 6/19 = 0.3158

no over o is positive which means it increased so there is approximately a 32% increase

**B. Solve the percent of change word problem**

**1) Anna's grade in Algebra changed from 88 to 94. What is the percent of change in her grade?**

new amount = 94

original amount = 88

(n-o)/o

(94-88)/88 = 6/88 = 3/44 = .068 = 6.8%

therefore it was a 6.8% increase

**2) Between 1940 and 1980 the Federal budget went from $725.3 billion to $9.5 billion. What was the percent of change?**

new amount = $9.5 billion

original amount = $725.3 billion

(n-o)/o

(9.5-725.3)/725.3 = -715.8/725.3 = -0.986 = -98.6%

therefore it was a 98.6% decrease

**C. Solve**

**1) If 46 is decreased by 20%, what is the result?**

new amount = x

original amount = 46

(n-o)/o

(x-46)/46 = -0.20

x-46 = -9.2

x = 36.8

**2) If 16 is increased by 30%, what is the result?**

new amount = x

original amount = 16

(n-o)/o

(x-16)/16 = 0.30

x-16 = 4.8

x = 20.8

## Practice Games[edit]

[2] (good to check your answers)

## Practice Problems[edit]