Question
Find the sum. \( -5 \frac{1}{3}+2 \frac{2}{3}=\square \)
Ask by Hart Wheeler. in the United States
Jan 24,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
The sum is \(-2\,\frac{2}{3}\).
Solution
To find the sum of \( -5 \frac{1}{3} + 2 \frac{2}{3} \), follow these steps:
1. **Convert Mixed Numbers to Improper Fractions:**
- \( -5 \frac{1}{3} = -\left(5 + \frac{1}{3}\right) = -\frac{16}{3} \)
- \( 2 \frac{2}{3} = \frac{8}{3} \)
2. **Add the Fractions:**
\[
-\frac{16}{3} + \frac{8}{3} = \frac{-16 + 8}{3} = \frac{-8}{3}
\]
3. **Convert Back to a Mixed Number:**
\[
\frac{-8}{3} = -2 \frac{2}{3}
\]
**Answer:** \(-2\,\frac{2}{3}\)
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Simplify this solution Beyond the Answer
To solve \(-5 \frac{1}{3} + 2 \frac{2}{3}\), we first convert the mixed numbers into improper fractions. For \(-5 \frac{1}{3}\): \[ -5 \frac{1}{3} = -\left(5 \times 3 + 1\right)/3 = -\frac{16}{3} \] For \(2 \frac{2}{3}\): \[ 2 \frac{2}{3} = (2 \times 3 + 2)/3 = \frac{8}{3} \] Now we add them together: \[ -\frac{16}{3} + \frac{8}{3} = \frac{-16 + 8}{3} = \frac{-8}{3} \] To convert \(\frac{-8}{3}\) back into a mixed number: \(-8 \div 3 = -2\) remainder \(-2\), which gives us: \[ -\frac{8}{3} = -2 \frac{2}{3} \] So the final sum is: \(-5 \frac{1}{3} + 2 \frac{2}{3} = -2 \frac{2}{3}\). Now, filling in the square, we get: -2 \frac{2}{3}
