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The image presents a problem about a rectangular table with a width of \( 2 \frac{1}{4} \) feet and an area of 15 square feet. The task is to find the length of the table. The solution is provided step-by-step.

### Breakdown of the Solution:

1. **Formula for Area**:  
   The area \( A \) of a rectangle is given by the formula \( A = l \times w \), where \( l \) is the length and \( w \) is the width.
   To find the length \( l \), we rearrange this formula:  
   \[
   l = \frac{A}{w}
   \]

2. **Substituting Values**:  
   Given \( A = 15 \) square feet and \( w = 2 \frac{1}{4} \) feet, the equation becomes:  
   \[
   l = \frac{15}{2 \frac{1}{4}}
   \]

3. **Converting Mixed Number to Improper Fraction**:  
   The width \( 2 \frac{1}{4} \) is converted into an improper fraction:  
   \[
   2 \frac{1}{4} = \frac{9}{4}
   \]
   Therefore, the equation becomes:  
   \[
   l = \frac{15}{\frac{9}{4}}
   \]

4. **Division as Multiplication by the Reciprocal**:  
   Dividing by a fraction is the same as multiplying by its reciprocal. So, this equation is rewritten as:  
   \[
   l = 15 \times \frac{4}{9}
   \]

5. **Simplification**:  
   Simplifying \( 15 \times \frac{4}{9} \):
   \[
   15 \times \frac{4}{9} = \frac{60}{9}
   \]
   This fraction simplifies to:  
   \[
   \frac{60}{9} = \frac{20}{3}
   \]

6. **Converting to a Mixed Number**:  
   The improper fraction \( \frac{20}{3} \) is converted to the mixed number:  
   \[
   \frac{20}{3} = 6 \frac{2}{3}
   \]

Therefore, **the length of the table is \( 6 \frac{2}{3} \) feet**.

### Would you like further details or have any questions?

Here are 5 related questions to explore:

1. How do you convert a mixed number to an improper fraction?
2. Why do we multiply by the reciprocal when dividing fractions?
3. Can you find the length of a rectangle if the width is given in decimal form?
4. How can you simplify large fractions efficiently?
5. What is the relationship between the area of a rectangle and its dimensions?

**Tip:** When converting mixed numbers to improper fractions, remember that the whole number is multiplied by the denominator, and then the numerator is added to it.

A rectangular table has a width of 2 1/4 feet and an area of 15 square feet. What is the length of the table?

This step-by-step solution demonstrates how to find the length of a rectangular table with a width of 2 1/4 feet and an area of 15 square feet. Key concepts include fractions and the area of a rectangle. Suitable for students in Grades 5-7.

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