Question

2 ( 9\frac{1}{2} - 5\frac{2}{3} = ) ______

Explanation:

Step1: Convert mixed numbers to improper fractions

To subtract mixed numbers \(9\frac{1}{2}\) and \(5\frac{2}{3}\), first convert them to improper fractions. For \(9\frac{1}{2}\), the formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So, \(9\frac{1}{2}=\frac{9\times2 + 1}{2}=\frac{18 + 1}{2}=\frac{19}{2}\). For \(5\frac{2}{3}\), we have \(5\frac{2}{3}=\frac{5\times3+2}{3}=\frac{15 + 2}{3}=\frac{17}{3}\).

Step2: Find a common denominator

The denominators are 2 and 3. The least common denominator (LCD) of 2 and 3 is \(2\times3 = 6\). Now, rewrite the fractions with the common denominator. For \(\frac{19}{2}\), multiply numerator and denominator by 3: \(\frac{19\times3}{2\times3}=\frac{57}{6}\). For \(\frac{17}{3}\), multiply numerator and denominator by 2: \(\frac{17\times2}{3\times2}=\frac{34}{6}\).

Step3: Subtract the fractions

Now subtract the two fractions: \(\frac{57}{6}-\frac{34}{6}=\frac{57 - 34}{6}=\frac{23}{6}\).

Step4: Convert back to mixed number (optional)

Convert \(\frac{23}{6}\) to a mixed number. Divide 23 by 6: \(23\div6 = 3\) with a remainder of 5. So, \(\frac{23}{6}=3\frac{5}{6}\).

Answer:

\(3\frac{5}{6}\)