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To solve this problem, we need to determine how many time slots Imani can plan for the performances. Here’s how we solve it:

1. Imani has a total of \( 3 \frac{1}{2} \) hours for the performances. Let's convert this to an improper fraction:
   \[
   3 \frac{1}{2} = \frac{7}{2} \text{ hours}.
   \]

2. Each performer's time slot lasts \( \frac{3}{4} \) hour.

3. To find out how many time slots fit into the total time, divide the total time by the duration of each slot:
   \[
   \frac{7}{2} \div \frac{3}{4} = \frac{7}{2} \times \frac{4}{3} = \frac{28}{6} = \frac{14}{3} = 4 \frac{2}{3}.
   \]

4. This means Imani can plan for 4 full time slots, and there will be \( \frac{2}{3} \) of an hour left over, which is not enough for another full slot.

**Answer:** Imani can plan for 4 full time slots.

Let me know if you'd like more details or have any questions! Here are some follow-up questions to think about:

1. How would the answer change if each performer's time slot was \(1 \, \text{hour}\)?
2. What if Imani only had \( 3 \, \text{hours}\) instead of \(3 \frac{1}{2}\)?
3. How many performers could fit if each slot lasted \( \frac{1}{2} \, \text{hour}\)?
4. What if Imani wanted to reduce the total performance time to exactly fit the time slots?
5. How can we use decimals instead of fractions to solve this problem?

**Tip:** When dividing fractions, remember to multiply by the reciprocal of the divisor!

Imani is planning her city's Juneteenth festival. There will be 3 1/2 hours of performances on the main stage. Each performer's time slot lasts 3/4 hour. How many time slots can Imani plan to have?

Learn how to calculate the number of 3/4-hour time slots that can fit into 3 1/2 hours for Imani's Juneteenth festival. This problem involves dividing fractions and converting mixed fractions to improper fractions. Suitable for students in Grades 5-7.

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