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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.

Phoebe has designed a rectangular rug. The length of the rug is 6 meters, and the width is 3 7/8 meters. What is the total area of the rug in m²?

Learn how to calculate the area of a rectangular rug with dimensions of 6 meters by 3 7/8 meters. This problem covers basic geometry concepts like area calculation, multiplying whole numbers by fractions, and simplifying the result. Suitable for students in Grades 5-7.

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