a) \(\dfrac{4}{7}\times\dfrac{3}{5}=\dfrac{4\times3}{7\times5}=\dfrac{12}{35}\)

b) \(\dfrac{1}{3}\times\dfrac{9}{10}=\dfrac{1\times9}{3\times10}=\dfrac{9}{30}=\dfrac{3}{10}\)

c) \(\dfrac{1}{6}\times\dfrac{1}{4}=\dfrac{1}{4\times6}=\dfrac{1}{24}\)

a) \(\dfrac{2}{3}+\dfrac{4}{9}=\dfrac{6}{9}+\dfrac{4}{9}+\dfrac{6+3}{9}=\dfrac{10}{9}\)

b)\(\dfrac{1}{10}+\dfrac{2}{5}=\dfrac{1}{10}+\dfrac{4}{10}=\dfrac{1+4}{10}=\dfrac{5}{10}=\dfrac{1}{2}\)

c) \(\dfrac{7}{22}-\dfrac{3}{11}=\dfrac{7}{22}-\dfrac{6}{22}=\dfrac{7-6}{22}=\dfrac{1}{22}\)

d) \(\dfrac{5}{6}-\dfrac{5}{12}=\dfrac{10}{12}-\dfrac{5}{12}=\dfrac{10-5}{12}=\dfrac{5}{12}\)

a) \(\dfrac{9}{11}-\dfrac{3}{11}=\dfrac{9-3}{11}=\dfrac{6}{11}\)

b) \(\dfrac{10}{4}-\dfrac{5}{4}=\dfrac{10-5}{4}=\dfrac{5}{4}\)

c) \(\dfrac{22}{15}-\dfrac{8}{15}=\dfrac{22-8}{15}=\dfrac{14}{15}\)

a) \(\dfrac{1}{2}-\dfrac{1}{6}=\dfrac{3}{6}-\dfrac{1}{6}=\dfrac{3-1}{6}=\dfrac{2}{6}=\dfrac{1}{3}\)

b) \(\dfrac{3}{4}-\dfrac{5}{8}=\dfrac{12}{8}-\dfrac{5}{8}=\dfrac{12-5}{8}=\dfrac{7}{8}\)

c) \(\dfrac{7}{10}-\dfrac{2}{5}=\dfrac{7}{10}-\dfrac{4}{10}=\dfrac{7-4}{10}=\dfrac{3}{10}\)

d) \(\dfrac{7}{12}-\dfrac{1}{3}=\dfrac{7}{12}-\dfrac{4}{12}=\dfrac{7-4}{12}=\dfrac{3}{12}=\dfrac{1}{4}\)

a) \(\dfrac{1}{3}\)
b)\(\dfrac{1}{8}\)
c)\(\dfrac{3}{10}\)
d)\(\dfrac{3}{12}\)

a) \(\left(\dfrac{1}{4}+\dfrac{1}{12}\right):\dfrac{1}{13}\)

\(=\left(\dfrac{3}{12}+\dfrac{1}{12}\right):\dfrac{1}{13}\)

\(=\dfrac{4}{12}\times13\)

\(=\dfrac{1}{3}\times13\)

\(=\dfrac{13}{3}\)

b) \(\dfrac{3}{5}:\dfrac{2}{9}-\dfrac{1}{10}\)

\(=\dfrac{3}{5}\times\dfrac{9}{2}-\dfrac{1}{10}\)

\(=\dfrac{27}{10}-\dfrac{1}{10}\)

\(=\dfrac{26}{10}\)

\(=\dfrac{13}{5}\)

a) \(\dfrac{4}{24}+\dfrac{7}{6}=\dfrac{4}{24}+\dfrac{28}{24}=\dfrac{4+28}{24}=\dfrac{32}{24}=\dfrac{4}{3}\)

b) \(\dfrac{10}{15}-\dfrac{1}{3}=\dfrac{10}{15}-\dfrac{5}{15}=\dfrac{10-5}{15}=\dfrac{5}{15}=\dfrac{1}{3}\)

c) \(\dfrac{21}{28}-\dfrac{1}{4}=\dfrac{21}{28}-\dfrac{7}{28}=\dfrac{21-7}{28}=\dfrac{14}{28}=\dfrac{1}{2}\)

d) \(\dfrac{35}{40}+\dfrac{5}{8}=\dfrac{35}{40}+\dfrac{25}{40}=\dfrac{35+25}{40}=\dfrac{60}{40}=\dfrac{3}{2}\)

\(a)\dfrac{4}{24}=\dfrac{1}{6} \\ \dfrac{1}{6}+\dfrac{7}{6}\\ =\dfrac{8}{6}=\dfrac{4}{3}\\ b)\dfrac{10}{15}=\dfrac{2}{3}-\dfrac{1}{3}\\ =\dfrac{1}{3}\\ c)\dfrac{21}{28}=\dfrac{3}{4}\\ \dfrac{3}{4}-\dfrac{1}{4}\\ =\dfrac{2}{4}=\dfrac{1}{2}\\ d)\dfrac{35}{40}=\dfrac{7}{8}\\ \dfrac{7}{8}+\dfrac{5}{8}\\ =\dfrac{12}{8}=\dfrac{3}{2}\)

a) \(\dfrac{3}{5}+\dfrac{7}{25}=\dfrac{15}{25}+\dfrac{7}{25}=\dfrac{15+7}{25}=\dfrac{22}{25}\)

b) \(\dfrac{8}{11}-\dfrac{19}{33}=\dfrac{24}{33}-\dfrac{19}{33}=\dfrac{24-19}{33}=\dfrac{5}{33}\)

c) \(\dfrac{16}{21}\times\dfrac{3}{5}=\dfrac{16\times3}{21\times5}=\dfrac{48}{105}=\dfrac{16}{35}\)

d) \(\dfrac{14}{41}\div\dfrac{7}{9}=\dfrac{14}{41}\times\dfrac{9}{7}=\dfrac{14\times9}{41\times7}=\dfrac{126}{287}=\dfrac{18}{41}\)

a) \(\dfrac{3}{11}+\dfrac{14}{11}=\dfrac{17}{11}\)

b) \(\dfrac{1}{16}+\dfrac{3}{4}=\dfrac{1}{16}+\dfrac{12}{16}=\dfrac{13}{16}\)

c) \(\dfrac{2}{20}+\dfrac{7}{10}=\dfrac{2}{20}+\dfrac{14}{20}=\dfrac{16}{20}=\dfrac{4}{5}\)

a) \(\dfrac{3}{5}:\dfrac{3}{4}=\dfrac{3}{5}\cdot\dfrac{4}{3}=\dfrac{4}{5}\)

b) \(\dfrac{2}{5}:\dfrac{3}{10}=\dfrac{2}{5}\cdot\dfrac{10}{3}=\dfrac{4}{3}\)

c) \(\dfrac{1}{8}:\dfrac{1}{6}=\dfrac{1}{8}\cdot6=\dfrac{6}{8}=\dfrac{3}{4}\)

a: \(=\dfrac{3}{5}\cdot\dfrac{4}{3}=\dfrac{12}{15}=\dfrac{4}{5}\)

b: \(=\dfrac{2}{5}\cdot\dfrac{10}{3}=\dfrac{20}{15}=\dfrac{4}{3}\)

c: \(=\dfrac{1}{8}\cdot6=\dfrac{6}{8}=\dfrac{3}{4}\)

a, \(\dfrac{3}{5}:\dfrac{3}{4}=\dfrac{3}{5}x\dfrac{4}{3}=\dfrac{12}{15}\)

b, \(\dfrac{2}{5}:\dfrac{3}{10}=\dfrac{2}{5}x\dfrac{10}{3}=\dfrac{4}{3}\)

c, \(\dfrac{1}{8}:\dfrac{1}{6}=\dfrac{1}{8}x\dfrac{6}{1}=\dfrac{3}{4}\)

\(a)\dfrac{5}{7}\times\dfrac{7}{15}\\ =\dfrac{5\times7}{7\times15}\\ =\dfrac{35}{105}=\dfrac{1}{3}\\ b)\dfrac{8}{21}\times3\\ =\dfrac{8\times3}{21}\\ =\dfrac{24}{21}=\dfrac{8}{7}\\ c)\dfrac{24}{17}:\dfrac{9}{17}\\ =\dfrac{24}{17}\times\dfrac{17}{9}\\ =\dfrac{24\times17}{17\times9}\\ =\dfrac{408}{153}=\dfrac{8}{3}\\ d)\dfrac{36}{5}:9\\ =\dfrac{36}{5}\times\dfrac{1}{9}\\ =\dfrac{36\times1}{5\times9}\\ =\dfrac{36}{45}=\dfrac{4}{5}\)

a) \(\dfrac{5}{7}\times\dfrac{7}{15}=\dfrac{5\times7}{7\times15}=\dfrac{35}{105}=\dfrac{1}{3}\)

b) \(\dfrac{8}{21}\times3=\dfrac{8\times3}{21}=\dfrac{24}{21}=\dfrac{8}{7}\)

c) \(\dfrac{24}{17}:\dfrac{9}{17}=\dfrac{24}{17}\times\dfrac{17}{9}=\dfrac{24\times17}{17\times9}=\dfrac{24}{9}=\dfrac{8}{3}\)

d) \(\dfrac{36}{5}:9=\dfrac{36}{5}\times\dfrac{1}{9}=\dfrac{36}{5\times9}=\dfrac{36}{45}=\dfrac{4}{5}\)