To find out how much sugar Roy would use for 3 1/2 batches of cookies, you need to multiply the amount of sugar required for one batch by the number of batches he's making.

Roy's recipe calls for 3 1/2 cups of sugar for one batch. He is making 3 1/2 batches. The calculation is:

$3 \frac{1}{2} \times 3 \frac{1}{2} = \frac{7}{2} \times \frac{7}{2} = \frac{49}{4} = 12 \frac{1}{4}$

So, Roy would need 12 1/4 cups of sugar for 3 1/2 batches of cookies.

Would you like more details or have any other questions?

Here are 5 related questions:

1. How would the sugar amount change if Roy made 2 1/2 batches instead of 3 1/2?
2. If Roy has only 10 cups of sugar, how many batches of cookies can he make?
3. How much sugar would Roy need for 5 batches of cookies?
4. What if Roy increases the sugar per batch by 25%? How much sugar would he need for 3 1/2 batches then?
5. How many cups of sugar would Roy need for half a batch of cookies?

Tip: When working with mixed numbers, converting them to improper fractions can make multiplication easier.