Solve Fraction Division: Calculate 3/4 ÷ 5/6 Step-by-Step

To solve the problem of dividing two fractions, we apply the method of multiplication by the reciprocal:

• Step 1: The given problem is $\frac{3}{4} \div \frac{5}{6}$.
• Step 2: Find the reciprocal of the divisor $\frac{5}{6}$, which is $\frac{6}{5}$.
• Step 3: Multiply the dividend $\frac{3}{4}$ by the reciprocal of the divisor: $\frac{3}{4} \times \frac{6}{5}$
• Step 4: Perform the multiplication: $\frac{3 \times 6}{4 \times 5} = \frac{18}{20}$
• Step 5: Simplify the resulting fraction $\frac{18}{20}$: $\frac{18 \div 2}{20 \div 2} = \frac{9}{10}$

Therefore, the correct result of the division $\frac{3}{4} \div \frac{5}{6}$ is $\frac{9}{10}$.