Solve Mixed Number Division: 3 2/5 ÷ 6 3/7 Step-by-Step

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

• Step 1: Convert the mixed numbers into improper fractions.
• Step 2: Multiply by the reciprocal of the second fraction.
• Step 3: Simplify the resulting fraction.

Now, let's work through each step:

Step 1: Conversion to improper fractions.
For the mixed number $3\frac{2}{5}$:

• Convert to an improper fraction: $3\frac{2}{5} = \frac{3 \times 5 + 2}{5} = \frac{17}{5}$

For the mixed number $6\frac{3}{7}$:

• Convert to an improper fraction: $6\frac{3}{7} = \frac{6 \times 7 + 3}{7} = \frac{45}{7}$

Step 2: Division using multiplication by the reciprocal.
Instead of dividing $\frac{17}{5}$ by $\frac{45}{7}$, multiply by the reciprocal of $\frac{45}{7}$:

$\frac{17}{5} \div \frac{45}{7} = \frac{17}{5} \times \frac{7}{45}$

Multiply the numerators and denominators:

$= \frac{17 \times 7}{5 \times 45} = \frac{119}{225}$

Step 3: Simplification of the fraction.
The fraction $\frac{119}{225}$ is already in its simplest form, as $119$ and $225$ have no common factors greater than 1.

Therefore, the solution to the problem is $\frac{119}{225}$.