To solve the proportion $\frac{0.4}{1.2} = \frac{x}{8}$, we can use cross-multiplication:

Step 1: Set up the cross-multiplication equation

$0.4 \cdot 8 = 1.2 \cdot x$

Step 2: Simplify the multiplication

$3.2 = 1.2x$

Step 3: Solve for $x$ by dividing both sides by $1.2$

$x = \frac{3.2}{1.2}$

Step 4: Simplify the fraction

$x = 2.6667 \quad (\text{or } \frac{8}{3} \text{ in fraction form})$

Final Answer:

$x = 2.67 \quad (\text{rounded to two decimal places})$

---

Do you want details or have any questions about the solution?

---

Here are 5 related questions to expand your understanding:

1. What is the general formula for solving proportions?
2. How do you convert decimals to fractions for precise answers?
3. How can cross-multiplication be applied to verify if two ratios are equivalent?
4. Can proportions be used to solve real-world problems, such as scaling recipes?
5. What happens if one side of a proportion has a variable in both the numerator and denominator?

Tip: Cross-multiplication is a powerful tool to solve proportions, but always check your solution by substituting it back into the original equation.