Question

3\frac{4}{9} \div \frac{1}{6}

Explanation:

Step1: Convert mixed number to improper fraction

To convert \( 3\frac{4}{9} \) to an improper fraction, we use the formula \( a\frac{b}{c}=\frac{a\times c + b}{c} \). So, \( 3\frac{4}{9}=\frac{3\times9 + 4}{9}=\frac{27+4}{9}=\frac{31}{9} \).

Step2: Divide by multiplying by reciprocal

Dividing by a fraction is the same as multiplying by its reciprocal. So, \( \frac{31}{9}\div\frac{1}{6}=\frac{31}{9}\times6 \).

Step3: Simplify the multiplication

\( \frac{31}{9}\times6=\frac{31\times6}{9}=\frac{186}{9} \). We can simplify this fraction by dividing numerator and denominator by their greatest common divisor, which is 3. So, \( \frac{186\div3}{9\div3}=\frac{62}{3} \), or as a mixed number \( 20\frac{2}{3} \).

Answer:

\( \frac{62}{3} \) (or \( 20\frac{2}{3} \))