To solve the problem in the image, we need to calculate how many pounds of cheese the school cafeteria uses for $3 \frac{1}{2}$ large pizzas, given that each large pizza uses $2 \frac{1}{3}$ pounds of cheese.

Step 1: Convert mixed numbers to improper fractions

• $2 \frac{1}{3}$ can be written as $\frac{7}{3}$.
• $3 \frac{1}{2}$ can be written as $\frac{7}{2}$.

Step 2: Multiply the amount of cheese per pizza by the number of pizzas

We now multiply $\frac{7}{3}$ (cheese per pizza) by $\frac{7}{2}$ (number of pizzas):

$\frac{7}{3} \times \frac{7}{2} = \frac{49}{6}$

Step 3: Convert the improper fraction to a mixed number

$\frac{49}{6} = 8 \frac{1}{6}$

Thus, the school cafeteria will use $8 \frac{1}{6}$ pounds of cheese to make $3 \frac{1}{2}$ large pizzas.

Would you like any more details or explanations?

Related Questions:

1. How would the total cheese amount change if the cafeteria made 5 pizzas?
2. How would you multiply two improper fractions in general?
3. Can you express $8 \frac{1}{6}$ as a decimal?
4. How much cheese would be needed if each pizza required $3 \frac{1}{2}$ pounds of cheese?
5. How would the solution change if they made $4 \frac{1}{4}$ pizzas instead of $3 \frac{1}{2}$?

Tip:

When dealing with mixed numbers, converting them to improper fractions first makes multiplication easier!