Question

-44/55*7/9+1/8*1/3+44/55*5/6 by using properties of rational numbers?

Answer 1

$$\begin{gathered} -\frac{44}{55}\times \frac{7}{9}+\frac{1}{8}\times \frac{1}{3}+\frac{44}{55}\times \frac{5}{6} \\ =\frac{44}{55}\times \left(-\frac{7}{9}\right)+\frac{44}{55}\times \frac{5}{6}+\frac{1}{8}\times \frac{1}{3}\left[\mathbf{Commutative}\mathbf{}\mathbf{law}\right] \\ =\frac{44}{55}\times \left[\left(-\frac{7}{9}\right)+\frac{5}{6}\right]+\frac{1}{24}\mathbf{}\left[\mathbf{Distributive}\mathbf{}\mathbf{law}\right] \\ =\frac{44}{55}\left[\frac{-14+15}{18}\right]+\frac{1}{24} \\ =\frac{4}{5}\times \frac{1}{18}+\frac{1}{24} \\ =\frac{2}{45}+\frac{1}{24} \\ =\frac{16+15}{360} \\ =\frac{31}{360} \end{gathered}$$