a) \(\dfrac{3}{5}\times\dfrac{17}{21}+\dfrac{2}{5}\times\dfrac{17}{21}\)

\(=\dfrac{17}{21}\times\left(\dfrac{3}{5}+\dfrac{2}{5}\right)\)

\(=\dfrac{17}{21}\times1\)

\(=\dfrac{17}{21}\)

b) \(\dfrac{11}{19}\times\dfrac{2}{7}+\dfrac{5}{7}\times\dfrac{11}{19}\)

\(=\dfrac{11}{19}\times\left(\dfrac{2}{7}+\dfrac{5}{7}\right)\)

\(=\dfrac{11}{19}\times1\)

\(=\dfrac{11}{19}\)

a: =17/21(3/5+2/5)

=17/21*5/5

=17/21

b: =11/19(2/7+5/7)

=11/19*1

=11/19

a) \(\dfrac{3}{8}:\dfrac{9}{4}\)

\(=\dfrac{3}{8}\times\dfrac{4}{9}\)

\(=\dfrac{3\times4}{8\times9}\)

\(=\dfrac{1\times1}{2\times3}\)

\(=\dfrac{1}{6}\)

b) \(\dfrac{8}{21}:\dfrac{4}{7}\)

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

\(=\dfrac{8\times7}{21\times4}\)

\(=\dfrac{2\times1}{3\times1}\)

\(=\dfrac{2}{3}\)

c) \(\dfrac{5}{8}:\dfrac{15}{8}\)

\(=\dfrac{5}{8}\times\dfrac{8}{15}\)

\(=\dfrac{5\times8}{8\times15}\)

\(=\dfrac{1\times1}{1\times3}\)

\(=\dfrac{1}{3}\)

a: \(=\dfrac{3}{8}\cdot\dfrac{4}{9}=\dfrac{12}{72}=\dfrac{1}{6}\)

b: \(=\dfrac{8}{21}\cdot\dfrac{7}{4}=\dfrac{56}{84}=\dfrac{2}{3}\)

c: \(=\dfrac{5}{8}\cdot\dfrac{8}{15}=\dfrac{5}{15}=\dfrac{1}{3}\)

\(a,?=\dfrac{5}{11}\times\dfrac{2}{7}=\dfrac{10}{77}\\ b,?=\dfrac{3}{4}:\dfrac{5}{8}=\dfrac{3}{4}\times\dfrac{8}{5}=\dfrac{6}{5}\\ c,?=1:\dfrac{6}{11}=\dfrac{11}{6}\)

a) \(?:\dfrac{2}{7}=\dfrac{5}{11}\)

\(?=\dfrac{5}{11}\times\dfrac{2}{7}\)

\(?=\dfrac{10}{77}\)

b) \(\dfrac{3}{4}:?=\dfrac{5}{8}\)

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

\(?=\dfrac{3}{4}\times\dfrac{8}{5}\)

\(?=\dfrac{6}{5}\)

c) \(?\times\dfrac{6}{11}=1\)

\(?=1:\dfrac{6}{11}\)

\(?=1\times\dfrac{11}{6}\)

\(?=\dfrac{11}{6}\)

a) \(\dfrac{2}{4}\times\dfrac{9}{5}=\dfrac{1}{2}\times\dfrac{9}{5}=\dfrac{1\times9}{2\times5}=\dfrac{9}{10}\)

b) \(\dfrac{13}{8}\times\dfrac{5}{15}=\dfrac{13}{8}\times\dfrac{1}{3}=\dfrac{13}{24}\)

c) \(\dfrac{3}{9}\times\dfrac{6}{12}=\dfrac{1}{3}\times\dfrac{1}{2}=\dfrac{1}{3\times2}=\dfrac{1}{6}\)

a: =18/20=9/10

b: \(=\dfrac{13\cdot5}{8\cdot15}=\dfrac{13}{8}\cdot\dfrac{1}{3}=\dfrac{13}{24}\)

c: \(=\dfrac{1}{3}\cdot\dfrac{1}{2}=\dfrac{1}{6}\)

\(A=\dfrac{-19}{9}.\dfrac{1}{2}-\dfrac{4}{11}.\dfrac{-11}{9}+\left(-\dfrac{2}{3}\right)=-\dfrac{23}{18}\)

\(B=\left(-\dfrac{15}{6}\right):\dfrac{-1}{2}+\dfrac{7}{-12}-\dfrac{1}{3}.\dfrac{-11}{2}=\dfrac{25}{4}\)

\(C=\dfrac{3}{4}.\left(-8\right)-\dfrac{1}{3}.\dfrac{-7}{2}-\dfrac{5}{18}=-\dfrac{46}{9}\)

\(A=\dfrac{-19}{18}+\dfrac{4}{9}-\dfrac{2}{3}=\dfrac{-19}{18}+\dfrac{8}{18}-\dfrac{12}{18}=\dfrac{-23}{18}\)

\(B=\dfrac{-5}{2}\cdot\dfrac{-2}{1}-\dfrac{7}{12}+\dfrac{11}{6}=\dfrac{5\cdot12-7+22}{12}=\dfrac{75}{12}=\dfrac{25}{4}\)

a)

\(\dfrac{3}{5}\times\dfrac{7}{11}\times\dfrac{5}{3}\times11\\ =\left(\dfrac{3}{5}\times\dfrac{5}{3}\right)\times\left(\dfrac{7}{11}\times11\right)\\ =\dfrac{3\times5}{5\times3}\times\dfrac{7\times11}{11}\\ =1\times7\\ =7\)

b)

\(\dfrac{3}{8}\times\dfrac{2}{7}+\dfrac{5}{7}\times\dfrac{3}{8}\\ =\dfrac{3}{8}\times\left(\dfrac{2}{7}+\dfrac{5}{7}\right)\\ =\dfrac{3}{8}\times\dfrac{7}{7}\\ =\dfrac{3}{8}\times1=\dfrac{3}{8}\)

a: \(\dfrac{5}{6}\cdot7=\dfrac{5\cdot7}{6}=\dfrac{35}{6}\)

b: \(\dfrac{7}{10}\cdot3=\dfrac{7\cdot3}{10}=\dfrac{21}{10}\)

c: \(5\cdot\dfrac{4}{21}=\dfrac{5\cdot4}{21}=\dfrac{20}{21}\)

d: \(2\cdot\dfrac{5}{9}=\dfrac{2\cdot5}{9}=\dfrac{10}{9}\)

a: \(\dfrac{3}{9}\times\dfrac{5}{4}=\dfrac{5}{4}\times\dfrac{1}{3}=\dfrac{5\times1}{4\times3}=\dfrac{5}{12}\)

b: \(\dfrac{10}{15}\times\dfrac{3}{5}=\dfrac{3}{5}\times\dfrac{2}{3}=\dfrac{3\times2}{5\times3}=\dfrac{2}{5}\)

c: \(\dfrac{5}{8}\times\dfrac{4}{12}=\dfrac{5}{8}\times\dfrac{1}{3}=\dfrac{5}{3\times8}=\dfrac{5}{24}\)

d: \(\dfrac{9}{27}\times\dfrac{3}{21}=\dfrac{1}{7}\times\dfrac{1}{3}=\dfrac{1\times1}{7\times3}=\dfrac{1}{21}\)