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 ​

When dealing with absolute value, it's essential to understand that the result is always non-negative. In this case, we're given a mixed number, $3 \frac{1}{2}$, and asked to find its absolute value. To approach this problem, let's first convert the mixed number to an improper fraction.

Converting Mixed Numbers to Improper Fractions

A mixed number is a combination of a whole number and a fraction. To convert a mixed number to an improper fraction, we multiply the whole number by the denominator and then add the numerator. In this case, we have:

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

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

Finding the Absolute Value

The absolute value of a number is its distance from zero on the number line. Since the absolute value is always non-negative, we can simply take the absolute value of the numerator and keep the denominator the same.

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

So, the absolute value of $3 \frac{1}{2}$ is $\frac{7}{2}$, which is equivalent to $3 \frac{1}{2}$.

Evaluating the Answer Choices

Now that we have found the absolute value of $3 \frac{1}{2}$, let's evaluate the answer choices:

A. $-\frac{2}{7}$: This is not the correct answer, as the absolute value is always non-negative.

B. $-3 \frac{1}{2}$: This is also not the correct answer, as the absolute value is always non-negative.

C. $3 \frac{1}{2}$: This is the correct answer, as we found that the absolute value of $3 \frac{1}{2}$ is indeed $3 \frac{1}{2}$.

D. $-\frac{2}{7}$: This is not the correct answer, as the absolute value is always non-negative.

Conclusion

In conclusion, the absolute value of $3 \frac{1}{2}$ is $3 \frac{1}{2}$. This is because the absolute value is always non-negative, and the absolute value of $3 \frac{1}{2}$ is equivalent to $3 \frac{1}{2}$.

Key Takeaways

• The absolute value of a number is its distance from zero on the number line.
• The absolute value is always non-negative.
• To find the absolute value of a mixed number, convert it to an improper fraction and take the absolute value of the numerator.
• The absolute value of $3 \frac{1}{2}$ is $3 \frac{1}{2}$.

Practice Problems

1. Find the absolute value of $2 \frac{3}{4}$.
2. Find the absolute value of $-5 \frac{1}{3}$.
3. Find the absolute value of $4 \frac{2}{5}$.

Solutions

1. The absolute value of $2 \frac{3}{4}$ is $\frac{11}{4}$, which is equivalent to $2 \frac{3}{4}$.
2. The absolute value of $-5 \frac{1}{3}$ is $\frac{16}{3}$, which is equivalent to $5 \frac{1}{3}$.
3. The absolute value of $4 \frac{2}{5}$ is $\frac{22}{5}$, which is equivalent to $4 \frac{2}{5}$.
   Absolute Value Q&A =====================

Q: What is the definition of absolute value?

A: The absolute value of a number is its distance from zero on the number line. It is always non-negative.

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

A: To find the absolute value of a mixed number, convert it to an improper fraction and take the absolute value of the numerator. For example, to find the absolute value of $3 \frac{1}{2}$, convert it to an improper fraction: $\frac{(3 \times 2) + 1}{2} = \frac{7}{2}$. Then, take the absolute value of the numerator: $\left|\frac{7}{2}\right| = \frac{7}{2}$.

Q: What is the difference between absolute value and negative value?

A: The absolute value of a number is its distance from zero on the number line, while the negative value of a number is its distance from zero in the opposite direction. For example, the absolute value of $-3$ is $3$, while the negative value of $3$ is $-3$.

Q: Can the absolute value of a number be negative?

A: No, the absolute value of a number is always non-negative.

Q: How do I find the absolute value of a decimal number?

A: To find the absolute value of a decimal number, simply remove the negative sign if it exists. For example, the absolute value of $-4.5$ is $4.5$.

Q: Can the absolute value of a fraction be a fraction?

A: Yes, the absolute value of a fraction can be a fraction. For example, the absolute value of $\frac{-3}{4}$ is $\frac{3}{4}$.

Q: How do I find the absolute value of a negative integer?

A: To find the absolute value of a negative integer, simply remove the negative sign. For example, the absolute value of $-5$ is $5$.

Q: Can the absolute value of a negative mixed number be a negative mixed number?

A: No, the absolute value of a negative mixed number is always a non-negative mixed number. For example, the absolute value of $-3 \frac{1}{2}$ is $3 \frac{1}{2}$.

Q: How do I find the absolute value of a negative decimal number?

A: To find the absolute value of a negative decimal number, simply remove the negative sign. For example, the absolute value of $-4.5$ is $4.5$.

Q: Can the absolute value of a negative fraction be a negative fraction?

A: No, the absolute value of a negative fraction is always a non-negative fraction. For example, the absolute value of $\frac{-3}{4}$ is $\frac{3}{4}$.

Q: How do I find the absolute value of a negative integer with a negative exponent?

A: To find the absolute value of a negative integer with a negative exponent, simply remove the negative sign from the exponent. For example, the absolute value of $-2^{-3}$ is $2^{-3}$.

Q: Can the absolute value of a negative mixed number with a negative exponent be a negative mixed number?

A: No, the absolute value of a negative mixed number with a negative exponent is always a non-negative mixed number. For example, the absolute value of $-3 \frac{1}{2}^{-2}$ is $3 \frac{1}{2}^{-2}$.

Q: How do I find the absolute value of a negative decimal number with a negative exponent?

A: To find the absolute value of a negative decimal number with a negative exponent, simply remove the negative sign from the exponent. For example, the absolute value of $-4.5^{-2}$ is $4.5^{-2}$.

Q: Can the absolute value of a negative fraction with a negative exponent be a negative fraction?

A: No, the absolute value of a negative fraction with a negative exponent is always a non-negative fraction. For example, the absolute value of $\frac{-3}{4}^{-2}$ is $\frac{3}{4}^{-2}$.