Question

How do you calculate percentages?

Answer 1

Calculating percentages involves a few straightforward steps. Here's how you can do it:

### Basic Percentage Calculation
To find what percentage one number (let's call it `part`) is of another number (`whole`), you can use this formula:

\[ \text{Percentage} = \left( \frac{\text{part}}{\text{whole}} \right) \times 100 \]

#### Steps:
1. **Divide** the part by the whole.
2. **Multiply** the result by 100 to get the percentage.

#### Example:
Suppose you want to find out what percentage 25 is of 200.

1. Divide 25 by 200:
\[ \frac{25}{200} = 0.125 \]
2. Multiply by 100:
\[ 0.125 \times 100 = 12.5 \]

So, 25 is 12.5% of 200.

### Finding the Part Given the Whole and Percentage
If you know the whole and the percentage and want to find the part, you can use the formula:

\[ \text{Part} = \left( \frac{\text{percentage}}{100} \right) \times \text{whole} \]

#### Example:
If you want to find out what 20% of 150 is:

1. Convert the percentage to a decimal:
\[ \frac{20}{100} = 0.2 \]
2. Multiply by the whole:
\[ 0.2 \times 150 = 30 \]

So, 20% of 150 is 30.

### Finding the Whole Given the Part and the Percentage
If you know the part and the percentage and want to find the whole, use:

\[ \text{Whole} = \frac{\text{part}}{\left( \frac{\text{percentage}}{100} \right)} \]

#### Example:
If 50 is 25% of a number, to find that number:

1. Convert the percentage to a decimal:
\[ \frac{25}{100} = 0.25 \]
2. Divide the part by this decimal:
\[ \frac{50}{0.25} = 200 \]

So, 50 is 25% of 200.

### Percentage Increase or Decrease
To calculate the percentage increase or decrease between two numbers, you use:

\[ \text{Percentage Change} = \left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100 \]

#### Example - Percentage Increase:
If a price rises from $150 to $180:

1. Calculate the change: $180 - $150 = $30.
2. Divide by the original value:
\[ \frac{30}{150} = 0.2 \]
3. Multiply by 100 to get the percentage:
\[ 0.2 \times 100 = 20\% \]

#### Example - Percentage Decrease:
If a price drops from $150 to $120:

1. Calculate the change: $120 - $150 = -$30.
2. Divide by the original value:
\[ \frac{-30}{150} = -0.2 \]
3. Multiply by 100 to get the percentage:
\[ -0.2 \times 100 = -20\% \]

So, the price decreased by 20%.

By following these methods, you can handle various percentage calculations with ease.