Patti's recipe calls for 3 ¼ cups of sugar to feed 10 people. To find out how much sugar she should use for 5 people, we first need to determine how much sugar is needed per person, and then multiply by the number of people.

1. Convert 3 ¼ cups to an improper fraction: $3 \frac{1}{4} = \frac{13}{4} \text{ cups}$

2. Calculate the amount of sugar per person: $\text{Sugar per person} = \frac{13}{4} \div 10 = \frac{13}{4} \times \frac{1}{10} = \frac{13}{40} \text{ cups}$

3. Calculate the amount of sugar for 5 people: $\text{Sugar for 5 people} = \frac{13}{40} \times 5 = \frac{65}{40} = \frac{13}{8} \text{ cups}$

4. Convert $\frac{13}{8}$ cups to a mixed number: $\frac{13}{8} = 1 \frac{5}{8} \text{ cups}$

So, Patti should use 1 $\frac{5}{8}$ cups of sugar to make ice cream for 5 people.

Would you like more details or have any questions?

Here are some related questions:

1. How much sugar would Patti need if she wanted to make ice cream for 15 people?
2. What if Patti only had 2 cups of sugar? How many people could she serve?
3. How much sugar should Patti use if she wanted to reduce the recipe to serve just 1 person?
4. What if Patti's recipe was doubled to serve 20 people? How much sugar would she need?
5. How would the sugar amount change if the recipe was altered to use 2 ½ cups of sugar for 10 people?

Tip: When dealing with fractions, converting to improper fractions can make calculations easier, especially for multiplication and division.