# The number of students in class increased from 10 to 15. What is the percent increase?

May 21, 2016

50/100 -> 50%

#### Explanation:

There are 2 ways of writing percent, both of which mean the same thing. They just look different.

Example: Suppose we had sixty percent. This can be written as

60%" or "60/100

The ward part of 'per' in percent means 'for each of'.
The word part of 'cent' in percent means 100. Think of century which is 100 years.
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The level of increase is 15-10=5, but this is part of the total original count of ten. So the change as a fraction is :

$\frac{15 - 10}{10} = \frac{5}{10}$

To change this to percentage we change the bottom number (denominator) to 100.

$\textcolor{b r o w n}{\text{What we do to the top we do to the bottom}}$

Multiply by 1 but in the form of $1 = \frac{10}{10}$

$\frac{5}{10} \times 1 \text{ "->" "5/10xx10/10" " =" } \frac{50}{100}$

color(green)("So the increase is "50/100 -> 50%)