Ryan made \( 8^{1} / 6 \) cups of soup on a cold winter day. His brother was hungry and ate \( 1^{1} / 2 \) cups and then his sister came in and ate 2 more cups. How much soup is left for Ryan to eat?

To find out how much soup is left for Ryan to eat, we need to subtract the amount of soup eaten by his brother and sister from the total amount of soup Ryan made. Given: - Ryan made \(8^{1}/6\) cups of soup. - His brother ate \(1^{1}/2\) cups. - His sister ate 2 cups. Let's calculate the amount of soup left for Ryan to eat. Calculate the value by following steps: - step0: Calculate: \(\frac{8^{1}}{6}-\frac{1^{1}}{2}-2\) - step1: Evaluate the power: \(\frac{8}{6}-\frac{1^{1}}{2}-2\) - step2: Evaluate the power: \(\frac{8}{6}-\frac{1}{2}-2\) - step3: Reduce the fraction: \(\frac{4}{3}-\frac{1}{2}-2\) - step4: Reduce fractions to a common denominator: \(\frac{4\times 2}{3\times 2}-\frac{3}{2\times 3}-\frac{2\times 3\times 2}{3\times 2}\) - step5: Multiply the numbers: \(\frac{4\times 2}{6}-\frac{3}{2\times 3}-\frac{2\times 3\times 2}{3\times 2}\) - step6: Multiply the numbers: \(\frac{4\times 2}{6}-\frac{3}{6}-\frac{2\times 3\times 2}{3\times 2}\) - step7: Multiply the numbers: \(\frac{4\times 2}{6}-\frac{3}{6}-\frac{2\times 3\times 2}{6}\) - step8: Transform the expression: \(\frac{4\times 2-3-2\times 3\times 2}{6}\) - step9: Multiply the numbers: \(\frac{8-3-2\times 3\times 2}{6}\) - step10: Multiply the terms: \(\frac{8-3-12}{6}\) - step11: Subtract the numbers: \(\frac{-7}{6}\) - step12: Rewrite the fraction: \(-\frac{7}{6}\) The amount of soup left for Ryan to eat is \( -\frac{7}{6} \) cups, which is equivalent to \( -1\frac{1}{6} \) cups or approximately \( -1.1\dot{6} \) cups. Therefore, Ryan has \( -\frac{7}{6} \) cups of soup left to eat.