(1⅚+⅗)×24

To solve the expression \((1 \frac{5}{6} + \frac{3}{5}) \times 24\), we begin by converting the mixed number to an improper fraction. 1. Convert \(1 \frac{5}{6}\) to an improper fraction: \[ 1 \frac{5}{6} = \frac{6 \times 1 + 5}{6} = \frac{6 + 5}{6} = \frac{11}{6} \] 2. Now add \(\frac{11}{6}\) and \(\frac{3}{5}\). First, we need a common denominator. The least common multiple of 6 and 5 is 30. Convert the fractions: \[ \frac{11}{6} = \frac{11 \times 5}{6 \times 5} = \frac{55}{30} \] \[ \frac{3}{5} = \frac{3 \times 6}{5 \times 6} = \frac{18}{30} \] 3. Now add the two fractions: \[ \frac{55}{30} + \frac{18}{30} = \frac{55 + 18}{30} = \frac{73}{30} \] 4. Now multiply the result by 24: \[ \left( \frac{73}{30} \right) \times 24 = \frac{73 \times 24}{30} \] To simplify: \[ \frac{73 \times 24}{30} = \frac{1752}{30} \] 5. Now simplify \(\frac{1752}{30}\). Divide both the numerator and denominator by 6: \[ \frac{1752 \div 6}{30 \div 6} = \frac{292}{5} \] 6. Finally, convert \(\frac{292}{5}\) to a mixed number: \[ 292 \div 5 = 58 \quad \text{remainder } 2 \] So, \(\frac{292}{5} = 58 \frac{2}{5}\). Therefore, \((1 \frac{5}{6} + \frac{3}{5}) \times 24 = 58 \frac{2}{5}\).