A change compares a new value with an original value. Changes can be described as a fraction or a percentage, and they may be an increase or a decrease.

 
To calculate the fractional change, subtract the original value from the new value, then divide by the original value.

$$
\text{fractional change} = \frac{\text{new value} - \text{original value}}{\text{original value}}
$$

If the result is positive, the change is an increase.
If the result is negative, the change is a decrease.

For example, if a value changes from \(20\) to \(25\):

$$
\frac{25 - 20}{20} = \frac{5}{20} = \frac{1}{4}
$$

This is a fractional increase of \(\frac{1}{4}\).

 
To calculate the percentage change, follow the same steps, then multiply by \(100\).

$$
\text{percentage change} = \frac{\text{change}}{\text{original value}} \times 100
$$

For example, if a price increases from \(40\) to \(50\):

$$
\frac{50 - 40}{40} = \frac{10}{40} = 0.25
$$

$$
0.25 = 25%
$$

This is a 25% increase.

 
For a percentage decrease, the method is the same — only the change will be negative.

For example, if a value decreases from \(80\) to \(68\):

$$
\frac{68 - 80}{80} = \frac{-12}{80} = -0.15
$$

$$
-0.15 = -15%
$$

This represents a 15% decrease.

 
Always use the original value in the denominator. Using the new value instead is a common mistake and will give the wrong answer, even if the arithmetic is correct.