The image contains a word problem about Luman preparing lemonade for a party. Here's a breakdown of the question and the relevant mathematical details:

Problem: Luman is preparing lemonade for a party. He uses $2 \frac{1}{2}$ tablespoons of lemon juice to prepare one glass of lemonade. He pours $4 \frac{1}{2}$ glasses of lemonade to fill a pitcher. The question asks how many tablespoons of lemon juice will be used to make $1 \frac{1}{2}$ pitchers of lemonade.

Solution Steps:

1. Determine lemon juice per pitcher:

   • Each glass requires $2 \frac{1}{2} = \frac{5}{2}$ tablespoons of lemon juice.
   • Luman pours $4 \frac{1}{2} = \frac{9}{2}$ glasses of lemonade per pitcher.
   • Therefore, the total tablespoons of lemon juice per pitcher is: $\frac{9}{2} \text{ glasses} \times \frac{5}{2} \text{ tablespoons/glass} = \frac{45}{4} \text{ tablespoons per pitcher.}$

2. Determine lemon juice for $1 \frac{1}{2}$ pitchers:

   • $1 \frac{1}{2} = \frac{3}{2}$ pitchers.
   • The total tablespoons for $1 \frac{1}{2}$ pitchers is: $\frac{3}{2} \text{ pitchers} \times \frac{45}{4} \text{ tablespoons/pitcher} = \frac{135}{8} \text{ tablespoons.}$

Thus, Luman uses $\frac{135}{8}$ tablespoons of lemon juice for $1 \frac{1}{2}$ pitchers.

This matches option d) $\frac{135}{8}$.

Would you like more details or clarifications?

Here are some questions to deepen your understanding:

1. How do you convert mixed numbers into improper fractions?
2. Why do we multiply when calculating the amount per pitcher?
3. How would you calculate the total lemon juice for different amounts of glasses?
4. What is the benefit of converting all measurements into fractions?
5. How can we simplify the fraction $\frac{135}{8}$ if required?

Tip: Always convert mixed numbers to improper fractions before performing multiplication for easier calculation.