A playground is rectangular with a length of \( \frac{2}{4} \) miles. If area of the playground is \( \frac{8}{12} \) square miles, what is its width? Input your answer as a fraction.

To find the width of the rectangular playground, we can use the formula for the area of a rectangle: \[ \text{Area} = \text{Length} \times \text{Width} \] Given: - Length of the playground = \( \frac{2}{4} \) miles - Area of the playground = \( \frac{8}{12} \) square miles We can substitute these values into the formula to find the width: \[ \frac{8}{12} = \frac{2}{4} \times \text{Width} \] Now, we can solve for the width. Solve the equation by following steps: - step0: Solve for \(w\): \(\frac{8}{12}=\frac{2}{4}w\) - step1: Reduce the fraction: \(\frac{2}{3}=\frac{1}{2}w\) - step2: Swap the sides: \(\frac{1}{2}w=\frac{2}{3}\) - step3: Multiply by the reciprocal: \(\frac{1}{2}w\times 2=\frac{2}{3}\times 2\) - step4: Multiply: \(w=\frac{4}{3}\) The width of the rectangular playground is \( \frac{4}{3} \) miles.