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

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

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Answer 1 · 2016-05-21T10:29:22

$\frac{50}{100} \to 50 %$ $50/100 -> 50%$

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

$60 % or \frac{60}{100}$ $60%" or "60/100$

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.
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
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 :

$\frac{15 - 10}{10} = \frac{5}{10}$ $(15-10)/10 = 5/10$

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

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

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

$\frac{5}{10} \times 1 \to \frac{5}{10} \times \frac{10}{10} = \frac{50}{100}$ $5/10xx1" "->" "5/10xx10/10" " =" " 50/100$

$So the increase is \frac{50}{100} \to 50 %$ $color(green)("So the increase is "50/100 -> 50%)$

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

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