Question

find the sum of 2.3- and 4.15-

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{x}=2.\overline{3} \\ \Rightarrow \mathrm{x}=2.3333............\left(1\right) \\ \mathrm{Multiply}\left(1\right)\mathrm{by}10,\mathrm{we}\mathrm{get} \\ 10\mathrm{x}=23.3333.............\left(2\right) \\ \mathrm{Subtracting}\left(1\right)\mathrm{from}\left(2\right),\mathrm{we}\mathrm{get} \\ 10\mathrm{x}-\mathrm{x}=23.3333...-2.333... \\ \Rightarrow 9\mathrm{x}=21 \\ \Rightarrow \mathrm{x}=\frac{21}{9}=\frac{7}{3} \\ \mathrm{Let}\mathrm{y}=4.1\overline{5} \\ \Rightarrow \mathrm{y}=4.15555.............\left(3\right) \\ \mathrm{Multiply}\left(3\right)\mathrm{by}10,\mathrm{we}\mathrm{get} \\ 10\mathrm{y}=41.5555..............\left(4\right) \\ \mathrm{Multiply}\left(4\right)\mathrm{by}10,\mathrm{we}\mathrm{get} \\ 100\mathrm{y}=415.5555...........\left(5\right) \\ \mathrm{Subtracting}\left(4\right)\mathrm{from}\left(5\right),\mathrm{we}\mathrm{get} \\ 100\mathrm{y}-10\mathrm{y}=415.55.....-41.55...... \\ \Rightarrow 90\mathrm{y}=374 \\ \Rightarrow \mathrm{y}=\frac{374}{90}=\frac{187}{45} \\ \mathrm{Now},\mathrm{x}+\mathrm{y}=\frac{7}{3}+\frac{187}{45}=\frac{105+187}{45}=\frac{292}{45} \end{gathered}$$