Question

(\frac{3}{4} div 5\frac{1}{5})

Explanation:

Step1: Convert mixed number to improper fraction

First, convert the mixed number \(5\frac{1}{5}\) to an improper fraction. The formula for converting a mixed number \(a\frac{b}{c}\) to an improper fraction is \(\frac{a\times c + b}{c}\). So for \(5\frac{1}{5}\), we have \(a = 5\), \(b = 1\), \(c = 5\). Then \(\frac{5\times5 + 1}{5}=\frac{25 + 1}{5}=\frac{26}{5}\).

Step2: Divide by multiplying by reciprocal

Dividing by a fraction is the same as multiplying by its reciprocal. So \(\frac{3}{4}\div\frac{26}{5}=\frac{3}{4}\times\frac{5}{26}\).

Step3: Multiply the numerators and denominators

Multiply the numerators: \(3\times5 = 15\). Multiply the denominators: \(4\times26 = 104\). So the result is \(\frac{15}{104}\).

Answer:

\(\frac{15}{104}\)