Percentage Word Problems

Understanding Percentages

Percentages represent a fraction of 100. To solve percentage word problems, you often need to find the percentage of a number, the whole when given a percentage, or the percentage when given the whole and part.

Key Formula

1. To find the percentage of a number: $\text{Percentage} = \text{Whole} \times \frac{ \text{Percent}}{100}$

2. To find the whole when given a part and a percentage: $\text{Whole} = \frac{ \text{Part}}{\frac{ \text{Percent}}{100}}$

3. To find the percent when given the whole and the part: $\text{Percent} = \frac{ \text{Part}}{ \text{Whole}} \times 100$

Example Problem

Problem: If 30% of a class of 40 students are girls, how many girls are there in the class?

Steps to Solve:

1. Identify the whole (total students) and the percentage:

   • Whole = 40 students
   • Percent = 30%

2. Use the formula for finding the part: $\text{Part} = \text{Whole} \times \frac{ \text{Percent}}{100}$ $\text{Part} = 40 \times \frac{30}{100}$ $\text{Part} = 40 \times 0.3 = 12$

Thus, there are 12 girls in the class.

Key Questions

• What is the formula to find the percentage of a number?
• How can you find the whole if you know the part and the percentage?
• What does it mean to express a number as a percentage?

Summary

Understanding how to manipulate the formulas for percentages is key to solving word problems effectively. Practice with varied examples to master the concepts!