Given The Equation As Shown Below:${ \begin{aligned} \frac{3}{5} X & = 30 \ \frac{5}{3}\left(\frac{3}{5}\right) X & = 30\left(\frac{3}{5}\right) \ x & = 18 \end{aligned} }$Which Best Describes The Error That Mia Made?A. Mia Did Not Use The

Introduction

Mathematics is a precise and logical subject that requires careful attention to detail. Even the smallest mistake can lead to incorrect conclusions and a complete misunderstanding of the problem. In this article, we will examine a mathematical equation and identify the error made by Mia, a student who attempted to solve it.

The Equation

The equation given is:

{ \begin{aligned} \frac{3}{5} x & = 30 \\ \frac{5}{3}\left(\frac{3}{5}\right) x & = 30\left(\frac{3}{5}\right) \\ x & = 18 \end{aligned} \}

The Error

At first glance, the equation appears to be correct, and the solution seems to be $x = 18$. However, upon closer inspection, we can see that Mia made a mistake. The error lies in the second step of the equation.

Step 1: Multiplying Both Sides

The first step is to multiply both sides of the equation by $\frac{5}{3}$:

{ \frac{5}{3}\left(\frac{3}{5}\right) x = 30\left(\frac{3}{5}\right) \}

This step is correct, as we are multiplying both sides of the equation by the same value.

Step 2: Simplifying the Equation

However, in the second step, Mia made a mistake. She simplified the equation incorrectly:

{ \begin{aligned} \frac{5}{3}\left(\frac{3}{5}\right) x & = 30\left(\frac{3}{5}\right) \\ x & = 18 \end{aligned} \}

The correct simplification of the equation is:

{ \begin{aligned} \frac{5}{3}\left(\frac{3}{5}\right) x & = 30\left(\frac{3}{5}\right) \\ \frac{5}{3} \cdot \frac{3}{5} & = \frac{5 \cdot 3}{3 \cdot 5} \\ \frac{5}{3} \cdot \frac{3}{5} & = 1 \\ x & = 30 \end{aligned} \}

Conclusion

In conclusion, Mia made a mistake in simplifying the equation. She incorrectly simplified the expression $\frac{5}{3}\left(\frac{3}{5}\right)$ to $1$, which led to an incorrect solution of $x = 18$. The correct solution is $x = 30$.

What Went Wrong?

So, what went wrong? There are several reasons why Mia made this mistake:

• Lack of attention to detail: Mia did not carefully examine the equation and the simplification process.
• Insufficient practice: Mia may not have practiced solving equations with fractions and simplifying expressions.
• Confusion between similar expressions: Mia may have gotten confused between the expressions $\frac{5}{3}\left(\frac{3}{5}\right)$ and $\frac{5}{3} \cdot \frac{3}{5}$.

Preventing Similar Mistakes

To prevent similar mistakes, it is essential to:

• Carefully read and understand the problem: Before starting to solve the equation, make sure you understand what is being asked.
• Check your work: Double-check your calculations and simplifications to ensure that they are correct.
• Practice, practice, practice: Regular practice helps to build confidence and fluency in solving equations and simplifying expressions.

Conclusion

Q: What is the main error that Mia made in the equation?

A: The main error that Mia made is in the second step of the equation, where she incorrectly simplified the expression $\frac{5}{3}\left(\frac{3}{5}\right)$ to $1$.

Q: Why did Mia make this mistake?

A: Mia made this mistake due to a combination of factors, including:

• Lack of attention to detail: Mia did not carefully examine the equation and the simplification process.
• Insufficient practice: Mia may not have practiced solving equations with fractions and simplifying expressions.
• Confusion between similar expressions: Mia may have gotten confused between the expressions $\frac{5}{3}\left(\frac{3}{5}\right)$ and $\frac{5}{3} \cdot \frac{3}{5}$.

Q: What is the correct solution to the equation?

A: The correct solution to the equation is $x = 30$.

Q: How can I prevent similar mistakes?

A: To prevent similar mistakes, it is essential to:

• Carefully read and understand the problem: Before starting to solve the equation, make sure you understand what is being asked.
• Check your work: Double-check your calculations and simplifications to ensure that they are correct.
• Practice, practice, practice: Regular practice helps to build confidence and fluency in solving equations and simplifying expressions.

Q: What are some common mistakes that students make when solving equations with fractions?

A: Some common mistakes that students make when solving equations with fractions include:

• Incorrectly simplifying expressions: Students may simplify expressions incorrectly, leading to incorrect solutions.
• Forgetting to multiply both sides of the equation: Students may forget to multiply both sides of the equation by the same value, leading to incorrect solutions.
• Confusing similar expressions: Students may get confused between similar expressions, leading to incorrect solutions.

Q: How can I improve my skills in solving equations with fractions?

A: To improve your skills in solving equations with fractions, try the following:

• Practice regularly: Regular practice helps to build confidence and fluency in solving equations and simplifying expressions.
• Use online resources: There are many online resources available that can help you practice solving equations with fractions, including video tutorials and practice problems.
• Seek help from a teacher or tutor: If you are struggling with solving equations with fractions, don't be afraid to seek help from a teacher or tutor.

Q: What are some tips for simplifying expressions with fractions?

A: Some tips for simplifying expressions with fractions include:

• Use the order of operations: When simplifying expressions with fractions, use the order of operations (PEMDAS) to ensure that you are simplifying the expression correctly.
• Simplify the numerator and denominator separately: When simplifying expressions with fractions, simplify the numerator and denominator separately before multiplying or dividing.
• Check your work: Double-check your calculations and simplifications to ensure that they are correct.

Conclusion

In conclusion, Mia's mistake was a result of a combination of factors, including lack of attention to detail, insufficient practice, and confusion between similar expressions. By understanding the error and taking steps to prevent similar mistakes, we can improve our mathematical skills and become more confident problem-solvers.