luis emplea 2/5 del dia para trabajar 1/74 para comer y 3/7 del dia para dormir ¿Que fraccion del dia lo dedica a otras cosas?

La respuesta es:

Un dia - 2/5 del dia - 1/74 del dia - 3/7 del dia.

= 1 - (2/5) - (1/74) - (3/7)

= $${\mathtt{1}}{\mathtt{\,-\,}}\left({\frac{{\mathtt{2}}}{{\mathtt{5}}}}\right){\mathtt{\,-\,}}\left({\frac{{\mathtt{1}}}{{\mathtt{74}}}}\right){\mathtt{\,-\,}}\left({\frac{{\mathtt{3}}}{{\mathtt{7}}}}\right) = {\frac{{\mathtt{409}}}{{\mathtt{2\,590}}}} = {\mathtt{0.157\: \!915\: \!057\: \!915\: \!057\: \!9}}$$ del dia.

Por lo tanto, es (409/2590) del dia.

En horas, es:

= $$\left({\frac{{\mathtt{409}}}{{\mathtt{2\,590}}}}\right){\mathtt{\,\times\,}}{\mathtt{24}} = {\frac{{\mathtt{4\,908}}}{{\mathtt{1\,295}}}} = {\mathtt{3.789\: \!961\: \!389\: \!961\: \!39}}$$

~ 3.8 horas.