Calculate Rectangle Area: 3 1/6 m × 2 1/3 m Mixed Number Multiplication

What is the area of the rectangle whose length $3\frac{1}{6}$ meters and the width $2\frac{1}{3}$?

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

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

Now, let's work through each step:

Step 1: Convert the mixed numbers to improper fractions.
$3\frac{1}{6} = \frac{3 \times 6 + 1}{6} = \frac{19}{6}$ $2\frac{1}{3} = \frac{2 \times 3 + 1}{3} = \frac{7}{3}$

Step 2: Multiply the improper fractions.
$\frac{19}{6} \times \frac{7}{3} = \frac{19 \times 7}{6 \times 3} = \frac{133}{18}$

Step 3: Simplify the resulting fraction, if possible.

Step 4: Convert back to a mixed number, since $\frac{133}{18}$ is an improper fraction:
Divide 133 by 18 to get the mixed number:
$133 \div 18 = 7$ remainder $7$.
Thus, $\frac{133}{18} = 7\frac{7}{18}$.

Therefore, the area of the rectangle is $7\frac{7}{18}$ square meters.