To convert the improper fraction [tex]\(\frac{23}{5}\)[/tex] to a mixed number, follow these steps:
1. Divide the numerator by the denominator to get the whole number part:
[tex]\[
23 \div 5 = 4 \quad \text{(whole number part)}
\][/tex]
2. Find the remainder of this division, which will be the numerator of the fractional part:
[tex]\[
23 \mod 5 = 3 \quad \text{(numerator of the fractional part)}
\][/tex]
3. The denominator remains the same:
[tex]\[
5 \quad \text{(denominator of the fractional part)}
\][/tex]
4. Combine the whole number part and the fractional part to form the mixed number:
[tex]\[
4 \frac{3}{5}
\][/tex]
Therefore, the improper fraction [tex]\(\frac{23}{5}\)[/tex] as a mixed number is [tex]\(4 \frac{3}{5}\)[/tex].
Among the given options, the correct answer is:
[tex]\[ 4 \frac{3}{5} \][/tex]
