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a,
\(=\frac{1+2+3+4+5+6+7+8+9}{10}=\frac{45}{10}=\frac{9}{2}\)
b,\(=9\times\left(\frac{26\times10101}{27\times10101}+\frac{8\times11111}{9\times11111}\right)=9\times\left(\frac{26}{27}+\frac{8}{9}\right)=9\times\frac{50}{27}=\frac{50}{3}\)
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\(a,\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}=\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}\)
\(=\frac{1}{2}-\frac{1}{6}=\frac{1}{3}\)
\(b,\left(1-\frac{1}{2}\right)\times\left(1-\frac{1}{3}\right)\times\left(1-\frac{1}{4}\right)=\frac{1}{2}\times\frac{2}{3}\times\frac{3}{4}\)
\(=\frac{1\times2\times3}{2\times3\times4}=\frac{1}{4}\)
1-(1-(1/2 × 3/5 + 1/5 × 1/2 + 2/10 × 1/2 +1/2)
=1-(1-(3/10 + 1/10 + 1/10 + 5/10)
=1-(1-(3+1+1+5/10)
=1-(1- 10/10)
=1-(1-1)
=1-0
=1
\(1-\left[1-\left(\frac{1}{2}\times\frac{3}{5}+\frac{1}{5}\times\frac{1}{2}+\frac{2}{10}\times\frac{1}{2}+\frac{1}{2}\right)\right]\)
\(=1-\left[1-\left\{\frac{1}{2}\times\left(\frac{3}{5}+\frac{1}{5}+\frac{2}{10}+\frac{1}{2}\right)\right\}\right]\)
\(=1-\left[1-\left\{\frac{1}{2}\times\left(\frac{6}{10}+\frac{2}{10}+\frac{2}{10}+\frac{5}{10}\right)\right\}\right]\)
\(=1-\left[1-\left\{\frac{1}{2}\times\left(\frac{6+2+2+5}{10}\right)\right\}\right]\)
\(=1-\left[1-\left\{\frac{1}{2}\times\frac{3}{2}\right\}\right]\)
\(=1-\left[1-\frac{3}{4}\right]\)
\(=1-\frac{1}{4}\)
\(=\frac{3}{4}\)
\(a.\left(\frac{6}{11}+\frac{5}{11}\right).\frac{3}{7}=1\cdot\frac{3}{7}=\frac{3}{7}b.\frac{3}{5}\cdot\frac{7}{9}+\frac{3}{5}\cdot\frac{2}{9}=\frac{3}{5}\cdot\left(\frac{7}{9}+\frac{2}{9}\right)=\frac{3}{5}\cdot1=\frac{3}{5}\)
\(=\frac{9}{10}-\frac{7}{10}+\frac{7}{20}=\frac{2}{10}+\frac{7}{20}=\frac{4}{20}+\frac{7}{20}=\frac{11}{20}\)
\(\frac{9}{10}-\left(\frac{2}{5}+\frac{3}{10}\right)+\frac{7}{20}=\frac{9}{10}-\frac{7}{10}+\frac{7}{20}=\frac{2}{10}+\frac{7}{20}=\frac{4+7}{20}=\frac{11}{20}\)
\(\frac{4}{5}+\left(x:\frac{2}{3}-\frac{1}{2}\right)=\frac{9}{10}\)
\(x:\frac{2}{3}-\frac{1}{2}=\frac{9}{10}-\frac{4}{5}\)
\(x:\frac{2}{3}-\frac{1}{2}=\frac{1}{10}\)
\(x:\frac{2}{3}=\frac{1}{10}-\frac{1}{2}\)
\(x:\frac{2}{3}=\frac{-2}{5}\)
\(x=\frac{-2}{5}X\frac{2}{3}\)
\(x=\frac{-4}{15}\)
\(\frac{4}{5}+\left(x:\frac{2}{3}-\frac{1}{2}\right)=\frac{9}{10}\)
\(x:\frac{2}{3}-\frac{1}{2}=\frac{1}{10}\)
\(x:\frac{2}{3}=\frac{3}{5}\)
\(x=\frac{2}{5}\)