\(\dfrac{3}{2}x-0,2=\dfrac{3}{5}\)

\(\dfrac{3}{2}x-\dfrac{1}{5}=\dfrac{3}{5}\)

\(\dfrac{3}{2}x=\dfrac{3}{5}+\dfrac{1}{5}\)

\(\dfrac{3}{2}x=\dfrac{4}{5}\)

   \(x=\dfrac{4}{5}:\dfrac{3}{2}\)

   \(x=\dfrac{4}{5}\cdot\dfrac{2}{3}\)

   \(x=\dfrac{8}{15}\)

\(\dfrac{1}{3}+x=\dfrac{3}{4}\)

        \(x=\dfrac{3}{4}-\dfrac{1}{3}\)

        \(x=\dfrac{9}{12}-\dfrac{4}{12}\)

        \(x=\dfrac{5}{12}\)

\(1\dfrac{1}{2}x-\dfrac{2}{5}=\dfrac{1}{4}\)

\(\dfrac{3}{2}x-\dfrac{2}{5}=\dfrac{1}{4}\)

\(\dfrac{3}{2}x=\dfrac{1}{4}+\dfrac{2}{5}\)

\(\dfrac{3}{2}x=\dfrac{13}{20}\)

   \(x=\dfrac{13}{20}:\dfrac{3}{2}\)

   \(x=\dfrac{13}{20}\cdot\dfrac{2}{3}\)

   \(x=\dfrac{13}{30}\)

\(\dfrac{11}{8}-\dfrac{3}{8}\cdot x=\dfrac{1}{8}\)

          \(\dfrac{3}{8}\cdot x=\dfrac{11}{8}-\dfrac{1}{8}\)

          \(\dfrac{3}{8}\cdot x=\dfrac{5}{4}\)

                \(x=\dfrac{5}{4}:\dfrac{3}{8}\)   

                \(x=\dfrac{5}{4}\cdot\dfrac{8}{3}\)

                \(x=\dfrac{10}{3}\)

Tham khảo:

a: \(=\dfrac{-7}{8}\left(\dfrac{3}{5}+\dfrac{2}{5}\right)+3+\dfrac{7}{8}=\dfrac{-7}{8}+\dfrac{7}{8}+3=3\)

b: \(=-\dfrac{8}{5}:\dfrac{5}{3}=-\dfrac{24}{25}\)

c: \(=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{3}{4}=\dfrac{6}{7}+\dfrac{1}{8}-\dfrac{6}{8}=\dfrac{6}{7}-\dfrac{5}{8}=\dfrac{48}{56}-\dfrac{35}{56}=\dfrac{13}{56}\)

Lời giải:

a)

\(\frac{\frac{2}{3}-\frac{2}{5}+\frac{2}{7}-\frac{2}{9}+\frac{2}{11}}{\frac{8}{3}-\frac{8}{5}+\frac{8}{7}-\frac{8}{9}+\frac{8}{11}}=\frac{2\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{7}-\frac{1}{9}+\frac{1}{11}\right)}{8\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{7}-\frac{1}{9}+\frac{1}{11}\right)}\) \(=\frac{2}{8}=\frac{1}{4}\)

b)

\(\left(\frac{1}{2}-1\right)\left(\frac{1}{3}-1\right)\left(\frac{1}{4}-1\right)....\left(\frac{1}{50}-1\right)\left(\frac{1}{51}-1\right)\)

\(=\frac{1-2}{2}.\frac{1-3}{3}.\frac{1-4}{4}....\frac{1-50}{50}.\frac{1-51}{2}=\frac{(-1)(-2)(-3)...(-49)(-50)}{2.3.4....50.51}\)

\(=\frac{(-1)^{50}.1.2.3....49.50}{2.3.4...50.51}=\frac{1}{51}\)

=1/8x(3/2-1/4)+3/8x5/4

=1/8x5/4+3/8x5/4

=5/4x(1/8+3/8)

=5/8

\(C=\dfrac{1}{8}\times\dfrac{3}{2}-\dfrac{1}{8}\times\dfrac{1}{4}+\dfrac{3}{8}\times\dfrac{5}{8}\)

\(C=\dfrac{1}{8}\times\left(\dfrac{3}{2}-\dfrac{1}{4}\right)+\dfrac{3}{8}\times\dfrac{5}{4}\)

\(C=\dfrac{1}{8}\times\dfrac{5}{4}+\dfrac{3}{8}\times\dfrac{5}{4}\)

\(C=\left(\dfrac{1}{8}+\dfrac{3}{8}\right)\times\dfrac{5}{4}\)

\(C=\dfrac{1}{2}\times\dfrac{5}{4}\)

\(C=\dfrac{5}{8}\)

a) \(\dfrac{7}{8} + \dfrac{7}{8}:\dfrac{1}{8} - \dfrac{1}{2}\)

\(\begin{array}{l} = \dfrac{7}{8} + \dfrac{7}{8}.8 - \dfrac{1}{2}\\ = \dfrac{7}{8}.1 + \dfrac{7}{8}.8 - \dfrac{1}{2}\\ = \left( {\dfrac{7}{8}.1 + \dfrac{7}{8}.8} \right) - \dfrac{1}{2}\\ = \dfrac{7}{8}.\left( {1 + 8} \right) - \dfrac{1}{2} = \dfrac{7}{8}.9 - \dfrac{1}{2}\\ = \dfrac{{63}}{8} - \dfrac{1}{2} = \dfrac{{63}}{8} - \dfrac{4}{8} = \dfrac{{63 - 4}}{8} = \dfrac{{59}}{8}\end{array}\)

b) \(\dfrac{6}{{11}} + \dfrac{{11}}{3}.\dfrac{3}{{22}}\)

\(\begin{array}{l} = \dfrac{6}{{11}} + \dfrac{{11.3}}{{3.22}} = \dfrac{6}{{11}} + \dfrac{1}{2}\\ = \dfrac{{12}}{{22}} + \dfrac{{11}}{{22}} = \dfrac{{12 + 11}}{{22}} = \dfrac{{23}}{{22}}\end{array}\)

\(\dfrac{3}{8}.19\dfrac{1}{3}-\dfrac{3}{8}.33\dfrac{1}{3}=\dfrac{3}{8}\left(19\dfrac{1}{3}-33\dfrac{1}{3}\right)=-\dfrac{3}{8}.\left(-14\right)=\dfrac{21}{4}\)

a) Các phân số đảo ngược là:

\(\dfrac{5}{8}\rightarrow\dfrac{8}{5};\dfrac{3}{4}\rightarrow\dfrac{4}{3};\dfrac{1}{2}\rightarrow\dfrac{2}{1}=2\)

b) \(\dfrac{3}{7}:\dfrac{5}{8}=\dfrac{3}{7}\times\dfrac{8}{5}=\dfrac{24}{35}\)

\(\dfrac{8}{7}:\dfrac{3}{4}=\dfrac{8}{7}\times\dfrac{4}{3}=\dfrac{32}{21}\)

\(\dfrac{1}{3}:\dfrac{1}{2}=\dfrac{1}{3}\times2=\dfrac{2\times1}{3}=\dfrac{2}{3}\)

\(\dfrac{2}{5}\times\dfrac{3}{4}-\dfrac{1}{8}=\dfrac{1}{5}\times\dfrac{3}{2}-\dfrac{1}{8}=\dfrac{3}{10}-\dfrac{1}{8}=\dfrac{24}{80}-\dfrac{10}{80}=\dfrac{14}{80}=\dfrac{7}{40}\\ \dfrac{4}{3}+\dfrac{1}{3}-\dfrac{1}{5}=\dfrac{5}{3}-\dfrac{1}{5}=\dfrac{25}{15}-\dfrac{3}{15}=\dfrac{22}{15}\\ \dfrac{9}{20}-\dfrac{3}{5}\times\dfrac{1}{4}=\dfrac{9}{20}-\dfrac{3}{20}=\dfrac{6}{20}=\dfrac{3}{10}\\ \dfrac{2}{8}+\dfrac{2}{3}:\dfrac{4}{5}=\dfrac{2}{8}+\dfrac{2}{3}\times\dfrac{5}{4}=\dfrac{2}{8}+\dfrac{1}{3}\times\dfrac{5}{2}=\dfrac{2}{8}+\dfrac{5}{6}=\dfrac{1}{4}+\dfrac{5}{6}=\dfrac{6}{24}+\dfrac{20}{24}=\dfrac{26}{24}=\dfrac{13}{12}\)