-7/8+(-5 1/3)

To solve the expression \(-\frac{7}{8} + \left(-5 \frac{1}{3}\right)\), we first convert \(-5 \frac{1}{3}\) to an improper fraction. 1. Convert \(5 \frac{1}{3}\) to an improper fraction: \[ 5 \frac{1}{3} = 5 \times 3 + 1 = 15 + 1 = 16 \quad \text{(the denominator is 3)} \] Thus, \(-5 \frac{1}{3} = -\frac{16}{3}\). Now our expression becomes: \[ -\frac{7}{8} - \frac{16}{3} \] 2. To add these two fractions, we need a common denominator. The least common multiple of 8 and 3 is 24. 3. Convert each fraction: \[ -\frac{7}{8} = -\frac{7 \times 3}{8 \times 3} = -\frac{21}{24} \] \[ -\frac{16}{3} = -\frac{16 \times 8}{3 \times 8} = -\frac{128}{24} \] 4. Now we can add the two fractions: \[ -\frac{21}{24} - \frac{128}{24} = -\frac{21 + 128}{24} = -\frac{149}{24} \] So, \(-\frac{7}{8} + \left(-5 \frac{1}{3}\right) = -\frac{149}{24}\). If you want it as a mixed number: \[ -\frac{149}{24} = -6 \frac{5}{24} \] Thus, the final answer is: \[ -\frac{149}{24} \quad \text{or} \quad -6 \frac{5}{24} \]