Matemática, perguntado por palomamottaferr, 11 meses atrás

Determine as expressões abaixo, simplifique se possível.

a) $4 -\frac{3/5 + 0,888}{(0,666 + 3/4)^{2} }$

b) $\frac{(0,666)^{2} + 7/9 }{0,555/2}$

ME AJUDAM, PFV

Soluções para a tarefa

Respondido por DalaryEstrillyt

A)

$4 -\frac{ \frac{3}{5} + 0,888}{(0,666 + \frac{3}{4} )^{2} } \\ \\ 4 -\frac{ \frac{3}{5} + \frac{111}{125} }{( \frac{333}{500} + \frac{3}{4} )^{2} } \\ \\4 -\frac{ \frac{75+111}{125} }{( \frac{333}{500} + \frac{3}{4} )^{2} } \\ \\ 4 -\frac{ \frac{75+111}{125} }{ ( \frac{333+375}{500} )^{2} } \\ \\ 4 -\frac{ \frac{186}{125} }{ ( \frac{708}{500} )^{2} } \\ \\4 -\frac{ \frac{186}{125} }{ ( \frac{177}{125} )^{2} } \\ \\4 -\frac{ \frac{186}{125} }{ \frac{177^{2}}{125^{2}} } \\ \\4 -\frac{186}{125} \times \frac{125^{2}}{177^{2}} \\ \\4 -\frac{186}{125} \times \frac{ 125 \times 125}{177 \times 177} \\ \\4 -\frac{186 \times 125 \times 125}{125 \times 177 \times 177} \\ \\4 -\frac{186 \times 125}{ 177 \times 177} \\ \\4 -\frac{62 \times 125}{ 59 \times 177} \\ \\4 -\frac{7750}{ 10443} \\ \\4 - 0,7421239108 \\\\ 3,2578760892$

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$4 - \frac{7750}{ 10443} \\ \\ \frac{4}{ 1} - \frac{7750}{ 10443} \\ \\ \frac{41772-7750}{ 10443} \\ \\ \frac{34022}{ 1445} \\ \\3,2578760892$

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Se 0,888 e 0,666 forem dízimas periódicas:

$4 -\frac{ \frac{3}{5} + 0,888...}{(0,666... + \frac{3}{4} )^{2} } \\ \\ 4 -\frac{ \frac{3}{5} + \frac{8}{9} }{( \frac{6}{9} + \frac{3}{4} )^{2} } \\ \\ 4 -\frac{ \frac{27 + 40}{45} }{( \frac{24 + 27}{36} )^{2} } \\ \\ 4 -\frac{ \frac{67}{45} }{( \frac{51}{36} )^{2} } \\ \\ 4 -\frac{ \frac{67}{45} }{( \frac{17}{12} )^{2} } \\ \\ 4 -\frac{ \frac{67}{45} }{ \frac{ {17}^{2} }{ {12}^{2} } } \\ \\ 4 -\frac{ \frac{67}{45} }{ \frac{ 289}{ 144} } \\ \\ 4 - \frac{67}{45} \times \frac{ 144}{ 289} \\ \\ 4 - \frac{ 67 \times 144}{ 45 \times 289} \\ \\ 4 - \frac{ 67 \times 48}{ 15 \times 289} \\ \\ 4 - \frac{ 67 \times 16}{ 5 \times 289}\\ \\ 4 - \frac{1072}{ 1445} \\ \\ 4 - 0,7413554633 \\ \\ 3,2586445367$

$\\$

$4 - \frac{1072}{ 1445} \\ \\ \frac{4}{ 1} - \frac{1072}{ 1445} \\ \\ \frac{5780-1072}{ 1445} \\ \\ \frac{4708}{ 1445}$

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B)

$\frac{(0,666)^{2} + \frac{7}{9} }{ \frac{0,555}{2}} \\ \\\frac{(\frac{333}{500})^{2} + \frac{7}{9} }{ \frac{\frac{111}{200}}{2}}\\ \\\frac{\frac{333^{2}}{500^{2}} + \frac{7}{9} }{ \frac{\frac{111}{200}}{\frac{2}{1}}}\\ \\\frac{\frac{333^{2}}{500^{2}} + \frac{7}{9} }{ \frac{111}{200} \times \frac{1}{2}}\\ \\\frac{\frac{333^{2}}{500^{2}} + \frac{7}{9} }{ \frac{111}{400}}\\ \\(\frac{333^{2}}{500^{2}} + \frac{7}{9}) \times \frac{400}{111}\\ \\(\frac{110889}{250000} + \frac{7}{9}) \times \frac{400}{111}\\ \\\frac{9 \times110889 \: \:+ \: \: 7 \times 250000 }{250000 \times 9} \times \frac{400}{111}\\ \\\frac{(9 \times110889 \: \:+ \: \: 7 \times 250000 ) \times 400}{250000 \times 9 \times 111}\\ \\\frac{ 998001\: \: + \: \: 1750000 ) \times 400}{250000 \times 9 \times 111}\\ \\\frac{ 2748001 \times 400}{250000 \times 9 \times 111}\\ \\\frac{ 2748001 \times 4}{2500 \times 9 \times 111}\\ \\\frac{ 2748001 }{625\times 9 \times 111}\\ \\\frac{ 2748001 }{624375}\\ \\4,4012028028$

$\\$

Se 0,666 e 0,555 forem dízimas periódicas:

$\frac{(0,666...)^{2} + \frac{7}{9} }{ \frac{0,555...}{2}} \\ \\ \frac{ (\frac{6}{9})^{2} + \frac{7}{9} }{ \frac{ \frac{5}{9} }{2}}\\ \\\frac{\frac{6^{2}}{9^{2}} + \frac{7}{9} }{ \frac{\frac{5}{9}}{\frac{2}{1}}}\\ \\\frac{\frac{6^{2}}{9^{2}} + \frac{7}{9} }{ \frac{5}{9} \times \frac{1}{2}}\\ \\\frac{\frac{6^{2}}{9^{2}} + \frac{7}{9} }{ \frac{5}{ 9 \times 2}}\\ \\\frac{\frac{36}{81} + \frac{7}{9}}{ \frac{5}{9 \times 2}}\\ \\\frac{ \frac{36 + 63}{81} }{ \frac{5}{9 \times 2} }\\ \\\frac{ \frac{ 99}{81} }{ \frac{5}{9 \times 2} }\\ \\\frac{ 99}{81} \times \frac{9 \times 2}{5}\\ \\\frac{ 99 \times 9 \times 2}{81 \times 5} \\ \\\frac{ 99 \times 2}{9 \times 5} \\ \\\frac{ 11 \times 2}{ 5} \\ \\\frac{ 22}{ 5} \\ \\4, 4$