To divide \( \frac{1}{4} \) by \( 2 \frac{2}{3} \), we first need to convert the mixed number \( 2 \frac{2}{3} \) into an improper fraction.
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Convert \( 2 \frac{2}{3} \): \[ 2 \frac{2}{3} = 2 \times 3 + 2 = 6 + 2 = 8 \] So, \[ 2 \frac{2}{3} = \frac{8}{3} \]
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Now, dividing \( \frac{1}{4} \) by \( \frac{8}{3} \) is the same as multiplying \( \frac{1}{4} \) by the reciprocal of \( \frac{8}{3} \): \[ \frac{1}{4} \div \frac{8}{3} = \frac{1}{4} \times \frac{3}{8} \]
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Now, multiply the fractions: \[ \frac{1 \times 3}{4 \times 8} = \frac{3}{32} \]
Thus, the quotient of \( \frac{1}{4} \) divided by \( 2 \frac{2}{3} \) is \( \frac{3}{32} \).
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