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

To solve this problem, we'll follow these steps:

• Step 1: Identify the given fractions.
• Step 2: Take the reciprocal of the second fraction.
• Step 3: Perform the multiplication using the reciprocal.
• Step 4: Simplify the resultant fraction if possible.
• Step 5: Convert to a mixed number if needed.

First, let's restate the problem equation:
We are to compute $\frac{5}{6} \div \frac{3}{5}$.

Step 1: Identify the fractions: $\frac{5}{6} \text{ and } \frac{3}{5}$.

Step 2: Take the reciprocal of $\frac{3}{5}$, which is $\frac{5}{3}$.

Step 3: Multiply $\frac{5}{6}$ by $\frac{5}{3}$:
$\frac{5}{6} \times \frac{5}{3} = \frac{5 \times 5}{6 \times 3} = \frac{25}{18}$.

Step 4: Convert $\frac{25}{18}$ to a mixed number:
$25 \div 18 = 1$ remainder $7$. Therefore, $\frac{25}{18} = 1\frac{7}{18}$.

Therefore, the result of $\frac{5}{6} \div \frac{3}{5}$ is $1\frac{7}{18}$.