Question
Subtract: \( 5 \frac{1}{6}-2 \frac{5}{6} \) Do not give your answer as an improper fraction. Give your answer as mixed number or proper fraction in lowest terms.
Ask by Horton Erickson. in the United States
Jan 22,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( 2 \frac{1}{3} \)
Solution
To subtract \( 5 \frac{1}{6} - 2 \frac{5}{6} \), follow these steps:
1. **Subtract the whole numbers:**
\[
5 - 2 = 3
\]
2. **Subtract the fractional parts:**
\[
\frac{1}{6} - \frac{5}{6} = -\frac{4}{6} = -\frac{2}{3}
\]
3. **Combine the results:**
\[
3 - \frac{2}{3} = 2 \frac{1}{3}
\]
**Final Answer:**
\[
2 \frac{1}{3}
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Beyond the Answer
To subtract \( 5 \frac{1}{6} - 2 \frac{5}{6} \), we first convert both mixed numbers into improper fractions. For \( 5 \frac{1}{6} \): \[ 5 \frac{1}{6} = 5 \times 6 + 1 = 30 + 1 = \frac{31}{6} \] For \( 2 \frac{5}{6} \): \[ 2 \frac{5}{6} = 2 \times 6 + 5 = 12 + 5 = \frac{17}{6} \] Now we subtract the improper fractions: \[ \frac{31}{6} - \frac{17}{6} = \frac{31 - 17}{6} = \frac{14}{6} \] Next, we simplify \( \frac{14}{6} \): \[ \frac{14 \div 2}{6 \div 2} = \frac{7}{3} \] Now, converting \( \frac{7}{3} \) back to a mixed number, we divide: \[ 7 \div 3 = 2 \quad \text{remainder } 1 \] This gives us: \[ \frac{7}{3} = 2 \frac{1}{3} \] Thus, the final answer is: \[ 2 \frac{1}{3} \]
