Solve the Ratio Equation: 3 to 5/6 Proportion Problem

To solve this problem, let's carry out the following steps:

• Step 1: Recognize that the expression $3 : \frac{5}{6}$ represents division, so it becomes $3 \div \frac{5}{6}$.
• Step 2: Use the rule that dividing by a fraction is the same as multiplying by its reciprocal. Thus, convert this to $3 \times \frac{6}{5}$.
• Step 3: Multiply 3 (which can be written as $\frac{3}{1}$) by $\frac{6}{5}$:
  $\frac{3}{1} \times \frac{6}{5} = \frac{3 \times 6}{1 \times 5} = \frac{18}{5}$.
• Step 4: Convert $\frac{18}{5}$ to a mixed number. Divide 18 by 5:
  - 5 goes into 18 three times with a remainder of 3.
  - Therefore, $\frac{18}{5} = 3\frac{3}{5}$.

Thus, the solution to the problem is $3\frac{3}{5}$.