Question

calcule o quociente 53°2’15’’ : 5.
pfv help...

Answer 1

Precisamos lembrar das relações entre graus, minutos e segundos:

$\left\{\begin{array}{ccc}1^\circ&=&60'\\\\1^\circ&=&3600''\\\\1'&=&60''\end{array}\right$

Assim, podemos utilizar o método das chaves para a divisão, acompanhe:

$\left\begin{array}{cccl}&53^\circ2'15''&~~&\underline{|~~5~~~~~~~~~~~~~~}\\-&\underline{~~50^\circ00'00''~~}&&10^\circ\\&3^\circ2'15''&&\end{array}\right\\\\\\3^\circ2'15''~=~180'+2'15''~=~\boxed{182'15''}\\\\\\\left\begin{array}{cccl}&53^\circ2'15''&~~&\underline{|~~5~~~~~~~~~~~~~~}\\-&\underline{~~50^\circ00'00''~~}&&10^\circ+36'\\&182'15''&&\\-&\underline{~~~~180'00''~~~~}&&\\&2'15''&&\end{array}\right\\\\\\2'15''~=~120''+15''~=~\boxed{135''}$

$\left\begin{array}{cccl}&53^\circ2'15''&~~&\underline{|~~5~~~~~~~~~~~~~~}\\-&\underline{~~50^\circ00'00''~~}&&10^\circ+36'+27''\\&182'15''&&\\-&\underline{~~~~180'00''~~~~}&&\\&135''&&\\-&\underline{~~~~~135''~~~~~}&&\\&0&&\end{array}\right$

Dessa forma, temos que o quociente entre 53°2'15'' e 5 vale 10°36'27''.