Solve: 5/6 Divided by 3 1/3 - Fraction Division Steps

To solve the problem $\frac{5}{6} : 3\frac{1}{3}$, we follow these steps:

• Step 1: Convert the mixed number to an improper fraction.
• Step 2: Multiply the dividend by the reciprocal of the improper fraction.
• Step 3: Simplify the resulting fraction.

Let's carry out these steps:
Step 1: Convert $3\frac{1}{3}$ into an improper fraction. We do this by multiplying the whole number $3$ by the denominator $3$ and adding the numerator $1$, giving us:

This yields the improper fraction $\frac{10}{3}$.

Step 2: Divide $\frac{5}{6}$ by $\frac{10}{3}$ involves multiplying $\frac{5}{6}$ by the reciprocal of $\frac{10}{3}$, which is $\frac{3}{10}$:

Step 3: Simplify $\frac{15}{60}$ by dividing both the numerator and denominator by their greatest common divisor, which is 15:

Thus, the solution to $\frac{5}{6} : 3\frac{1}{3}$ is $\frac{1}{4}$.