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To solve this problem, we need to match the given equations with the appropriate situations about how many pints of broth are needed for \( \frac{1}{4} \) pot of soup and \( 2 \frac{3}{4} \) pots of soup.

1. **For \( \frac{1}{4} \) pot of soup**:
   Since each pot requires \( 2 \frac{1}{2} \) pints of broth, the amount of broth needed for \( \frac{1}{4} \) pot would be:
   \[
   \frac{1}{4} \times 2 \frac{1}{2}
   \]
   Converting \( 2 \frac{1}{2} \) to an improper fraction:
   \[
   2 \frac{1}{2} = \frac{5}{2}
   \]
   Now, multiply:
   \[
   \frac{1}{4} \times \frac{5}{2} = \frac{5}{8}
   \]
   So, the equation for \( \frac{1}{4} \) pot of soup is \( \frac{1}{4} \times 2 \frac{1}{2} = \frac{5}{8} \).

2. **For \( 2 \frac{3}{4} \) pots of soup**:
   The amount of broth needed for \( 2 \frac{3}{4} \) pots would be:
   \[
   2 \frac{3}{4} \times 2 \frac{1}{2}
   \]
   Converting both mixed numbers to improper fractions:
   \[
   2 \frac{3}{4} = \frac{11}{4} \quad \text{and} \quad 2 \frac{1}{2} = \frac{5}{2}
   \]
   Now, multiply:
   \[
   \frac{11}{4} \times \frac{5}{2} = \frac{55}{8} = 6 \frac{7}{8}
   \]
   So, the equation for \( 2 \frac{3}{4} \) pots of soup is \( 2 \frac{3}{4} \times 2 \frac{1}{2} = 6 \frac{7}{8} \).

Thus, the correct equations for each situation are:
- \( \frac{1}{4} \times 2 \frac{1}{2} = \frac{5}{8} \) for \( \frac{1}{4} \) pot of soup.
- \( 2 \frac{3}{4} \times 2 \frac{1}{2} = 6 \frac{7}{8} \) for \( 2 \frac{3}{4} \) pots of soup.

Would you like any more details or clarifications?

Here are five questions to expand on the topic:
1. How do you convert a mixed number to an improper fraction?
2. What is the process for multiplying two fractions?
3. Can you explain why multiplying by \( \frac{1}{4} \) reduces the total broth needed?
4. How would the equation change if \( 1 \frac{1}{2} \) pots of soup were required?
5. What happens to the result if you divide instead of multiply fractions?

**Tip:** Always convert mixed numbers to improper fractions when multiplying or dividing them for easier calculations!

How many pints are needed for 1/4 pot of soup? How many pints are needed for 2 3/4 pots of soup?

This problem involves calculating how many pints of broth are needed for a fraction or multiple pots of soup. Learn how to multiply fractions and mixed numbers to find the answers for 1/4 and 2 3/4 pots of soup.

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