To determine the fraction to divide \( \frac{3}{8} \), we can interpret this in terms of multiplication by the reciprocal. Dividing by a fraction is the same as multiplying by its reciprocal.
If \(\frac{3}{8}\) is being divided by a fraction \(x\), this can be represented mathematically as:
\[ \frac{3}{8} ÷ x = \frac{3}{8} \times \frac{1}{x} \]
Let's evaluate the provided options to find a suitable fraction \(x\) that, when used to divide \( \frac{3}{8} \), gives us a concrete answer (often we look for a simplified or common fraction).
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\( \frac{3}{4} \):
- This would result in \( \frac{3}{8} ÷ \frac{3}{4} = \frac{3}{8} \times \frac{4}{3} = \frac{4}{8} = \frac{1}{2} \).
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\( \frac{10}{16} \):
- This fraction simplifies to \( \frac{5}{8} \).
- The operation becomes \( \frac{3}{8} ÷ \frac{5}{8} = \frac{3}{8} \times \frac{8}{5} = \frac{3}{5} \).
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\( \frac{5}{8} \):
- Here, \( \frac{3}{8} ÷ \frac{5}{8} = \frac{3}{8} \times \frac{8}{5} = \frac{3}{5} \).
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\( \frac{1}{2} \):
- This operation gives \( \frac{3}{8} ÷ \frac{1}{2} = \frac{3}{8} \times 2 = \frac{6}{8} = \frac{3}{4} \).
To summarize, the viable options that divide \( \frac{3}{8} \) yield varying outcomes, and we notice that dividing by \( \frac{3}{4} \) results in a fraction of \( \frac{1}{2} \).
Since the question specifically asks for the fraction used to divide \( \frac{3}{8} \), we can say that:
The answer is \( \frac{3}{4} \).
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