Question

Simplify:
$6\frac{1}{6}-5\frac{1}{5}+3\frac{1}{3}$

Answer 1

We have:
$$\begin{gathered} 6\frac{1}{6}-5\frac{1}{5}+3\frac{1}{3} \\ =\frac{37}{6}-\frac{26}{5}+\frac{10}{3} \\ 2\underline{\overline{)6,5,3}} \\ 3\underline{\underline{\overline{)3,5}},3} \\ 5\underline{\underline{\overline{)1,5}},1} \\ \underline{\underline{\overline{)1,1}},1} \\ \mathrm{L}.\mathrm{C}.\mathrm{M}.\mathrm{of}6,5\mathrm{and}3=(2\times 5\times 3)=30 \\ =\frac{\left(185-156+100\right)}{30}\left\{\left[30÷6=5,5\times 37=185\right],\left[30÷5=6,6\times 26=156\right],\mathrm{and}\left[30÷3=10,10\times 10=100\right]\right\} \\ =\frac{\left(285-156\right)}{30}=\frac{{\cancel{129}}^{43}}{{\cancel{30}}_{10}}=4\frac{3}{10} \end{gathered}$$