wieviel ist eine hälfte plus ein drittel plus ein achtel plus 1

$${\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}$$  =   $${\frac{{\mathtt{12}}}{{\mathtt{24}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{8}}}{{\mathtt{24}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{3}}}{{\mathtt{24}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}}$$    =  $${\mathtt{1}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{23}}}{{\mathtt{24}}}}$$    =  $$1\frac{23}{24}$$

$${\frac{{\mathtt{1}}}{{\mathtt{2}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{3}}}}{\mathtt{\,\small\textbf+\,}}{\frac{{\mathtt{1}}}{{\mathtt{8}}}}{\mathtt{\,\small\textbf+\,}}{\mathtt{1}} = {\frac{{\mathtt{47}}}{{\mathtt{24}}}} = {\mathtt{1.958\: \!333\: \!333\: \!333\: \!333\: \!3}}$$   

=  $$1.958\overline3$$

Gruß radix !

du must die Nenner gleichnamig machen. Der kleinste gemeinsame Teiler ist 24:

12/24+8/24+3/24+24/24= 47/24