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The problem states:

"A recipe that serves 8 people requires \(1 \frac{1}{4}\) cups of sugar. Using this recipe, how many cups of sugar are needed to serve 12 people?"

### Solution:

1. Convert \(1 \frac{1}{4}\) cups of sugar to an improper fraction:
   \[
   1 \frac{1}{4} = \frac{5}{4}
   \]
2. Now, we know that \(\frac{5}{4}\) cups of sugar serve 8 people. To find how many cups are needed for 1 person, divide by 8:
   \[
   \text{Sugar per person} = \frac{5}{4} \div 8 = \frac{5}{4} \times \frac{1}{8} = \frac{5}{32}
   \]
3. To find the sugar required for 12 people, multiply by 12:
   \[
   \text{Sugar for 12 people} = \frac{5}{32} \times 12 = \frac{60}{32} = \frac{15}{8} = 1 \frac{7}{8}
   \]

Thus, \(1 \frac{7}{8}\) cups of sugar are needed to serve 12 people.

Would you like further details on any step?

### Related Questions:
1. How do you convert a mixed fraction to an improper fraction?
2. What is the process for dividing fractions?
3. How do you multiply fractions?
4. How do you simplify improper fractions into mixed numbers?
5. How can this method be applied to other ingredients in a recipe?

**Tip**: Always convert mixed numbers into improper fractions when performing multiplication or division with fractions.

A recipe that serves 8 people requires 1 1/4 cups of sugar. Using this recipe, how many cups of sugar are needed to serve 12 people?

Learn how to adjust a recipe serving 8 people that requires 1 1/4 cups of sugar, to calculate the correct amount of sugar needed to serve 12 people. This solution covers key concepts like improper fractions, ratios, and proportions, suitable for students in Grades 6-8.

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