X:1/3=3/4:1/2

To solve the proportion \( \frac{x}{\frac{1}{3}} = \frac{\frac{3}{4}}{\frac{1}{2}} \), we can cross-multiply or simplify the right side first. First, simplify \( \frac{\frac{3}{4}}{\frac{1}{2}} \): \[ \frac{\frac{3}{4}}{\frac{1}{2}} = \frac{3}{4} \times \frac{2}{1} = \frac{3 \times 2}{4 \times 1} = \frac{6}{4} = \frac{3}{2} \] Now, the equation simplifies to: \[ \frac{x}{\frac{1}{3}} = \frac{3}{2} \] Next, we can multiply both sides by \( \frac{1}{3} \): \[ x = \frac{3}{2} \times \frac{1}{3} = \frac{3 \times 1}{2 \times 3} = \frac{1}{2} \] Thus, the solution is: \[ x = \frac{1}{2} \]