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Math Example--Percents--Equations with Percents: Example 14

Math Example--Percents--Equations with Percents: Example 14

Equations with Percents Example 14

Topic

Solving Equations

Description

This math example demonstrates solving percent equations by asking "6 is what percent of 2.3?" The solution involves setting up the equation 2.3 * (x / 100) = 6, then solving for x to get x = 6 * (100 / 2.3), which is approximately 260.87%. This example introduces a scenario where the resulting percentage is greater than 100% 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 exceeds 100%. This skill is crucial for more advanced mathematical concepts and real-world problem-solving scenarios, such as calculating percentage increases, analyzing growth rates, or understanding relative values 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 with decimal numbers and percentages above 100%. 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 greater than 100%, 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, '6 is what percent of 2.3?' To solve this, we set up the equation 2.3 * (x / 100) = 6. Now, how do we solve for x? We multiply both sides by 100/2.3. This gives us x = 6 * (100 / 2.3), which is approximately 260.87%. Notice that our result is greater than 100%. This means that 6 is more than twice 2.3. In real-world scenarios, you might encounter situations where one value is significantly larger than another, resulting in percentages above 100%. For example, if a company's profits more than doubled, we might say they increased by over 200%. Understanding these concepts is crucial for analyzing growth, comparing values, and interpreting data in various fields."

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

Common Core Standards CCSS.MATH.CONTENT.6.EE.B.5, CCSS.MATH.CONTENT.7.RP.A.3, CCSS.MATH.CONTENT.6.RP.A.3.C
Grade Range 5 - 8
Curriculum Nodes Algebra
    • Expressions, Equations, and Inequalities
        • Solving Percent Equations
Copyright Year 2013
Keywords Percent, equation, solution, solving equation, percentage