Question
(1) What is the sum? \( \begin{aligned}-1 \frac{1}{8}+\left(-\frac{1}{2}\right) & =-1 \frac{1}{8}+\left(-\frac{4}{8}\right) \\ & =?\end{aligned} \)
Ask by Pollard Vargas. in the United States
Jan 27,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The sum is \( -1 \frac{5}{8} \).
Solution
To find the sum of \( -1 \frac{1}{8} + \left(-\frac{1}{2}\right) \), follow these steps:
1. **Convert Mixed Number to Improper Fraction:**
\[
-1 \frac{1}{8} = -\left(1 + \frac{1}{8}\right) = -\frac{8}{8} - \frac{1}{8} = -\frac{9}{8}
\]
2. **Express Both Fractions with a Common Denominator:**
The denominators are already 8 and 2. To have a common denominator of 8:
\[
-\frac{1}{2} = -\frac{4}{8}
\]
3. **Add the Fractions:**
\[
-\frac{9}{8} + \left(-\frac{4}{8}\right) = -\frac{9 + 4}{8} = -\frac{13}{8}
\]
4. **Convert the Improper Fraction Back to a Mixed Number:**
\[
-\frac{13}{8} = -1 \frac{5}{8}
\]
**Final Answer:**
\[
-1 \frac{5}{8}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To solve the problem, we need to convert \(-1 \frac{1}{8}\) into an improper fraction. This gives us: \(-1 \frac{1}{8} = -\frac{9}{8}\). Now we can add the fractions: \[ -\frac{9}{8} + \left(-\frac{4}{8}\right) = -\frac{9 + 4}{8} = -\frac{13}{8}. \] This can also be expressed as a mixed number: \(-\frac{13}{8} = -1 \frac{5}{8}\). So the sum is \(-1 \frac{5}{8}\).
