To subtract the mixed numbers \(8 \frac{1}{2}\) and \(6 \frac{1}{3}\), follow these steps:
-
Convert mixed numbers to improper fractions:
- \(8 \frac{1}{2} = 8 \times 2 + 1 = 16 + 1 = 17/2\)
- \(6 \frac{1}{3} = 6 \times 3 + 1 = 18 + 1 = 19/3\)
-
Find a common denominator:
- The denominators are 2 and 3. The least common multiple (LCM) of 2 and 3 is 6.
-
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: \[ \frac{19}{3} \times \frac{2}{2} = \frac{38}{6} \]
-
Subtract the two fractions: \[ \frac{51}{6} - \frac{38}{6} = \frac{51 - 38}{6} = \frac{13}{6} \]
-
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, \(\frac{13}{6} = 2 \frac{1}{6}\)
- Divide 13 by 6:
\[
13 \div 6 = 2 \quad \text{(whole number part)}
\]
Thus, the final answer is: \[ 2 \frac{1}{6} \]
In the format requested, it is: \[ [2] [1]/[6] \]