Select The Correct Answer.What Is ∣ 3 1 2 ∣ \left|3 \frac{1}{2}\right| ​ 3 2 1 ​ ​ ?A. − 2 7 -\frac{2}{7} − 7 2 ​ B. − 3 1 2 -3 \frac{1}{2} − 3 2 1 ​ C. 3 1 2 3 \frac{1}{2} 3 2 1 ​ D. − 2 7 -\frac{2}{7} − 7 2 ​

Introduction

In mathematics, absolute value is a fundamental concept that deals with the magnitude or size of a number, without considering its direction or sign. When we encounter mixed numbers, such as $3 \frac{1}{2}$, we need to understand how to apply absolute value to these types of numbers. In this article, we will explore the concept of absolute value in mixed numbers and determine the correct answer to the given problem.

What is Absolute Value?

Absolute value is a mathematical operation that returns the distance of a number from zero on the number line. It is denoted by the symbol $|x|$, where $x$ is the number being evaluated. The absolute value of a number is always non-negative, meaning it is either positive or zero.

Evaluating Absolute Value in Mixed Numbers

To evaluate the absolute value of a mixed number, we need to convert the mixed number to an improper fraction. An improper fraction is a fraction where the numerator is greater than or equal to the denominator. To convert a mixed number to an improper fraction, we multiply the whole number part by the denominator and add the numerator.

For example, let's convert the mixed number $3 \frac{1}{2}$ to an improper fraction:

$$3 \frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}$$

Now that we have the mixed number in improper fraction form, we can evaluate its absolute value.

Evaluating the Absolute Value of $\frac{7}{2}$

The absolute value of a fraction is equal to the absolute value of its numerator divided by the absolute value of its denominator. In this case, the absolute value of $\frac{7}{2}$ is:

$$\left|\frac{7}{2}\right| = \frac{|7|}{|2|} = \frac{7}{2}$$

Since the absolute value of a number is always non-negative, the absolute value of $\frac{7}{2}$ is also non-negative.

Determining the Correct Answer

Now that we have evaluated the absolute value of $\frac{7}{2}$, we can determine the correct answer to the given problem.

The correct answer is the option that matches the absolute value of $\frac{7}{2}$. Let's examine the options:

A. $-\frac{2}{7}$

B. $-3 \frac{1}{2}$

C. $3 \frac{1}{2}$

D. $-\frac{2}{7}$

The only option that matches the absolute value of $\frac{7}{2}$ is option C, $3 \frac{1}{2}$.

Conclusion

In conclusion, the absolute value of a mixed number is equal to the absolute value of its improper fraction form. To evaluate the absolute value of a mixed number, we need to convert it to an improper fraction and then evaluate the absolute value of the resulting fraction. In this article, we evaluated the absolute value of $3 \frac{1}{2}$ and determined that the correct answer is option C, $3 \frac{1}{2}$.

Final Answer

The final answer is:

Introduction

In our previous article, we explored the concept of absolute value in mixed numbers and determined the correct answer to the given problem. In this article, we will provide a Q&A guide to help you better understand the concept of absolute value in mixed numbers.

Q: What is absolute value?

A: Absolute value is a mathematical operation that returns the distance of a number from zero on the number line. It is denoted by the symbol $|x|$, where $x$ is the number being evaluated. The absolute value of a number is always non-negative, meaning it is either positive or zero.

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

A: To convert a mixed number to an improper fraction, you need to multiply the whole number part by the denominator and add the numerator. For example, let's convert the mixed number $3 \frac{1}{2}$ to an improper fraction:

$$3 \frac{1}{2} = \frac{(3 \times 2) + 1}{2} = \frac{6 + 1}{2} = \frac{7}{2}$$

Q: How do I evaluate the absolute value of a mixed number?

A: To evaluate the absolute value of a mixed number, you need to convert it to an improper fraction and then evaluate the absolute value of the resulting fraction. For example, let's evaluate the absolute value of $3 \frac{1}{2}$:

$$\left|3 \frac{1}{2}\right| = \left|\frac{7}{2}\right| = \frac{|7|}{|2|} = \frac{7}{2}$$

Q: What is the correct answer to the problem $\left|3 \frac{1}{2}\right|$?

A: The correct answer is option C, $3 \frac{1}{2}$.

Q: Can I use absolute value to solve equations with mixed numbers?

A: Yes, you can use absolute value to solve equations with mixed numbers. However, you need to follow the same steps as before: convert the mixed number to an improper fraction, evaluate the absolute value of the resulting fraction, and then solve the equation.

Q: What are some common mistakes to avoid when working with absolute value in mixed numbers?

A: Some common mistakes to avoid when working with absolute value in mixed numbers include:

• Not converting the mixed number to an improper fraction before evaluating the absolute value
• Not evaluating the absolute value of the resulting fraction
• Not following the correct order of operations when solving equations with mixed numbers

Q: How can I practice working with absolute value in mixed numbers?

A: You can practice working with absolute value in mixed numbers by:

• Converting mixed numbers to improper fractions and evaluating their absolute values
• Solving equations with mixed numbers using absolute value
• Creating your own problems and solutions to practice working with absolute value in mixed numbers

Conclusion

In conclusion, absolute value in mixed numbers is an important concept in mathematics that can be used to solve equations and evaluate the magnitude of numbers. By following the steps outlined in this article, you can better understand and work with absolute value in mixed numbers. Remember to practice regularly to build your skills and confidence.

Final Tips

• Always convert mixed numbers to improper fractions before evaluating their absolute values
• Follow the correct order of operations when solving equations with mixed numbers
• Practice regularly to build your skills and confidence working with absolute value in mixed numbers