The problem asks to calculate the area of a rectangle using the given dimensions in mixed numbers.

The length is $5 \frac{1}{6}$ cm and the width is $2 \frac{2}{7}$ cm. The area of a rectangle is calculated as:

$\text{Area} = \text{Length} \times \text{Width}$

Step 1: Convert the mixed numbers to improper fractions

• $5 \frac{1}{6} = \frac{31}{6}$
• $2 \frac{2}{7} = \frac{16}{7}$

Step 2: Multiply the improper fractions

$\frac{31}{6} \times \frac{16}{7} = \frac{31 \times 16}{6 \times 7} = \frac{496}{42}$

Step 3: Simplify the fraction

$\frac{496}{42} = \frac{248}{21} \quad \text{(after dividing numerator and denominator by 2)}$

Step 4: Convert the improper fraction to a mixed number

$\frac{248}{21} = 11 \frac{17}{21}$

Thus, the area of the rectangle is $11 \frac{17}{21}$ square centimeters.

Would you like more details on any part of this solution?

Here are some related questions to deepen understanding:

1. How do you convert a mixed number to an improper fraction?
2. Why is simplifying fractions important when solving problems like this?
3. Can you show how to multiply fractions step-by-step in detail?
4. How can we convert an improper fraction back into a mixed number?
5. What is the practical significance of the area in this problem?

Tip: When converting mixed numbers to improper fractions, remember to multiply the whole number by the denominator and then add the numerator!