# Percentage Multiplication

\[\frac{a\times b}{100}=\frac{a}{100}\times\frac{b}{100} \]

## Percentage Multiplication

A percentage multiplication calculator is a tool designed to quickly and accurately calculate the value of a specified percentage of a given number. This can be particularly useful for tasks like calculating discounts, interest, taxes, and other financial metrics.

#### Features of a Percentage Multiplication Calculator

**Input Fields**:**Original Number**: The initial value or the number to which the percentage will be applied.**Percentage**: The percentage value that you want to calculate.

**Calculation**:- Converts the percentage to a decimal by dividing by 100.
- Multiplies the original number by this decimal.

**Output**:- Displays the result of the percentage of the original number.

#### Formula

The formula used by a percentage multiplication calculator is:

\[ \text{Result} = \text{Original Number} \times \left( \frac{\text{Percentage}}{100} \right) \]

### Percentage Multiplication

#### Introduction to Percentage Multiplication

Percentage Multiplication involves finding a certain percentage of a given number by multiplying the number by the percentage (expressed as a decimal). This concept is frequently used in various real-world situations, such as calculating taxes, interest, tips, and more.

#### Key Concepts

1. Percentage: A fraction of 100, denoted using the symbol `%`.

2. Original Number: The initial value or the number to which the percentage will be applied.

3. Percentage Value: The portion of the original number represented by the percentage.

#### Formula for Percentage Multiplication

The basic formula to find the percentage of a number is:

\[ \text{Result} = \text{Original Number} \times \left( \frac{\text{Percentage}}{100} \right) \]

#### Steps to Perform Percentage Multiplication

1. Convert the percentage to a decimal: Divide the percentage by 100.

2. Multiply the original number by this decimal: This gives you the value of the percentage of the original number.

#### Examples

**Example 1: Basic Percentage Multiplication**

Problem: Find 20% of 150.

1. Convert Percentage to Decimal:

\[ \frac{20}{100} = 0.20 \]

2. Multiply by the Original Number:

\[ 150 \times 0.20 = 30 \]

Result: 30

**Example 2: Finding a Smaller Percentage**

Problem: Find 5% of 200.

1. Convert Percentage to Decimal:

\[ \frac{5}{100} = 0.05 \]

2. Multiply by the Original Number:

\[ 200 \times 0.05 = 10 \]

Result: 10

**Example 3: Finding a Larger Percentage**

Problem: Find 75% of 400.

1. Convert Percentage to Decimal:

\[ \frac{75}{100} = 0.75 \]

2. Multiply by the Original Number:

\[ 400 \times 0.75 = 300 \]

Result: 300

#### Practical Applications

1. Shopping and Sales Tax: Calculating the amount of sales tax on a purchase.

– Example: If an item costs $50 and the sales tax is 8%:

\[ \text{Tax Amount} = 50 \times 0.08 = 4 \]

\[ \text{Total Cost} = 50 + 4 = 54 \]

2. Financial Calculations: Calculating interest earned or paid.

– Example: If you earn 5% interest on a $1000 investment:

\[ \text{Interest Earned} = 1000 \times 0.05 = 50 \]

\[ \text{Total Value} = 1000 + 50 = 1050 \]

3. Tips and Gratuities: Determining the amount of tip to leave at a restaurant.

– Example: If your bill is $80 and you want to leave a 15% tip:

\[ \text{Tip Amount} = 80 \times 0.15 = 12 \]

\[ \text{Total Payment} = 80 + 12 = 92 \]

#### Practice Problems

1. Find 25% of 80.

2. Find 10% of 450.

3. Find 50% of 120.

4. Find 33% of 300.

5. Find 12% of 75.

Solutions to Practice Problems

1. 25% of 80:

\[ \frac{25}{100} = 0.25 \]

\[ 80 \times 0.25 = 20 \]

Result: 20

2. 10% of 450:

\[ \frac{10}{100} = 0.10 \]

\[ 450 \times 0.10 = 45 \]

Result: 45

3. 50% of 120:

\[ \frac{50}{100} = 0.50 \]

\[ 120 \times 0.50 = 60 \]

Result: 60

4. 33% of 300:

\[ \frac{33}{100} = 0.33 \]

\[ 300 \times 0.33 = 99 \]

Result: 99

5. 12% of 75:

\[ \frac{12}{100} = 0.12 \]

\[ 75 \times 0.12 = 9 \]

Result: 9

#### Summary

– Percentage Multiplication is a useful mathematical tool for various applications like calculating taxes, interest, and tips.

– The formula is straightforward: convert the percentage to a decimal, then multiply it by the original number.

– Practice with real-life examples to become proficient in percentage multiplication.

Understanding percentage multiplication is essential for managing finances, making informed purchasing decisions, and solving everyday problems efficiently.