To solve the equation:

\[
\frac{x}{\frac{2}{5}} = \frac{3}{4}
\]

we can rewrite it as:

1. Multiply both sides by \(\frac{2}{5}\) to isolate \(x\):
   \[
   x = \frac{3}{4} \times \frac{2}{5}
   \]

2. Now, calculate the product:
   \[
   x = \frac{3 \times 2}{4 \times 5} = \frac{6}{20}
   \]

3. Simplify \(\frac{6}{20}\) by dividing both the numerator and the denominator by 2:
   \[
   x = \frac{3}{10}
   \]

**Final Answer:**
\[
x = \frac{3}{10}
\]

Would you like further details or have any questions?

1. How do we multiply fractions?
2. Why did we isolate \(x\) by multiplying by \(\frac{2}{5}\)?
3. How can we verify if \(\frac{3}{10}\) is correct?
4. What if the equation was \(x \div \frac{3}{5} = \frac{3}{4}\) instead?
5. How do we handle more complex equations involving fractions?

**Tip:** When dividing by a fraction, remember to multiply by its reciprocal!

This solution provides a step-by-step approach to solving the equation x ÷ 2/5 = 3/4. It covers algebraic manipulation of fractions, including multiplying by the reciprocal, and is suitable for students in Grades 6-8.

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