Question

find the quotient
1/4 divided by 2 and 2/3

Answer 1

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.

1. Convert \( 2 \frac{2}{3} \):
\[
2 \frac{2}{3} = 2 \times 3 + 2 = 6 + 2 = 8
\]
So,
\[
2 \frac{2}{3} = \frac{8}{3}
\]

2. Now, dividing \( \frac{1}{4} \) by \( \frac{8}{3} \) is the same as multiplying \( \frac{1}{4} \) by the reciprocal of \( \frac{8}{3} \):
\[
\frac{1}{4} \div \frac{8}{3} = \frac{1}{4} \times \frac{3}{8}
\]

3. 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 \( \frac{3}{32} \).