Math Example--Percents--Equations with Percents: Example 15

Topic

Solving Equations

Description

This math example focuses on solving percent equations by asking "9 is what percent of 38?" The solution involves setting up the equation 38 * (x / 100) = 9, then solving for x to get x = 9 * (100 / 38), which is approximately 23.68%. This example demonstrates how to calculate a percentage when the first number is smaller than the second, resulting in a percentage less than 100%.

Solving equations with percents is a critical skill in mathematics that finds applications in various fields such as finance, statistics, and data analysis. These examples help students grasp the fundamental concept of relating two values through percentages and how to set up equations to solve for unknown percentages, particularly when dealing with fractions of a whole. This understanding forms the basis for more complex mathematical operations and real-world problem-solving scenarios, such as calculating percentage decreases, analyzing proportions, or understanding relative values in different contexts.

Providing multiple worked-out examples is essential for students to fully comprehend this concept. Each new example reinforces the process while introducing different scenarios and number relationships. This approach allows students to recognize patterns, adapt their problem-solving strategies, and build confidence in handling diverse percentage-based calculations. By practicing with various value pairs, including those that result in percentages less than 100%, students develop a more nuanced understanding of how percentages relate different quantities and prepare for more advanced mathematical challenges they may encounter in higher education or professional settings.

Teacher Script: "Let's examine this percent problem. We're asked, '9 is what percent of 38?' To solve this, we set up the equation 38 * (x / 100) = 9. Now, how do we solve for x? We multiply both sides by 100/38. This gives us x = 9 * (100 / 38), which is approximately 23.68%. Notice that our result is less than 100%. This means that 9 is less than 38. In real-world scenarios, you might encounter situations where you need to express one value as a percentage of a larger value. For example, if a store sold 9 items out of their stock of 38, you could say they sold about 23.68% of their inventory. Understanding these concepts is crucial for analyzing data, comparing values, and interpreting proportions in various fields like business, science, and social studies."

For a complete collection of math examples related to Solving Equations click on this link: Math Examples: Equations with Percents Collection.