The problem asks for the total area of a rectangular rug with the given dimensions:

• The length of the rug is 6 meters.
• The width of the rug is 3 7/8 meters.

Step-by-Step Solution:

1. Convert the mixed fraction (3 7/8) to an improper fraction: $3\frac{7}{8} = \frac{(3 \times 8) + 7}{8} = \frac{24 + 7}{8} = \frac{31}{8}$

2. Area formula for a rectangle: $\text{Area} = \text{length} \times \text{width}$ Substituting the given values: $\text{Area} = 6 \times \frac{31}{8}$

3. Simplify: Multiply the whole number 6 by the fraction $\frac{31}{8}$: $\text{Area} = \frac{6 \times 31}{8} = \frac{186}{8}$

4. Simplify the fraction: $\frac{186}{8} = \frac{93}{4} = 23 \frac{1}{4} \, \text{m}^2$

Final Answer:

The total area of the rug is $23 \frac{1}{4} \, \text{m}^2$.

Would you like further details or clarifications?

Here are 5 related questions:

1. How do you convert a mixed number to an improper fraction?
2. How would you calculate the area if the rug had a different shape?
3. Can the area of the rug also be expressed as a decimal?
4. What is the importance of simplifying fractions in geometry problems?
5. How do improper fractions help in multiplication compared to mixed numbers?

Tip: When working with fractions, it's often easier to convert mixed numbers into improper fractions before performing operations like multiplication.