Let's solve each equation step by step:

### a. \(\frac{x}{3} = \frac{1.5}{7}\)

1. To eliminate the denominators, multiply both sides by 3 and 7:
   \[
   x \cdot 7 = 1.5 \cdot 3
   \]

2. Simplify:
   \[
   7x = 4.5
   \]

3. Now, solve for \(x\):
   \[
   x = \frac{4.5}{7} = 0.642857 \approx 0.643
   \]

So, \(x \approx 0.643\).

---

### b. \(\frac{x}{5} = \frac{16}{20}\)

1. Cross-multiply to get rid of the fractions:
   \[
   x \cdot 20 = 5 \cdot 16
   \]

2. Simplify:
   \[
   20x = 80
   \]

3. Now, solve for \(x\):
   \[
   x = \frac{80}{20} = 4
   \]

So, \(x = 4\).

---

Would you like further details or clarifications on any of the steps?

Here are 5 related questions:
1. How do you solve equations involving fractions and cross-multiplication?
2. What are other ways to handle proportions in algebra?
3. How can decimal numbers affect solving algebraic equations?
4. How can you simplify fractions before solving for a variable?
5. What is the importance of verifying solutions in proportional equations?

**Tip:** Always check your solution by substituting the value of \(x\) back into the original equation to ensure correctness.

Learn how to solve proportion equations like x/3 = 1.5/7 and x/5 = 16/20 using cross-multiplication. This solution walks through each step in detail, including the algebraic concepts and formulas involved. Suitable for students in Grades 6-8.

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