Solve Mixed Number Multiplication: 3⅓ × 2⅕ Step-by-Step

To solve this problem, follow these steps:

• Step 1: Convert mixed numbers to improper fractions.
• Step 2: Simplify the fractions if feasible.
• Step 3: Multiply the improper fractions.
• Step 4: Convert the result back to a mixed number.

Let's work through the steps:

Step 1: Convert the mixed numbers to improper fractions.

$3\frac{5}{15} = 3 + \frac{5}{15} = \frac{45}{15} + \frac{5}{15} = \frac{50}{15}$, simplifying yields $\frac{10}{3}$.

$2\frac{2}{10} = 2 + \frac{2}{10} = \frac{20}{10} + \frac{2}{10} = \frac{22}{10}$, simplifying yields $\frac{11}{5}$.

Step 2: Multiply the fractions.

$\frac{10}{3} \times \frac{11}{5} = \frac{110}{15}$.

Step 3: Simplify the result of the multiplication.

$\frac{110}{15}$ can be simplified by dividing the numerator and the denominator by 5, yielding $\frac{22}{3}$.

Step 4: Convert the resulting improper fraction back to a mixed number.

Dividing, $22 \div 3 = 7$ with a remainder of 1, so $\frac{22}{3} = 7\frac{1}{3}$.

Therefore, the solution to the problem is $7\frac{1}{3}$.