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Want to watch animated videos and solve interactive exercises about finding relative percentage?

Here you will learn about the calculation of percentage change. You might have heard that the prices of housing has risen by $20$ %, but what does it actually mean when people say that something has risen or fallen by a certain percentage?

This type of increase or decrease is called a percentage change. The answer to the question asked above is then: The price for housing at two different times are compared, and the change in price is converted to a percentage relative to the original price. This is what you will learn here.

You want to compare old value to new value and find the percentage change. Have a look at the formula written below.

Formula

$$\text{\%change}=\frac{\text{newvalue}-\text{oldvalue}}{\text{oldvalue}}$$ |

If you get a positive number, something has grown in value.

If you get a negative number, something has declined in value.

Example 1

**You bought a Playstation for $\text{\$}\text{}320\text{}$. You decided to sell it two years later. You sold it for $\text{\$}\text{}175\text{}$. What was the percentage change? **

The percentage change is: $$\begin{array}{llll}\hfill \frac{175-320}{320}& \approx -0.453\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =-45.3\phantom{\rule{0.17em}{0ex}}\text{\%}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$

This means that the change in value was $-45.3\phantom{\rule{0.17em}{0ex}}\text{\%}$. You got a negative percentage, meaning that the Playstation declined in value. It has fallen by $45.3\phantom{\rule{0.17em}{0ex}}\text{\%}$ in value.

Example 2

**You deposit $\text{\$}\text{}5000\text{}$ to the bank. A year later you find that this has grown to $\text{\$}\text{}5200\text{}$. What is the percentage change? **

The percentage change is: $$\begin{array}{llll}\hfill \frac{5200-5000}{5000}& =0.04\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =4\phantom{\rule{0.17em}{0ex}}\text{\%}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$

The percentage change is $4$ %. Since you found a positive number, the money you deposited has grown in value by $4$ %.

Example 3

**Four years ago a house cost $\text{\$}\text{}350\phantom{\rule{0.17em}{0ex}}000\text{}$, now the same house costs $\text{\$}\text{}420\phantom{\rule{0.17em}{0ex}}000\text{}$. How many percent has the house grown in value? **

You have to calculate the percentage change. $$\begin{array}{llll}\hfill \frac{420\phantom{\rule{0.17em}{0ex}}000-350\phantom{\rule{0.17em}{0ex}}000}{350\phantom{\rule{0.17em}{0ex}}000}& =0.20\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =20\phantom{\rule{0.17em}{0ex}}\text{\%}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$$

In four years the value of the house has grown by $20$ %.