$$\left({\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{4}}}{{\mathtt{5}}}}\right){\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{9}}}}$$
2/3+4/5 = (10+12)/(3*5) = 22/15
$${\frac{{\mathtt{22}}}{{\mathtt{15}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{9}}}}$$
22/15 + 1/9 = (198+15)/(15*9) = 213/135
213/135 = 71/45
$${\frac{{\mathtt{2}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{4}}}{{\mathtt{5}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{9}}}} = {\frac{{\mathtt{71}}}{{\mathtt{45}}}}$$
.
