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The problem asks to determine how many students will get a piece of cake after Sarah cuts and distributes it.

Here’s the breakdown of the situation:

1. **Sarah cuts the cake into** \( \frac{3}{4} \) **of its original size.**
2. **She wants to divide this portion among** \( \frac{1}{6} \) **of her classmates.**

Let’s walk through the steps:

### Step 1: Understanding the fractions

- \( \frac{3}{4} \) of the cake is available to be shared.
- She is dividing this cake among \( \frac{1}{6} \) of her classmates.

### Step 2: Setting up the calculation

If the total number of classmates is \( x \), then \( \frac{1}{6} \) of them will receive the cake. This means the number of students getting cake is:

\[
\text{Number of students} = x \times \frac{1}{6}
\]

Now, she is dividing the \( \frac{3}{4} \) part of the cake among these students. So the number of students who get cake is just the number of students represented by \( \frac{1}{6} \) of the total.

But to fully answer this, we need to know the total number of classmates \( x \), which is not directly given in the problem. This seems to be the missing information needed to proceed fully.

Let me know if you would like more details or have any questions.

### 5 Related Questions:
1. What if Sarah divided the entire cake equally among all of her classmates?
2. How would the solution change if she divided \( \frac{2}{3} \) of the cake instead of \( \frac{3}{4} \)?
3. What if the fraction of classmates was \( \frac{1}{3} \) instead of \( \frac{1}{6} \)?
4. How can we find the total number of classmates if we know how many pieces were given out?
5. What if Sarah wanted to keep some cake for herself and divide the rest among her classmates?

### Tip:
When working with fractions, always carefully distinguish between the "whole" and the "part" being divided, to avoid confusion in solving real-life fraction problems.

Sarah baked a large rectangular cake for her class party. She cut the cake into \( \frac{3}{4} \) of its original size. If she wants to divide this portion equally among \( \frac{1}{6} \) of her classmates, how many students will get a piece of cake?

Find out how to solve a problem involving fractions as Sarah divides \( \frac{3}{4} \) of a cake equally among \( \frac{1}{6} \) of her classmates. This problem covers division and multiplication of fractions, making it suitable for students in Grades 6-8.

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