Question

X =[3/8+(2/5:8/15)],Y =[(1/3+3/5):21/10] e Z = (3-1/3:1/8), DETERMINE O VALOR NUMERICO DA EXPRESSÃO X+Y+Z

Answer 1

Resposta:

$\dfrac{1649}{72}$

Explicação passo-a-passo:

$x=\dfrac{3}{8}+\dfrac{\left(\dfrac{2}{5}\right)}{\left(\dfrac{8}{15}\right)} =\dfrac{3}{8}+\dfrac{2}{5}\times\dfrac{15}{8} =\dfrac{3}{8}+\dfrac{30}{40} =\dfrac{15+30}{40} =\dfrac{45}{40}=\dfrac{9}{8}$

$y= \dfrac{\left(\dfrac{1}{3}+\dfrac{3}{5} \right)}{\left(\dfrac{21}{10} \right)} =\dfrac{\left(\dfrac{5+9}{15}\right)}{\left(\dfrac{21}{10} \right)} = \dfrac{\left(\dfrac{14}{15}\right)}{\left(\dfrac{21}{10} \right)}=\dfrac{14}{15}\times\dfrac{10}{21}=\dfrac{140}{315}=\dfrac{4}{9}$

$z=\dfrac{\left(3-\dfrac{1}{3}\right) }{\left(\dfrac{1}{8}\right) } =\dfrac{\left(\dfrac{9-1}{3}\right) }{\left(\dfrac{1}{8}\right) } =\dfrac{\left(\dfrac{8}{3}\right) }{\left(\dfrac{1}{8}\right) } =\dfrac{8}{3}\times\dfrac{8}{1}=\dfrac{64}{3}$

$\Rightarrow x+y+z=\dfrac{9}{8} +\dfrac{4}{9} +\dfrac{64}{3} =\dfrac{81+32+1536}{72} =\dfrac{1649}{72}$

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