Lesson: Percentage Operations

In this lesson, we will explore how to perform operations involving percentages. Understanding percentages is crucial for comparing quantities and solving real-world problems.

What is a Percentage?

A percentage is a way of expressing a number as a fraction of 100. It is denoted using the symbol %. For example, 25% means 25 out of 100 or $\frac{25}{100}$.

Key Percentage Operations

1. Finding a Percentage of a Number: To find a percentage of a number, multiply the number by the percentage (in decimal form).

   For example, to find 20% of 50:

   $$20\% \text{ of } 50 = \frac{20}{100} \times 50 = 10$$

2. Increasing a Number by a Percentage: To increase a number by a percentage, first find the percentage of the number, then add it to the original number.

   Example: Increase 80 by 15%.

   $$15\% \text{ of } 80 = \frac{15}{100} \times 80 = 12 \\ 80 + 12 = 92$$

3. Decreasing a Number by a Percentage: To decrease a number by a percentage, find the percentage of the number and subtract it from the original number.

   Example: Decrease 60 by 25%.

   $$25\% \text{ of } 60 = \frac{25}{100} \times 60 = 15 \\ 60 - 15 = 45$$

Key Questions

• How do you convert a percentage to a decimal?
• What is the formula for finding a percentage of a number?
• How can you increase a number by a given percentage?
• How do you decrease a number by a percentage?

Conclusion

Mastering percentage operations is essential for solving problems in everyday life, from calculating discounts to understanding statistics.