Multiply Mixed Numbers: 1⅞ × 2⅓ Step-by-Step Solution

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.
• Step 4: Convert the improper fraction back to a mixed number if necessary.

Let's begin:

Step 1: Convert to improper fractions
Convert $1\frac{6}{8}$ to an improper fraction:
$\frac{8 \times 1 + 6}{8} = \frac{14}{8}$.

Convert $2\frac{2}{6}$ to an improper fraction:
$\frac{6 \times 2 + 2}{6} = \frac{14}{6}$.

Step 2: Multiply the fractions
Multiply $\frac{14}{8}$ and $\frac{14}{6}$:
$\frac{14}{8} \times \frac{14}{6} = \frac{196}{48}$.

Step 3: Simplify the fraction
Find the greatest common divisor (GCD) of 196 and 48, which is 4. Simplify $\frac{196}{48}$:
$\frac{196 \div 4}{48 \div 4} = \frac{49}{12}$.

Step 4: Convert to a mixed number
$\frac{49}{12}$ as a mixed number is $4\frac{1}{12}$ since 49 divided by 12 is 4 with a remainder of 1.

Therefore, the solution to the problem is $4\frac{1}{12}$.