Math Example--Percents--Equations with Percents: Example 22

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "52.2 is what percent of 98.5?" The solution involves setting up the equation 98.5 * (x / 100) = 52.2, then solving for x to get x = 52.2 * (100 / 98.5), which is approximately 52.99%. This example introduces a scenario where both the numerator and denominator are decimal numbers, resulting in a percentage that is also close to the original numerator.

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 decimal numbers are involved. This skill is crucial for more advanced mathematical concepts and real-world problem-solving scenarios, such as calculating percentage changes in precise measurements, analyzing proportions in scientific data, or understanding relative values in various contexts where accuracy 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 in both parts of the fraction. 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 percentages close to the original values, 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, '52.2 is what percent of 98.5?' To solve this, we set up the equation 98.5 * (x / 100) = 52.2. Now, how do we solve for x? We multiply both sides by 100/98.5. This gives us x = 52.2 * (100 / 98.5), which is approximately 52.99%. Notice that our result is close to the original numerator of 52.2. This often happens when the two numbers in the problem are relatively close to each other. In real-world scenarios, you might encounter situations where you need to express one precise measurement as a percentage of another similar measurement. For example, if a scientist measured 52.2 grams of a substance in a 98.5-gram sample, they could report that the substance makes up about 52.99% of the sample. Understanding these concepts is crucial for analyzing data in scientific experiments, comparing precise measurements, and interpreting proportions in various fields like chemistry, physics, or quality control in manufacturing."

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