Math Example--Percents--Equations with Percents: Example 32

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "7 is 1% of what number?" The solution involves setting up the equation 7 = 0.01 * x, then solving for x to get x = 7 / 0.01, which equals 700. This example introduces a scenario where we need to find the whole when given a small percentage of it, resulting in a number 100 times larger than the given value.

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 we need to work backwards from a part to find the whole. This skill is crucial for more advanced mathematical concepts and real-world problem-solving scenarios, such as estimating total populations from samples, calculating original prices from discounted prices, or understanding scale in various contexts.

The importance of presenting multiple worked-out examples cannot be overstated. Each new example reinforces the concept while introducing different scenarios, including those where we work with small percentages to find larger wholes. 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, 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, '7 is 1% of what number?' To solve this, we first convert 1% to a decimal, which is 0.01. Then we set up the equation 7 = 0.01 * x. Now, how do we solve for x? We divide both sides by 0.01. This gives us x = 7 / 0.01, which equals 700. Notice that our result is 100 times larger than the given number 7. This is because 1% is one-hundredth of the whole, so to find the whole, we multiply by 100. In real-world scenarios, you might encounter situations where you need to estimate a total from a small percentage. For example, if 7 students in a school represent 1% of the total student body, you could calculate that the school has 700 students in total. Understanding these concepts is crucial for analyzing survey data, estimating populations from samples, and interpreting proportions in various fields like market research, demographic studies, or financial planning."

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