To solve \( 113 \div 23 \):
- Calculate how many times 23 fits into 113.
- \( 23 \times 4 = 92 \) and \( 23 \times 5 = 115 \). Thus, 23 fits into 113 four times.
- Now subtract: \( 113 - 92 = 21 \).
- So, \( 113 \div 23 = 4 \) remainder \( 21 \).
To express this as a mixed number:
- The result is \( 4 \) with a remainder of \( 21 \) out of \( 23 \). This can be written as:
\[ 4\frac{21}{23} \]
None of the answer choices directly match, but we can also express it as:
- \( 4\) which is \( 4 \times 23 + 21 = 113\), and can be interpreted as \( 4\) and some extra portion which is the remainder.
None of the answer choices seem to match directly with the computed result, but \( 4\frac{21}{23} \) can be equated to the option that limits the result to a specific form.
However, if we consider just the integer part, the closest representation we have from your provided answer choices are:
- \( 11\) halves and \( 13\) sixths also do not accurately represent the division \( 113 \div 23\).
Thus, strictly answering based on the quotient, The most accurate answer should be listed based on choices given.
None of the choices reflect \( 4\) as we computed, but just remaining with noting the calculation:
- The answer \( 4\) or \( 4\frac{21}{23}\) is what \( 113 \div 23 \) signifies.
In conclusion, none of the provided options seem to fit based on the numerical computations from \( 113 \div 23 = 4 \frac{21}{23}\).