Question

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

Answer 1

`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 :

`(15-10)/10 = 5/10`

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

`color(brown)("What we do to the top we do to the bottom")`

Multiply by 1 but in the form of `1=10/10`

`5/10xx1" "->" "5/10xx10/10" " =" " 50/100`

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