Question

divide.
$-4\frac{2}{5} \div -0.5 = \square$
submit

Explanation:

Step1: Convert mixed number to improper fraction

First, convert \(-4\frac{2}{5}\) 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 \(-4\frac{2}{5}\), we have \(a = - 4\), \(b = 2\), \(c = 5\). Then \(-4\frac{2}{5}=-\frac{4\times5 + 2}{5}=-\frac{20 + 2}{5}=-\frac{22}{5}\).

Step2: Convert decimal to fraction

Convert \(-0.5\) to a fraction. We know that \(0.5=\frac{1}{2}\), so \(-0.5 =-\frac{1}{2}\).

Step3: Divide the fractions

When dividing fractions, we multiply the first fraction by the reciprocal of the second fraction. So \(-\frac{22}{5}\div(-\frac{1}{2})=-\frac{22}{5}\times(-\frac{2}{1})\). The product of two negative numbers is positive, and multiplying the numerators and denominators gives \(\frac{22\times2}{5\times1}=\frac{44}{5}\).

Step4: Convert improper fraction to mixed number (optional, but can also be left as decimal)

Convert \(\frac{44}{5}\) to a decimal or a mixed number. \(\frac{44}{5}=8.8\) or \(8\frac{4}{5}\). But since we can see that \(\frac{44}{5}=8.8\) and also from the multiplication step we can verify: \(-\frac{22}{5}\times(-2)=\frac{44}{5} = 8.8\).

Answer:

\(8.8\) (or \(\frac{44}{5}\) or \(8\frac{4}{5}\))