To compute \( \frac{6}{7} \div \frac{3}{5} \), you can multiply by the reciprocal of the second fraction:
\[ \frac{6}{7} \div \frac{3}{5} = \frac{6}{7} \times \frac{5}{3} \]
Next, multiply the numerators together and the denominators together:
\[ = \frac{6 \times 5}{7 \times 3} = \frac{30}{21} \]
Now, simplify \( \frac{30}{21} \). The greatest common divisor (GCD) of 30 and 21 is 3, so you divide both the numerator and the denominator by 3:
\[ \frac{30 \div 3}{21 \div 3} = \frac{10}{7} \]
Thus, the simplified answer is:
\[ \frac{10}{7} \]
or \( 1 \frac{3}{7} \) as a mixed number.
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