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.