\frac{16\ people}{3\ pies}=\frac{ }{12\ pies}

To solve the proportion \(\frac{16 \text{ people}}{3 \text{ pies}} = \frac{x \text{ people}}{12 \text{ pies}}\), you need to find the value of \(x\) that maintains the equality. Here's how you can solve it:

1. **Set up the proportion:**

   \[
   \frac{16 \text{ people}}{3 \text{ pies}} = \frac{x \text{ people}}{12 \text{ pies}}
   \]

2. **Cross multiply** to find \(x\):

   \[
   16 \times 12 = 3 \times x
   \]

3. **Multiply** the numbers on each side:

   \[
   192 = 3x
   \]

4. **Solve for \(x\)** by dividing both sides by 3:

   \[
   x = \frac{192}{3} = 64
   \]

So, \(x = 64\). This means that if 3 pies are shared among 16 people, then 12 pies would be shared among 64 people.

Would you like more details on any part of the process?

Here are five related questions you might find interesting:
1. How would you solve this problem if the number of pies or people changed?
2. Can this method be applied to other similar ratios?
3. What if there were only 1.5 pies instead of 3—how would you adjust the equation?
4. How can you use this proportionality in real-life situations?
5. What would happen if you had to solve for the number of pies instead of people?

**Tip:** When working with proportions, always ensure that the units are consistent across the equation to avoid confusion.

Learn how to solve a proportional problem where 16 people share 3 pies, and find out how many people would share 12 pies using cross multiplication and proportionality principles. Suitable for students in Grades 6-8.

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