Let's solve the proportion \( \frac{13}{362} = \frac{21}{x} \).

### Step-by-Step Solution:

1. **Set up the equation:**
   \[
   \frac{13}{362} = \frac{21}{x}
   \]

2. **Cross-multiply:**
   \[
   13 \cdot x = 362 \cdot 21
   \]

3. **Simplify the multiplication on the right side:**
   \[
   362 \times 21 = 7602
   \]
   So:
   \[
   13x = 7602
   \]

4. **Solve for \(x\):**
   \[
   x = \frac{7602}{13}
   \]
   \[
   x = 585.54
   \]

Thus, the value of \(x\) is approximately **585.54**.

---

Would you like more details on the process or have any other questions?  
Here are five related questions to explore further:

1. How do you know if two ratios form a proportion?
2. Can this solution be confirmed by another method, such as decimals?
3. What are other real-life applications of proportions?
4. What happens if one of the numbers in the proportion is negative?
5. How do you set up proportions when working with three or more variables?

**Tip:** Cross-multiplying is a quick and reliable way to solve proportions, but always remember to simplify the fractions first if possible!

Learn how to solve the proportion 13/362 = 21/x using cross-multiplication. This detailed guide walks through each step, including setting up the equation, multiplying across, and solving for x. Suitable for students in Grades 6-8.

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