Math Example--Percents--Equations with Percents: Example 16

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "2 is what percent of 55.5?" The solution involves setting up the equation 55.5 * (x / 100) = 2, then solving for x to get x = 2 * (100 / 55.5), which is approximately 3.6036%. This example introduces a scenario where the resulting percentage is a small fraction, less than 5%, and involves a decimal base number.

Solving equations with percents is a fundamental skill in mathematics that has wide-ranging applications in finance, statistics, and data analysis. These examples help students understand how to set up and solve equations involving percentages, especially in cases where the result is a small fraction of the whole. This skill is crucial for more advanced mathematical concepts and real-world problem-solving scenarios, such as calculating small percentage changes, analyzing minor fluctuations in data, or understanding relative values in various contexts where precision is important.

The importance of presenting multiple worked-out examples cannot be overstated. Each new example reinforces the concept while introducing different scenarios, including those with decimal numbers and small percentages. This approach helps students recognize patterns, adapt their problem-solving strategies, and gain confidence in their ability to handle diverse percentage-based calculations. By practicing with various value pairs, including those that result in small percentages, students develop a more comprehensive understanding of how percentages relate different quantities and prepare for more complex mathematical challenges they may encounter in higher education or professional settings.

Teacher Script: "Let's tackle this interesting percent problem. We're asked, '2 is what percent of 55.5?' To solve this, we set up the equation 55.5 * (x / 100) = 2. Now, how do we solve for x? We multiply both sides by 100/55.5. This gives us x = 2 * (100 / 55.5), which is approximately 3.6036%. Notice that our result is a small percentage, less than 5%. This means that 2 is a small fraction of 55.5. In real-world scenarios, you might encounter situations where you need to express small changes or differences as percentages. For example, if a scientist measured a 2-gram change in a 55.5-gram sample, they might report it as a 3.6% change. Understanding these concepts is crucial for analyzing subtle changes, comparing small variations, and interpreting precise data in various fields like science, engineering, and economics."

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