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a) \(\frac{5}{12}+\frac{5}{6}-\frac{3}{4}=\frac{5}{12}+\frac{10}{12}-\frac{9}{12}=\frac{5+10-9}{12}=\frac{6}{12}=\frac{1}{2}.\)
b) \(1-\left(\frac{1}{5}+\frac{1}{2}\right)=1-\left(\frac{2}{10}+\frac{5}{10}\right)=1-\frac{7}{10}=\frac{3}{10}\)
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=17/6+1/2×13/3-9/4:3/5
=17/6+13/6-9/4×5/3
=17/6+13/6-15/4
=68+52-90/24
=30/24
=5/4
\(2\frac{5}{6}+0,5\times4\frac{1}{3}-2\frac{1}{4}:\frac{3}{5}\)
\(=\frac{17}{6}+\frac{1}{2}\times\frac{13}{3}-\frac{9}{4}:\frac{3}{5}\)
\(=\frac{17}{6}+\frac{13}{6}-\frac{9}{4}\times\frac{5}{3}\)
\(=5-\frac{9\times5}{4\times3}\)
\(=5-\frac{3\times5}{4\times1}\)
\(=5-\frac{15}{4}=\frac{20-15}{4}=\frac{5}{4}\)
\(\frac{6:\frac{3}{5}-1\frac{1}{6}\cdot\frac{6}{7}}{4\frac{1}{5}\cdot\frac{10}{11}+5\frac{2}{11}}=1\)
\(\left(1-\frac{1}{2}\right)x\left(1-\frac{1}{3}\right)x\left(1-\frac{1}{4}\right)x\left(1-\frac{1}{5}\right)x\left(1-\frac{1}{6}\right)\)
\(=\frac{1}{2}.\frac{2}{3}.\frac{3}{4}.\frac{4}{5}.\frac{5}{6}\)
\(=\frac{1.2.3.4.5}{2.3.4.5.6}=\frac{1}{6}\)
\(\left(\frac{1}{6}+\frac{1}{10}+\frac{1}{15}\right):\left(\frac{1}{6}+\frac{1}{10}-\frac{1}{15}\right)\)
=\(\frac{1}{3}+\frac{1}{5}\)
=\(\frac{5}{3}\)
\(\frac{6:\frac{3}{5}-1\frac{1}{6}\times\frac{6}{7}}{4\frac{1}{5}\times\frac{10}{11}+5\frac{2}{11}}\)
\(=\frac{\frac{6}{1}:\frac{3}{5}-\frac{7}{6}\times\frac{6}{7}}{\frac{21}{5}\times\frac{10}{11}\times\frac{57}{11}}\)
\(=\frac{\frac{6}{1}\times\frac{5}{3}-1}{\frac{210}{55}+\frac{57}{11}}\)
\(=\frac{\frac{30}{3}-1}{\frac{42}{11}+\frac{57}{11}}\)
\(=\frac{10-1}{\frac{99}{11}}\)
\(=\frac{9}{9}\)
\(=1\)
\(6:\frac{3}{5}-1\frac{1}{6}\)X \(\frac{6}{7}\) \(4\frac{1}{5}\)X \(\frac{10}{11}+5\frac{2}{11}\)
\(=\frac{33}{5}-\frac{7}{6}\)X \(\frac{6}{7}\) \(=\) \(\frac{21}{5}\)X \(\frac{10}{11}+\frac{57}{11}\)
\(=\frac{33}{5}-1\) \(=\frac{42}{11}+\frac{57}{11}\)
\(=\frac{28}{5}\) \(=\frac{99}{11}=9\)