\( \frac { 1 \times \square } { 10 \times \square } = \frac { \square } { 100 } \)

To solve the equation \[ \frac { 1 \times x } { 10 \times x } = \frac { x } { 100 } \] we can start by simplifying both sides. 1. **Simplify the left side:** The left side can be simplified as follows: \[ \frac { 1 \times x } { 10 \times x } = \frac {1}{10} \] (assuming \( x \neq 0 \) to avoid division by zero). 2. **Set the equation:** Now we have: \[ \frac {1}{10} = \frac {x}{100} \] 3. **Cross-multiply:** Cross-multiplying gives us: \[ 1 \times 100 = 10 \times x \] which simplifies to: \[ 100 = 10x \] 4. **Solve for \( x \):** Dividing both sides by 10: \[ x = \frac{100}{10} = 10 \] Thus, the solution to the equation is \[ x = 10 \]