Question

Calculati
[1, 2(3)-3(7)-1.5]:[2.0(2)];​

Answer 1

   

$\displaystyle\bf\\~[1,\!2(3)-3,\!(7)-1,\!5]:[2,\!0(2)]=?\\\\\textbf{Transformam numerele zecimale in fractii.}\\\\1,\!2(3)=\frac{123-12}{90}=\frac{111}{90}=\frac{37}{30}\\\\3,\!(7)=\frac{37-3}{9}=\frac{34}{9}\\\\1,\!5=\frac{15}{10}=\frac{3}{2}\\\\2,\!0(2)=\frac{202-20}{90}=\frac{182}{90}=\frac{91}{45}\\\\\\~[1,\!2(3)-3,\!(7)-1,\!5]:[2,\!0(2)]=\\\\=\left(\frac{37}{30}-\frac{34}{9}-\frac{3}{2}\right):\left(\frac{91}{45}\right)=$

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$\displaystyle\bf\\=\left(\frac{111}{90}-\frac{340}{90}-\frac{135}{90}\right):\left(\frac{91}{45}\right)=\\\\\\=\left(\frac{111-340-135}{90}\right):\left(\frac{91}{45}\right)=\\\\\\=\left(\frac{-364}{90}\right):\left(\frac{91}{45}\right)=\\\\\\=-\frac{364}{90}\times\frac{45}{91}=\\\\\\=-\frac{4}{2}\times\frac{1}{1}=\\\\\\=-\frac{4}{2}=\boxed{\bf~-2}$