Question

Am nevoie rapid va dau 30 de puncte plssss​

Answer 1

 

$\displaystyle\bf\\1)\\\\3,\!75:0,\!2(7)\cdot0,\!(1)+0,\!5=\\\\=\frac{375}{100}:\frac{27-2}{90}\times\frac{1}{9}+\frac{5}{10}=\\\\=\frac{15}{4}:\frac{5}{18}\times\frac{1}{9}+\frac{1}{2}=\\\\=\frac{15}{4}\times\frac{18}{5}\times\frac{1}{9}+\frac{1}{2}=\\\\=\frac{3}{4}\times\frac{2}{1}\times\frac{1}{1}+\frac{1}{2}=\\\\=\frac{3}{2}\times\frac{1}{1}\times\frac{1}{1}+\frac{1}{2}=\\\\=\frac{3}{2}+\frac{1}{2}=\frac{4}{2}=\boxed{\bf2}$

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$\displaystyle\bf\\2)\\\\\left\{2+\left[0,\!(6)+1\frac{1}{5}\right]:2\frac{1}{3}\right\}\cdot\frac{5}{42}+0,\!(6)=\\\\=\left\{2+\left[\frac{6}{9}+\frac{6}{5}\right]:\frac{7}{3}\right\}\times\frac{5}{42}+\frac{6}{9}=\\\\=\left\{2+\left[\frac{2}{3}+\frac{6}{5}\right]:\frac{7}{3}\right\}\times\frac{5}{42}+\frac{2}{3}=\\\\=\left\{2+\left[\frac{10}{15}+\frac{18}{15}\right]:\frac{7}{3}\right\}\times\frac{5}{42}+\frac{2}{3}=$

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$\displaystyle\bf\\=\left\{2+\frac{28}{15}\times\frac{3}{7}\right\}\times\frac{5}{42}+\frac{2}{3}=\\\\=\left\{2+\frac{4}{5}\times\frac{1}{1}\right\}\times\frac{5}{42}+\frac{2}{3}=\\\\=\left\{\frac{10}{5}+\frac{4}{5}\right\}\times\frac{5}{42}+\frac{2}{3}=\\\\=\frac{14}{5}\times\frac{5}{42}+\frac{2}{3}=\\\\=\frac{1}{1}\times\frac{1}{3}+\frac{2}{3}=\\\\=\frac{1}{3}+\frac{2}{3}=\frac{3}{3}=\boxed{\bf1}$

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$\displaystyle\bf\\3)\\2,\!75:\left(1\frac{1}{2}-0,\!4\right)+\left(\frac{3}{4}+0,\!8(3)\right):3,\!1(6)=\\\\=\frac{275}{100}:\left(\frac{3}{2}-\frac{4}{10}\right)+\left(\frac{3}{4}+\frac{83-8}{90} \right):\frac{316-31}{90}=\\\\=\frac{11}{4}:\left(\frac{3}{2}-\frac{4}{10}\right)+\left(\frac{3}{4}+\frac{5}{6} \right):\frac{19}{6}=\\\\=\frac{11}{4}:\left(\frac{15}{10}-\frac{4}{10}\right)+\left(\frac{9}{12}+\frac{10}{12} \right):\frac{19}{6}=$

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$\displaystyle\bf\\=\frac{11}{4}:\frac{11}{10}+\frac{19}{12}:\frac{19}{6}=\\\\=\frac{11}{4}\times\frac{10}{11}+\frac{19}{12}\times\frac{6}{19}=\\\\=\frac{1}{2}\times\frac{5}{1}+\frac{1}{2}\times\frac{1}{1}=\\\\=\frac{5}{2}+\frac{1}{2}=\frac{6}{2}=\boxed{\bf3}$

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$\displaystyle\bf\\ 4)\\\\9\cdot\left[\left(0,\!8(3)-\frac{3}{8}\right):\frac{3}{4}-\left(0,\!375+\frac{7}{20} \right):1\frac{9}{20}\right]=\\\\=9\cdot\left[\left(\frac{83-8}{90}-\frac{3}{8}\right):\frac{3}{4}-\left(\frac{375}{1000} +\frac{7}{20} \right):\frac{29}{20}\right]=\\\\=9\cdot\left[\left(\frac{5}{6}-\frac{3}{8}\right):\frac{3}{4}-\left(\frac{3}{8}+\frac{7}{20} \right):\frac{29}{20}\right]=$

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$\displaystyle\bf\\=9\cdot\left[\left(\frac{20}{24}-\frac{9}{24}\right):\frac{3}{4}-\left(\frac{15}{40}+\frac{14}{40} \right):\frac{29}{20}\right]=\\\\=9\cdot\left[\frac{11}{24}:\frac{3}{4}-\frac{29}{40}:\frac{29}{20}\right]=\\\\=9\cdot\left[\frac{11}{24}\times\frac{4}{3}-\frac{29}{40}\times\frac{20}{29}\right]=\\\\=9\cdot\left[\frac{11}{6}\times\frac{1}{3}-\frac{1}{2}\times\frac{1}{1}\right]=$

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$\displaystyle\bf\\=9\cdot\left[\frac{11}{18}-\frac{1}{2}\right]=\\\\=9\cdot\left[\frac{11}{18}-\frac{9}{18}\right]=\\\\=9\cdot\frac{2}{18}=\frac{18}{18}=\boxed{\bf1}$