Jermaine's Solution:$ 5\left(-2 \frac{1}{4}\right) }$ { 5\left(-2-\frac{1}{4}\right) \} ${ -10-\frac{1}{4} }$ { -10 \frac{1}{4} \} Mildred's Solution $[ \begin{array {l} 5\left(-2 \frac{1}{4}\right)

Introduction

In mathematics, solving expressions involving fractions and decimals requires a clear understanding of the order of operations and the rules of arithmetic. Two students, Jermaine and Mildred, were given the task of simplifying the expression $5\left(-2 \frac{1}{4}\right)$. However, their solutions differed, sparking a discussion about the correct approach. In this article, we will delve into the solutions provided by Jermaine and Mildred, analyze their methods, and determine the correct answer.

Jermaine's Solution

Jermaine's solution is as follows:

{ 5\left(-2 \frac{1}{4}\right) \} { 5\left(-2-\frac{1}{4}\right) \} { -10-\frac{1}{4} \} { -10 \frac{1}{4} \}

Jermaine's approach involves first simplifying the expression inside the parentheses by converting the mixed number $-2 \frac{1}{4}$ to an improper fraction. He then multiplies the result by 5, which leads to the final answer of $-10 \frac{1}{4}$.

Mildred's Solution

Mildred's solution is as follows:

$${ \begin{array}{l} 5\left(-2 \frac{1}{4}\right) \end{array} }$$

Mildred's approach involves multiplying the mixed number $-2 \frac{1}{4}$ by 5 directly, without converting it to an improper fraction first. This leads to the result of $-10 \frac{5}{20}$, which can be simplified further to $-10 \frac{1}{4}$.

Discussion

The discussion surrounding Jermaine's and Mildred's solutions revolves around the correct approach to simplifying the expression $5\left(-2 \frac{1}{4}\right)$. Jermaine's method involves converting the mixed number to an improper fraction before multiplying, while Mildred's approach involves multiplying the mixed number directly.

Analysis

To determine the correct answer, let's analyze the solutions provided by Jermaine and Mildred.

Jermaine's Method

Jermaine's method involves converting the mixed number $-2 \frac{1}{4}$ to an improper fraction. This can be done by multiplying the whole number part by the denominator and adding the numerator:

$-2 \frac{1}{4} = \frac{-8}{4} + \frac{1}{4} = \frac{-7}{4}$

Now, Jermaine multiplies the result by 5:

$5\left(\frac{-7}{4}\right) = \frac{-35}{4} = -8 \frac{3}{4}$

However, Jermaine's final answer is $-10 \frac{1}{4}$, which is incorrect.

Mildred's Method

Mildred's method involves multiplying the mixed number $-2 \frac{1}{4}$ by 5 directly. This can be done by multiplying the whole number part by 5 and adding the result of multiplying the numerator by 5:

$-2 \frac{1}{4} = -10 + \frac{5}{20} = -10 + \frac{1}{4}$

Now, Mildred multiplies the result by 5:

$5\left(-10 + \frac{1}{4}\right) = -50 + \frac{5}{4} = -50 + 1 \frac{1}{4} = -49 \frac{1}{4}$

However, Mildred's final answer is $-10 \frac{1}{4}$, which is also incorrect.

Conclusion

In conclusion, both Jermaine's and Mildred's solutions are incorrect. The correct approach to simplifying the expression $5\left(-2 \frac{1}{4}\right)$ involves converting the mixed number to an improper fraction before multiplying. This leads to the result of $-8 \frac{3}{4}$.

Correct Solution

The correct solution is as follows:

$${ \begin{array}{l} 5\left(-2 \frac{1}{4}\right) \end{array} }$$

$= 5\left(\frac{-7}{4}\right)$

$= \frac{-35}{4}$

$= -8 \frac{3}{4}$

Final Answer

The final answer is $-8 \frac{3}{4}$.

Key Takeaways

• When simplifying expressions involving fractions and decimals, it's essential to follow the order of operations and the rules of arithmetic.
• Converting mixed numbers to improper fractions before multiplying can help avoid errors.
• The correct approach to simplifying the expression $5\left(-2 \frac{1}{4}\right)$ involves converting the mixed number to an improper fraction before multiplying.

Recommendations

• When working with fractions and decimals, always follow the order of operations and the rules of arithmetic.
• Convert mixed numbers to improper fractions before multiplying to avoid errors.
• Practice simplifying expressions involving fractions and decimals to develop your skills and confidence.

Conclusion

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Introduction

In our previous article, we analyzed the solutions provided by Jermaine and Mildred for the expression $5\left(-2 \frac{1}{4}\right)$. We determined that both solutions were incorrect and provided the correct approach to simplifying the expression. In this article, we will answer some frequently asked questions (FAQs) related to the topic.

Q: What is the correct approach to simplifying the expression $5\left(-2 \frac{1}{4}\right)$?

A: The correct approach involves converting the mixed number $-2 \frac{1}{4}$ to an improper fraction before multiplying. This leads to the result of $-8 \frac{3}{4}$.

Q: Why is Jermaine's method incorrect?

A: Jermaine's method involves multiplying the mixed number $-2 \frac{1}{4}$ by 5 directly, without converting it to an improper fraction first. This leads to an incorrect result.

Q: Why is Mildred's method incorrect?

A: Mildred's method involves multiplying the mixed number $-2 \frac{1}{4}$ by 5 directly, without converting it to an improper fraction first. This leads to an incorrect result.

Q: What is the difference between a mixed number and an improper fraction?

A: A mixed number is a combination of a whole number and a fraction, while an improper fraction is a fraction with a numerator greater than or equal to the denominator.

Q: How do I convert a mixed number to an improper fraction?

A: To convert a mixed number to an improper fraction, multiply the whole number part by the denominator and add the numerator. Then, write the result as a fraction with the denominator.

Q: What are some common mistakes to avoid when simplifying expressions involving fractions and decimals?

A: Some common mistakes to avoid include:

• Not following the order of operations
• Not converting mixed numbers to improper fractions before multiplying
• Not simplifying fractions before multiplying

Q: How can I practice simplifying expressions involving fractions and decimals?

A: You can practice simplifying expressions involving fractions and decimals by working through problems in a textbook or online resource. You can also try creating your own problems and solving them.

Q: What are some real-world applications of simplifying expressions involving fractions and decimals?

A: Simplifying expressions involving fractions and decimals has many real-world applications, including:

• Cooking and recipe scaling
• Finance and budgeting
• Science and engineering

Conclusion

In conclusion, we have answered some frequently asked questions related to the topic of Jermaine's solution vs Mildred's solution. We hope that this article has provided you with a better understanding of the correct approach to simplifying expressions involving fractions and decimals.

Key Takeaways

• The correct approach to simplifying the expression $5\left(-2 \frac{1}{4}\right)$ involves converting the mixed number to an improper fraction before multiplying.
• Jermaine's and Mildred's solutions were incorrect.
• Converting mixed numbers to improper fractions before multiplying can help avoid errors.
• Practice simplifying expressions involving fractions and decimals to develop your skills and confidence.

Recommendations

• When working with fractions and decimals, always follow the order of operations and the rules of arithmetic.
• Convert mixed numbers to improper fractions before multiplying to avoid errors.
• Practice simplifying expressions involving fractions and decimals to develop your skills and confidence.

Final Answer

The final answer is $-8 \frac{3}{4}$.