To determine which improper fraction is equivalent to the mixed number [tex]\(4 \frac{6}{8}\)[/tex], follow these steps:
1. Understand the Mixed Number: A mixed number consists of a whole number and a fraction. Here, the mixed number is [tex]\(4 \frac{6}{8}\)[/tex], where the whole number is 4 and the fractional part is [tex]\(\frac{6}{8}\)[/tex].
2. Convert the Mixed Number to an Improper Fraction:
- The whole number part (4) needs to be converted to a fraction with the same denominator as the fractional part (8).
- Multiply the whole number by the denominator of the fraction to convert it:
[tex]\[
4 \times 8 = 32
\][/tex]
- Add the numerator of the fractional part to this product:
[tex]\[
32 + 6 = 38
\][/tex]
- So, the improper fraction will have 38 as its numerator and retain 8 as the denominator, which gives us:
[tex]\[
\frac{38}{8}
\][/tex]
3. Select the Correct Option:
- Option A: [tex]\(\frac{12}{6}\)[/tex] does not match.
- Option B: [tex]\(\frac{72}{8}\)[/tex] does not match.
- Option C: [tex]\(\frac{38}{8}\)[/tex] matches.
- Option D: [tex]\(\frac{18}{8}\)[/tex] does not match.
Therefore, the improper fraction equivalent to the mixed number [tex]\(4 \frac{6}{8}\)[/tex] is [tex]\(\frac{38}{8}\)[/tex].
Thus, the correct option is:
[tex]\[
\boxed{C}
\][/tex]
