Solve Mixed Number Multiplication: 2⅓ × 1⅖ Step-by-Step

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

• Step 1: Convert each mixed number to an improper fraction.
• Step 2: Multiply the improper fractions.
• Step 3: Simplify the resulting fraction, if necessary.
• Step 4: Convert the result back to a mixed number.

Now, let's work through each step:

Step 1: Convert each mixed number to an improper fraction.

For $2\frac{2}{6}$:

$2\frac{2}{6} = \frac{2 \times 6 + 2}{6} = \frac{12 + 2}{6} = \frac{14}{6}$

Simplifying $\frac{14}{6}$ by dividing the numerator and the denominator by 2, we get $\frac{14}{6} = \frac{7}{3}$.

For $1\frac{4}{10}$:

$1\frac{4}{10} = \frac{1 \times 10 + 4}{10} = \frac{10 + 4}{10} = \frac{14}{10}$

Simplifying $\frac{14}{10}$ by dividing the numerator and the denominator by 2, we get $\frac{14}{10} = \frac{7}{5}$.

Step 2: Multiply the improper fractions:

$\frac{7}{3} \times \frac{7}{5} = \frac{7 \times 7}{3 \times 5} = \frac{49}{15}$

Step 3: Simplify the resulting fraction, if necessary. In this case, $\frac{49}{15}$ is already in its simplest form.

Step 4: Convert the result back to a mixed number:

$\frac{49}{15}$ can be rewritten as $3\frac{4}{15}$, since 49 divided by 15 is 3 with a remainder of 4.

Therefore, the solution to the problem is $3\frac{4}{15}$.