What is the result of dividing the fraction \( \frac{3}{4} \) by the fraction \( \frac{5}{6} \) ?

Step 1 ：To divide fractions, we multiply the first fraction by the reciprocal of the second fraction. The reciprocal of a fraction is obtained by interchanging the numerator and the denominator. So, the reciprocal of \( \frac{5}{6} \) is \( \frac{6}{5} \).

Step 2 ：Now, multiply \( \frac{3}{4} \) by \( \frac{6}{5} \) . In multiplying fractions, we simply multiply the numerators together to get the new numerator, and the denominators together to get the new denominator.

Step 3 ：So, \( \frac{3}{4} \times \frac{6}{5} = \frac{3 \times 6}{4 \times 5} = \frac{18}{20} \)

Step 4 ：Lastly, we simplify the fraction \( \frac{18}{20} \) by dividing both the numerator and the denominator by their greatest common divisor, which is 2. So, \( \frac{18}{20} = \frac{9}{10} \)