To divide \(\frac{17}{4}\) by \(4\), you can rewrite the division by multiplying \(\frac{17}{4}\) by the reciprocal of \(4\):
\[ 4 = \frac{4}{1} \]
Now, the reciprocal of \(\frac{4}{1}\) is \(\frac{1}{4}\). So, we have:
\[ \frac{17}{4} \div 4 = \frac{17}{4} \times \frac{1}{4} \]
Now, multiply the fractions:
\[ \frac{17 \times 1}{4 \times 4} = \frac{17}{16} \]
Now, we check if \(\frac{17}{16}\) is in simplest form. Since \(17\) is a prime number and does not share any common factors with \(16\), \(\frac{17}{16}\) is already in simplest form.
Since \(17\) is greater than \(16\), we can also express it as a mixed number:
\[ \frac{17}{16} = 1 \frac{1}{16} \]
Thus, the answer can be provided either as an improper fraction or a mixed number:
\[ \frac{17}{16} \quad \text{or} \quad 1 \frac{1}{16} \]
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