Question

2/3 divided by 2 5/7

Answer 1

To divide \( \frac{2}{3} \) by \( 2 \frac{5}{7} \), we first need to convert the mixed number \( 2 \frac{5}{7} \) into an improper fraction.

1. Convert \( 2 \frac{5}{7} \):
\[
2 \frac{5}{7} = 2 \times 7 + 5 = 14 + 5 = 19
\]
So, \( 2 \frac{5}{7} = \frac{19}{7} \).

2. Now, to divide \( \frac{2}{3} \) by \( \frac{19}{7} \), we multiply by the reciprocal of \( \frac{19}{7} \):
\[
\frac{2}{3} \div \frac{19}{7} = \frac{2}{3} \times \frac{7}{19}
\]

3. Multiply the fractions:
\[
\frac{2 \times 7}{3 \times 19} = \frac{14}{57}
\]

Thus, \( \frac{2}{3} \div 2 \frac{5}{7} = \frac{14}{57} \).

This fraction can be simplified further if possible, though \( 14 \) and \( 57 \) have no common factors (other than 1).

Therefore, the final answer is:
\[
\frac{14}{57}
\]