To simplify \( 64 \frac{4}{3} \), we first convert the mixed number to an improper fraction.
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Convert \( 64 \frac{4}{3} \) to an improper fraction:
\( 64 \) can be rewritten as \( \frac{64 \times 3}{3} = \frac{192}{3} \).
Now, add the fraction part \( \frac{4}{3} \):
\[ \frac{192}{3} + \frac{4}{3} = \frac{192 + 4}{3} = \frac{196}{3} \]
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Simplify \( \frac{196}{3} \): Since \( 196 \) is not divisible by \( 3 \), \( \frac{196}{3} \) is already in simplest form.
If we want a decimal approximation:
\[ \frac{196}{3} \approx 65.33 \]
Comparing to the given options:
- 16 → not \( 64 \frac{4}{3} \)
- 256 → \( 64 \times 4 = 256 \) but not the quantity we are simplifying.
- 85.3 → incorrect.
- 4,096 → not relevant here.
Therefore, \( 64 \frac{4}{3} \) remains as \( \frac{196}{3} \) or approximately \( 65.33 \), which is not listed in the options provided. It seems there might have been a misunderstanding of the question. Can you clarify what is being asked?