To solve the equation \(\frac{3}{2} \times \frac{2}{5} = \frac{10}{x}\), follow these steps:

### Step 1: Simplify the left side
Simplify the multiplication on the left side:

\[
\frac{3}{2} \times \frac{2}{5} = \frac{3 \times 2}{2 \times 5} = \frac{6}{10}
\]

Next, simplify \(\frac{6}{10}\):

\[
\frac{6}{10} = \frac{3}{5}
\]

So, the equation now becomes:

\[
\frac{3}{5} = \frac{10}{x}
\]

### Step 2: Solve for \(x\)
To solve for \(x\), cross multiply:

\[
3x = 5 \times 10
\]

This simplifies to:

\[
3x = 50
\]

Finally, divide both sides by 3:

\[
x = \frac{50}{3}
\]

So, the solution is:

\[
x = \frac{50}{3} \approx 16.67
\]

Would you like further details or have any questions?

### Related Questions:
1. How do you simplify fractions in multiplication?
2. What is the cross-multiplication method?
3. How do you solve equations involving fractions?
4. How can you check if your solution is correct?
5. What is the decimal form of \(\frac{50}{3}\)?
6. How do you find the least common denominator?
7. How would the solution change if the equation were \(\frac{3}{2} \times \frac{2}{5} = \frac{20}{x}\)?
8. Can you solve the equation using a different method?

**Tip:** Always simplify fractions before performing operations to make calculations easier.

Learn how to solve the equation 3/2 * 2/5 = 10/x step-by-step with detailed explanations and calculations. This problem involves fractions and equations, suitable for students in Grades 7-9.

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