(1) Find \( -1 \frac{1}{8}+\left(-\frac{1}{2}\right) \). (4)) What is a common denominator for the two addends 12 6, 8 Practice: Add and Subtract Ration

To solve the problem \( -1 \frac{1}{8} + \left(-\frac{1}{2}\right) \), we will follow these steps: 1. **Convert the mixed number to an improper fraction**: - The mixed number \( -1 \frac{1}{8} \) can be converted to an improper fraction. - To do this, multiply the whole number part by the denominator and add the numerator: \[ -1 \frac{1}{8} = -\left(1 \times 8 + 1\right) / 8 = -\frac{9}{8} \] 2. **Convert the second fraction to have a common denominator**: - The second fraction is \( -\frac{1}{2} \). To add it to \( -\frac{9}{8} \), we need a common denominator. - The denominators are 8 and 2. The least common multiple (LCM) of 8 and 2 is 8. 3. **Convert \( -\frac{1}{2} \) to have a denominator of 8**: - To convert \( -\frac{1}{2} \) to a fraction with a denominator of 8, multiply the numerator and denominator by 4: \[ -\frac{1}{2} = -\frac{1 \times 4}{2 \times 4} = -\frac{4}{8} \] 4. **Add the two fractions**: - Now we can add \( -\frac{9}{8} \) and \( -\frac{4}{8} \): \[ -\frac{9}{8} + \left(-\frac{4}{8}\right) = -\frac{9 + 4}{8} = -\frac{13}{8} \] 5. **Convert back to a mixed number (if needed)**: - The improper fraction \( -\frac{13}{8} \) can be converted back to a mixed number: \[ -\frac{13}{8} = -1 \frac{5}{8} \] Thus, the final answer is: \[ -1 \frac{5}{8} \] ### Common Denominator The common denominator for the two addends \( -1 \frac{1}{8} \) and \( -\frac{1}{2} \) is 8.