# An increase from 16 to 20 is what percent of increase?

Oct 5, 2016

25%

#### Explanation:

Your measure start at 16. So that is the basis (unless stated otherwise) upon which you reference the change.

That is: $\frac{20 - 16}{16}$ is you fraction.

This gives: $\frac{4}{16} \to \frac{4 \div 4}{16 \div 4} = \frac{1}{4}$

For this to be a percentage we need the denominator such that it becomes 100. Thus we have:

$\frac{1}{4} \to \left(\frac{1}{4} \times 1\right) \to \left(\frac{1}{4} \times \frac{25}{25}\right) = \frac{25}{100}$

To express this in the standard script form we have 25%

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Foot note:

Sometimes the use of % and its meaning is misunderstood.
The % that follows the 25 really means that we have 25 parts out of 100. In other words: $\frac{25}{100}$

To coin a phrase; 25% and $\frac{25}{100}$ are 'one and the same thing'.