Question

divide.
$2 \frac{4}{5} \div \frac{1}{2} = $

Explanation:

Step1: Convert mixed number to improper fraction

A mixed number \(2\frac{4}{5}\) can be converted to an improper fraction by multiplying the whole number part by the denominator of the fraction part and adding the numerator. So, \(2\frac{4}{5}=\frac{2\times5 + 4}{5}=\frac{10+4}{5}=\frac{14}{5}\).

Step2: Divide by multiplying with reciprocal

Dividing by a fraction is the same as multiplying by its reciprocal. So, \(\frac{14}{5}\div\frac{1}{2}=\frac{14}{5}\times2\).

Step3: Multiply the fractions

Multiply the numerator with the whole number: \(\frac{14\times2}{5}=\frac{28}{5}\). We can also write this as a mixed number \(5\frac{3}{5}\) or as a decimal \(5.6\), but as an improper fraction, it is \(\frac{28}{5}\).

Answer:

\(\frac{28}{5}\) (or \(5\frac{3}{5}\) or \(5.6\))