Question

Simplify:
$8\frac{5}{6}-3\frac{3}{8}+2\frac{7}{12}$

Answer 1

We have:
$$\begin{gathered} 8\frac{5}{6}-3\frac{3}{8}+2\frac{7}{12} \\ =\frac{53}{6}-\frac{27}{8}+\frac{31}{12} \\ 2\underline{\overline{)6,8,12}} \\ 2\underline{\underline{\overline{)3,4}},6} \\ 3\overline{)\underline{3,2,3}} \\ 2\overline{)\underline{1,2,1}} \\ \overline{)\underline{1,1,1}} \\ \mathrm{L}.\mathrm{C}.\mathrm{M}.\mathrm{of}6,8\mathrm{and}12=(2\times 2\times 2\times 3)=24 \\ =\frac{\left(212-81+62\right)}{24}\left\{\left[24÷6=4,4\times 53=212\right],\left[24÷8=3,3\times 27=81\right]\mathrm{and}\left[24÷12=2,2\times 31=62\right]\right\} \\ =\frac{\left(274-81\right)}{24}=\frac{193}{24}=8\frac{1}{24} \end{gathered}$$