# How do you calculate the percentage difference between two numbers?

#### Understand the Problem

The question is asking how to determine the percentage difference between two numbers. This involves a calculation that compares the difference between the two numbers relative to their average or one of the values, usually resulting in a percentage.

\left( \frac{|A - B|}{\frac{A + B}{2}} \right) \times 100

To calculate the percentage difference between two numbers, use the formula: $$\left( \frac{|A - B|}{\frac{A + B}{2}} \right) \times 100$$

#### Steps to Solve

1. Identify the two numbers

Choose the two numbers you want to find the percentage difference between. Let's denote them as $A$ and $B$.

1. Calculate the absolute difference between the two numbers

Subtract the smaller number from the larger number to get the absolute difference: $$ext{Difference} = |A - B|$$

1. Calculate the average of the two numbers

Find the average of $A$ and $B$ by adding them together and dividing by 2: $$ext{Average} = \frac{A + B}{2}$$

1. Divide the difference by the average

Divide the absolute difference by the average to get the relative difference: $$ext{Relative Difference} = \frac{|A - B|}{\frac{A + B}{2}}$$

1. Convert to a percentage

Multiply the relative difference by 100 to get the percentage difference: $$ext{Percentage Difference} = \left( \frac{|A - B|}{\frac{A + B}{2}} \right) \times 100$$

Example Calculation

Suppose $A = 40$ and $B = 50$:

1. The absolute difference: $$|40 - 50| = 10$$
2. Calculate the average: $$\frac{40 + 50}{2} = 45$$
3. Relative difference: $$\frac{10}{45} \approx 0.2222$$
4. Percentage difference: $$0.2222 \times 100 \approx 22.22%$$

To calculate the percentage difference between two numbers, use the formula: $$\left( \frac{|A - B|}{\frac{A + B}{2}} \right) \times 100$$