Question

Subtract, answer as a mixed number in simplest form.
8 1/2 - 6 1/3
[__] [__]/[__]

Answer 1

To subtract the mixed numbers \(8 \frac{1}{2}\) and \(6 \frac{1}{3}\), follow these steps:

1. **Convert mixed numbers to improper fractions**:
- \(8 \frac{1}{2} = 8 \times 2 + 1 = 16 + 1 = 17/2\)
- \(6 \frac{1}{3} = 6 \times 3 + 1 = 18 + 1 = 19/3\)

2. **Find a common denominator**:
- The denominators are 2 and 3. The least common multiple (LCM) of 2 and 3 is 6.

3. **Convert both fractions to the common denominator**:
- For \(17/2\), multiply the numerator and denominator by 3:
\[
\frac{17}{2} \times \frac{3}{3} = \frac{51}{6}
\]
- For \(19/3\), multiply the numerator and denominator by 2:
\[
\frac{19}{3} \times \frac{2}{2} = \frac{38}{6}
\]

4. **Subtract the two fractions**:
\[
\frac{51}{6} - \frac{38}{6} = \frac{51 - 38}{6} = \frac{13}{6}
\]

5. **Convert the improper fraction back to a mixed number**:
- Divide 13 by 6:
\[
13 \div 6 = 2 \quad \text{(whole number part)}
\]
- Remainder: \(13 - (6 \times 2) = 1\)
- So, \(\frac{13}{6} = 2 \frac{1}{6}\)

Thus, the final answer is:
\[
2 \frac{1}{6}
\]

In the format requested, it is:
\[
[2] [1]/[6]
\]