Question

9 ( 8\frac{2}{3} - 3\frac{4}{5} )

Explanation:

Step1: Convert mixed numbers to improper fractions

To subtract mixed numbers, first convert them to improper fractions. For \(8\frac{2}{3}\), multiply the whole number 8 by the denominator 3 and add the numerator 2: \(8\times3 + 2 = 26\), so \(8\frac{2}{3}=\frac{26}{3}\). For \(3\frac{4}{5}\), multiply 3 by 5 and add 4: \(3\times5 + 4 = 19\), so \(3\frac{4}{5}=\frac{19}{5}\).

Step2: Find a common denominator

The denominators are 3 and 5, so the least common denominator (LCD) is \(3\times5 = 15\). Convert \(\frac{26}{3}\) to a fraction with denominator 15: \(\frac{26}{3}=\frac{26\times5}{3\times5}=\frac{130}{15}\). Convert \(\frac{19}{5}\) to a fraction with denominator 15: \(\frac{19}{5}=\frac{19\times3}{5\times3}=\frac{57}{15}\).

Step3: Subtract the fractions

Now subtract the two fractions: \(\frac{130}{15}-\frac{57}{15}=\frac{130 - 57}{15}=\frac{73}{15}\).

Step4: Convert back to a mixed number (optional)

Divide 73 by 15: \(73\div15 = 4\) with a remainder of 13, so \(\frac{73}{15}=4\frac{13}{15}\).

Answer:

\(4\frac{13}{15}\) (or \(\frac{73}{15}\))