To convert the improper fraction [tex]\(\frac{153}{5}\)[/tex] to a mixed number, follow these steps:
1. Divide the numerator by the denominator to find the whole number part of the mixed number.
[tex]\[
153 \div 5 = 30 \quad \text{(whole number part)}
\][/tex]
2. Calculate the remainder when the numerator is divided by the denominator.
[tex]\[
153 \mod 5 = 3 \quad \text{(remainder)}
\][/tex]
3. Form the mixed number by combining the whole number and the remainder over the original denominator. Thus, the mixed number is:
[tex]\[
30 \frac{3}{5}
\][/tex]
Given the options:
- [tex]\(30 \frac{5}{3}\)[/tex]
- [tex]\(30 \frac{3}{5}\)[/tex]
- [tex]\(5 \frac{3}{30}\)[/tex]
- [tex]\(3 \frac{3}{5}\)[/tex]
The correct mixed number is [tex]\(30 \frac{3}{5}\)[/tex].
Therefore, the answer is [tex]\( \boxed{30 \frac{3}{5}}\)[/tex].
