4. Mr. Corwin gave his students \( \frac{3}{4} \) hour to study for a test. After \( \frac{1}{3} \) hour, he played a review game for the remaining time. How much time did Mr. Corwin spend playing the review game?

Let's denote the total time Mr. Corwin gave his students to study for the test as \( t \) hours. Given that Mr. Corwin gave his students \( \frac{3}{4} \) hour to study for the test, we can set up the equation: \[ t = \frac{3}{4} \] After \( \frac{1}{3} \) hour, Mr. Corwin played a review game for the remaining time. The time spent playing the review game can be calculated as: \[ \text{Time spent playing review game} = t - \frac{1}{3} \] Substitute the value of \( t \) into the equation: \[ \text{Time spent playing review game} = \frac{3}{4} - \frac{1}{3} \] Now, let's calculate the time spent playing the review game. Calculate the value by following steps: - step0: Calculate: \(\frac{3}{4}-\frac{1}{3}\) - step1: Reduce fractions to a common denominator: \(\frac{3\times 3}{4\times 3}-\frac{4}{3\times 4}\) - step2: Multiply the numbers: \(\frac{3\times 3}{12}-\frac{4}{3\times 4}\) - step3: Multiply the numbers: \(\frac{3\times 3}{12}-\frac{4}{12}\) - step4: Transform the expression: \(\frac{3\times 3-4}{12}\) - step5: Multiply the numbers: \(\frac{9-4}{12}\) - step6: Subtract the numbers: \(\frac{5}{12}\) Mr. Corwin spent \( \frac{5}{12} \) hour playing the review game.