A)(3/4 + 1/3 . 2/5 ):(4/3 . 5/2 - 3/4

B)(1 . 2/3 . 12/5 + 3/8):(3/8 + 1/8 + 1/3 :4/3)

Porfavor me ajudem !!!!

Tanjirooni: resolvam as seguintes expressões, simplificado quando possivel

Respostas

respondido por: Aleske

Respostas:

$\large\text{A~=~{}^{\sf{53}} / {}_{\sf{155}}$}\\\\\large\text{B~=~{}^{\sf{79}} / {}_{\sf{30}}$}$

Cálculos:

Primeiro deve-se resolver o que está dentro de cada parênteses.

Dentro dos parênteses: deve-se resolver primeiro multiplicação e divisão, em seguida adição e subtração.

Nas divisões entre frações: repete a primeira e multiplica pelo inverso da segunda.

Em soma ou subtração de frações: os denominadores devem ser iguais.

$\large\text{$\Bigg(\dfrac{\sf{3}}{\sf{4}}$~+~$\dfrac{\sf{1}}{\sf{3}}$~.~$\dfrac{\sf{2}}{\sf{5}}\Bigg)$~:~$\Bigg(\dfrac{\sf{4}}{\sf{3}}$~.~$\dfrac{\sf{5}}{\sf{2}}$~-~$\dfrac{\sf{3}}{\sf{4}}\Bigg)$}\\\\\\\large\text{$\Bigg(\dfrac{\sf{3}}{\sf{4}}$~+~$\dfrac{\sf{2}}{\sf{15}}\Bigg)$~:~$\Bigg(\dfrac{\sf{20}}{\sf{6}}$~-~$\dfrac{\sf{3}}{\sf{4}}\Bigg)$}$

$\large\text{$\Bigg(\dfrac{\sf{3~.~15}}{\sf{4~.~15}}$~+~$\dfrac{\sf{2~.~4}}{\sf{15~.~4}}\Bigg)$~:~$\Bigg(\dfrac{\sf{20~.~4}}{\sf{6~.~4}}$~-~$\dfrac{\sf{3~.~6}}{\sf{4~.~6}}\Bigg)$}\\\\\\\large\text{$\Bigg(\dfrac{\sf{45}}{\sf{60}}$~+~$\dfrac{\sf{8}}{\sf{60}}\Bigg)$~:~$\Bigg(\dfrac{\sf{80}}{\sf{24}}$~-~$\dfrac{\sf{18}}{\sf{24}}\Bigg)$}$

$\large\text{$\Bigg(\dfrac{\sf{45~+~8}}{\sf{60}}\Bigg)$~:~$\Bigg(\dfrac{\sf{80~-~18}}{\sf{24}}\Bigg)$}$

$\large\text{$\Bigg(\dfrac{\sf{53}}{\sf{60}}\Bigg)$~:~$\Bigg(\dfrac{\sf{62}}{\sf{24}}\Bigg)$}$

$\large\text{$\Bigg(\dfrac{\sf{53}}{\sf{60}}\Bigg)$~.~$\Bigg(\dfrac{\sf{24}}{\sf{62}}\Bigg)$}$

$\large\text{$\Bigg(\dfrac{\sf{1272}}{\sf{3720}}\Bigg)$}$

$\large\text{$\dfrac{\sf{1272^\div^2^4}}{\sf{3720^\div^2^4}}$~=~$\boxed{\boxed{\dfrac{\sf{53}}{\sf{155}}}}$}$

$\large\text{$\Bigg(1~.~\dfrac{\sf{2}}{\sf{3}}$~.~$\dfrac{\sf{12}}{\sf{5}}$~+~$\dfrac{\sf{3}}{\sf{8}}\Bigg)$~:~$\Bigg(\dfrac{\sf{3}}{\sf{8}}$~+~$\dfrac{\sf{1}}{\sf{8}}$~+~$\dfrac{\sf{1}}{\sf{3}}$~:~$\dfrac{\sf{4}}{\sf{3}}\Bigg)$}$

$\large\text{$\Bigg(\dfrac{1}{1}~.~\dfrac{\sf{2}}{\sf{3}}$~.~$\dfrac{\sf{12}}{\sf{5}}$~+~$\dfrac{\sf{3}}{\sf{8}}\Bigg)$~:~$\Bigg(\dfrac{\sf{3}}{\sf{8}}$~+~$\dfrac{\sf{1}}{\sf{8}}$~+~$\dfrac{\sf{1}}{\sf{3}}$~:~$\dfrac{\sf{4}}{\sf{3}}\Bigg)$}$

$\large\text{$\Bigg(\dfrac{\sf{24}}{\sf{15}}$~+~$\dfrac{\sf{3}}{\sf{8}}\Bigg)$~:~$\Bigg(\dfrac{\sf{3}}{\sf{8}}$~+~$\dfrac{\sf{1}}{\sf{8}}$~+~$\dfrac{\sf{1}}{\sf{3}}$~.~$\dfrac{\sf{3}}{\sf{4}}\Bigg)$}$

$\large\text{$\Bigg(\dfrac{\sf{24}}{\sf{15}}$~+~$\dfrac{\sf{3}}{\sf{8}}\Bigg)$~:~$\Bigg(\dfrac{\sf{3}}{\sf{8}}$~+~$\dfrac{\sf{1}}{\sf{8}}$~+~$\dfrac{\sf{3}}{\sf{12}}\Bigg)$}$

$\large\text{$\Bigg(\dfrac{\sf{24~.~8}}{\sf{15~.~8}}$~+~$\dfrac{\sf{3~.~15}}{\sf{8~.~15}}\Bigg)$~:~$\Bigg(\dfrac{\sf{3~.~12}}{\sf{8~.~12}}$~+~$\dfrac{\sf{1~.~12}}{\sf{8~.~12}}$~+~$\dfrac{\sf{3~.~8}}{\sf{12~.~8}}\Bigg)$}$ $\large\text{$\Bigg(\dfrac{\sf{192}}{\sf{120}}$~+~$\dfrac{\sf{45}}{\sf{120}}\Bigg)$~:~$\Bigg(\dfrac{\sf{36}}{\sf{96}}$~+~$\dfrac{\sf{12}}{\sf{96}}$~+~$\dfrac{\sf{24}}{\sf{96}}\Bigg)$}$

$\large\text{$\Bigg(\dfrac{\sf{237}}{\sf{120}}\Bigg)$~:~$\Bigg(\dfrac{\sf{72}}{\sf{96}}\Bigg)$}$

$\large\text{$\Bigg(\dfrac{\sf{237}}{\sf{120}}\Bigg)$~.~$\Bigg(\dfrac{\sf{96}}{\sf{72}}\Bigg)$}$

$\large\text{$\Bigg(\dfrac{\sf{22752}}{\sf{8640}}\Bigg)$}$

$\large\text{$\dfrac{\sf{22752^\div^1^8}}{\sf{8640^\div^1^8}}$~=~$\dfrac{\sf{1264^\div^8}}{\sf{480^\div^8}}$~=~$\dfrac{\sf{158^\div^2}}{\sf{60^\div^2}}$~=~{$\boxed{\boxed{\dfrac{\sf{79}}{\sf{30}}}}$}}}$