Solve Fraction Division: Find the Missing Number in 5/6 ÷ ? = 3/4

To solve this problem, we must find the missing number in the division of fractions equation $\frac{5}{6} : \text{—} = \frac{3}{4}$. We do this by dividing $\frac{5}{6}$ by $\frac{3}{4}$.

Step-by-step solution:

• Step 1: Set up the equation to find the missing number:

$\text{missing number} = \frac{5}{6} \div \frac{3}{4}$

• Step 2: Recall that dividing by a fraction is the same as multiplying by its reciprocal:

$\text{missing number} = \frac{5}{6} \times \frac{4}{3}$

• Step 3: Multiply the fractions:

$\text{missing number} = \frac{5 \times 4}{6 \times 3} = \frac{20}{18}$

• Step 4: Simplify the fraction:

The greatest common divisor of 20 and 18 is 2, so:

$\frac{20}{18} = \frac{20 \div 2}{18 \div 2} = \frac{10}{9}$

• Step 5: Double-check the simplification and calculations to ensure accuracy.

The missing number that completes the equation is $\frac{10}{9}$.

Therefore, the answer is $\frac{9}{10}$.