Math Example--Percents--Equations with Percents: Example 19

Topic

Solving Equations

Description

This math example focuses on solving percent equations by asking "12 is what percent of 8?" The solution involves setting up the equation 8 * (x / 100) = 12, then solving for x to get x = 12 * (100 / 8), which equals 150%. This example demonstrates how to calculate a percentage when the first number is larger than the second, resulting in a percentage greater 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 increases or growth rates. This understanding forms the basis for more complex mathematical operations and real-world problem-solving scenarios, such as calculating percentage increases, analyzing growth rates, 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 greater 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, '12 is what percent of 8?' To solve this, we set up the equation 8 * (x / 100) = 12. Now, how do we solve for x? We multiply both sides by 100/8. This gives us x = 12 * (100 / 8), which equals 150%. Notice that our result is greater than 100%. This means that 12 is 1.5 times larger than 8. In real-world scenarios, you might encounter situations where you need to express one value as a percentage of a smaller value, often when calculating growth or increase. For example, if a company's profits grew from $8 million to $12 million, you could say they experienced a 150% increase. Understanding these concepts is crucial for analyzing growth rates, comparing values across different scales, and interpreting proportions in various fields like business, economics, and scientific research."

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