a) Uprośćmy podane wyrażenie:

$\frac{\left(3,24-0,24\cdot \frac{1}{3}\right):0,4+0,6\cdot 1\frac{1}{6}}{2-2:1\frac{5}{8}\cdot 3\frac{1}{4}}=\frac{\left(3\frac{24}{100}-\frac{{\cancel{24}}^8}{100}\cdot \frac{1}{{\cancel{3}}_1}\right):\frac{4}{10}+\frac{{\cancel{6}}^1}{10}\cdot \frac{7}{{\cancel{6}}_1}}{2-2:\frac{13}{8}\cdot \frac{13}{4}}=$   
$=\frac{\left(\frac{324}{100}-\frac{8}{100}\right)\cdot \frac{10}{4}+\frac{7}{10}}{2-2\cdot \frac{8}{{\cancel{13}}_1}\cdot \frac{{\cancel{13}}^1}{4}}=\frac{\frac{{\cancel{316}}^{79}}{100}\cdot \frac{10}{{\cancel{4}}_1}+\frac{7}{10}}{2-2\cdot {\cancel{8}}^2\cdot \frac{1}{{\cancel{4}}_1}}=\frac{\frac{79}{{\cancel{100}}_{10}}\cdot {\cancel{10}}^1+\frac{7}{10}}{2-4}=$   
$=\frac{\frac{79}{10}+\frac{7}{10}}{-2}=\frac{{\cancel{86}}^{43}}{10}\cdot \left(-\frac{1}{{\cancel{2}}_1}\right)=-\frac{43}{10}=-4,3=-4,30$  

Odp. 430

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b) Uprośćmy wyrażenie postaci:

$\left\{\left[\left(4\frac{1}{5}:1\frac{1}{3}-2\frac{3}{4}\right):\frac{7}{15}\right]-4\frac{1}{3}\right\}\cdot \frac{5}{6}=\left\{\left[\left(\frac{21}{5}:\frac{4}{3}-\frac{11}{4}\right)\cdot \frac{15}{7}\right]-\frac{13}{3}\right\}\cdot \frac{5}{6}=$ $=\left\{\left[\left(\frac{21}{5}\cdot \frac{3}{4}-\frac{11}{4}\right)\cdot \frac{15}{7}\right]-\frac{13}{3}\right\}\cdot \frac{5}{6}=\left\{\left[\left(\frac{63}{20}-\frac{55}{20}\right)\cdot \frac{15}{7}\right]-\frac{13}{3}\right\}\cdot \frac{5}{6}=$  

$=\left(\frac{8}{{\cancel{20}}_4}\cdot \frac{{\cancel{15}}^3}{7}-\frac{13}{3}\right)\cdot \frac{5}{6}=\left(\frac{{\cancel{8}}^2}{{\cancel{4}}_1}\cdot \frac{3}{7}-\frac{13}{3}\right)\cdot \frac{5}{6}=\left(\frac{6}{7}-\frac{13}{3}\right)\cdot \frac{5}{6}=$  

$=\left(\frac{18}{21}-\frac{91}{21}\right)\cdot \frac{5}{6}=-\frac{73}{21}\cdot \frac{5}{6}=-\frac{365}{126}=2\frac{113}{126}\approx 2,897$  

 

Odp. 289

 

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c) Uprośćmy następujące wyrażenie:

$\frac{\left[\left(4,625-\frac{13}{18}\cdot \frac{9}{26}\right):2,25+\left(2,5:1\frac{1}{4}\right):6,75\right]:1\frac{53}{68}}{\frac{2}{3}:\frac{4}{7}-1\frac{1}{18}}=\frac{\left[\left(4\frac{5}{8}-\frac{{\cancel{13}}^1}{18}\cdot \frac{9}{{\cancel{26}}_2}\right):2\frac{1}{4}+\left(2\frac{1}{2}:\frac{5}{4}\right):6\frac{3}{4}\right]:\frac{121}{68}}{\frac{{\cancel{2}}^1}{3}\cdot \frac{7}{{\cancel{4}}_2}-\frac{19}{18}}$   

$=\frac{\left[\left(\frac{37}{8}-\frac{1}{{\cancel{18}}_2}\cdot \frac{{\cancel{9}}^1}{2}\right):\frac{9}{4}+\left(\frac{{\cancel{5}}^1}{2}\cdot \frac{4}{{\cancel{5}}_1}\right):\frac{27}{4}\right]\cdot \frac{68}{121}}{\frac{7}{6}-\frac{19}{18}}=\frac{\left[\left(\frac{37}{8}-\frac{1}{4}\right)\cdot \frac{4}{9}+\left(\frac{1}{{\cancel{2}}_1}\cdot {\cancel{4}}^2\right)\cdot \frac{4}{27}\right]\cdot \frac{68}{121}}{\frac{21}{18}-\frac{19}{18}}=$  

$=\frac{\left[\left(\frac{37}{8}-\frac{2}{8}\right)\cdot \frac{4}{9}+2\cdot \frac{4}{27}\right]\cdot \frac{68}{121}}{\frac{{\cancel{2}}^1}{{\cancel{18}}_9}}=\frac{\left[\frac{35}{{\cancel{8}}_2}\cdot \frac{{\cancel{4}}^1}{9}+\frac{8}{27}\right]\cdot \frac{68}{121}}{\frac{1}{9}}=\frac{\left[\frac{35}{18}+\frac{8}{27}\right]\cdot \frac{68}{121}}{\frac{1}{9}}=$

  $=\frac{\left[\frac{105}{54}+\frac{16}{54}\right]\cdot \frac{68}{121}}{\frac{1}{9}}=\frac{\frac{{\cancel{121}}^1}{54}\cdot \frac{68}{{\cancel{121}}_1}}{\frac{1}{9}}=\frac{68}{{\cancel{54}}_6}\cdot {\cancel{9}}^1=\frac{{\cancel{68}}^{34}}{{\cancel{6}}^3}=\frac{34}{3}=11\frac{1}{3}=11,\left(3\right)$  

Odp. 133