Question

reperdee va rog frumos dau 40 puncte​

Answer 1

$\displaystyle b)~\frac{2}{35}\cdot \Bigg(2\frac{1}{2} +1\frac{7}{5} \Bigg)\cdot 3\frac{4}{7} -\Bigg(\frac{^{3)}1}{2} +\frac{^{2)}1}{3} +\frac{1}{6}\Bigg)= \\\\=\frac{2}{35}\cdot\Bigg(\frac{2 \cdot 2+1}{2} +\frac{1\cdot5+7}{5} \Bigg) \cdot \frac{3\cdot7+4}{7} -\frac{3\cdot1+2\cdot1+1}{6} =\\\\=\frac{2}{35} \cdot \Bigg(\frac{4+1}{2} +\frac{5+7}{5} \Bigg)\cdot \frac{21+4}{7} -\frac{3+2+1}{6} =$

$\displaystyle =\frac{2}{35}\cdot \Bigg(\frac{^{5)}5}{2} +\frac{^{2)}12}{5} \Bigg)\cdot \frac{25}{7} -\frac{6}{6} =\frac{2}{35} \cdot \frac{5\cdot5+2\cdot12}{10} \cdot \frac{25}{7} -1=\\\\=\frac{2}{35} \cdot \frac{25+24}{10} \cdot \frac{25}{7} -1=\frac{2}{35} \cdot \frac{49}{10} \cdot \frac{25}{7} -1=\frac{7\cdot 5}{7 \cdot 5 } -1=\frac{35}{35} -1=1-1=0$

$c)~\displaystyle \Bigg(3\frac{1}{3} :2\frac{1}{6}\Bigg):\Bigg(9:\frac{13}{14} \Bigg)=\Bigg(\frac{3\cdot3+1}{3} :\frac{2\cdot6+1}{6} \Bigg):\Bigg(9:\frac{13}{14}\Bigg)=\\\\=\Bigg(\frac{9+1}{3} :\frac{12+1}{6} \Bigg):\Bigg(9: \frac{13}{14}\Bigg)=\Bigg(\frac{10}{3} :\frac{13}{6} \Bigg):\Bigg(9:\frac{13}{14}\Bigg)=\\\\=\Bigg(\frac{10}{3} \cdot \frac{6}{13} \Bigg):\Bigg(9 \cdot \frac{14}{13} \Bigg)=\frac{60}{39} :\frac{126}{13} =\frac{60}{39}\cdot \frac{13}{126}=\frac{780}{4914} =\frac{10}{63}$

$\displaystyle d)~\Bigg(\frac{2}{5} :4+\frac{1}{3}:\frac{5}{6} \Bigg):\Bigg(\frac{4}{10} +^{10)}1\Bigg):\Bigg( \frac{11}{10} -^{10)}1\Bigg)=\\\\=\Bigg(\frac{2}{5} \cdot \frac{1}{4} +\frac{1}{3} \cdot \frac{6}{5}\Bigg): \frac{4+10}{10} :\frac{11-10}{10} =\Bigg(\frac{^{3)}2}{20} +\frac{^{4)}6}{15} \Bigg):\frac{14}{10}:\frac{1}{10}=\\\\=\frac{3\cdot 2+4 \cdot 6}{60} \cdot \frac{10}{14} \cdot 10=\frac{6+24}{60}\cdot\frac{10}{14} \cdot 10=\frac{30}{60} \cdot \frac{10}{14}\cdot10=\frac{5\cdot5}{7} =\frac{25}{7}$