a) \( \dfrac{3}{10}\times \dfrac{4}{9} =\dfrac{3 \times 4}{10 \times 9}\) \(= \dfrac{3 \times 2 \times 2}{5 \times 2 \times 3 \times 3} = \dfrac{2}{5 \times 3}=\dfrac{2}{15}\);
b) \( \dfrac{6}{5}:\dfrac{3}{7}\) \( =\dfrac{6}{5}\times \dfrac{7}{3}=\dfrac{42}{15}=\dfrac{14}{5}\) ;
c) \( \dfrac{3}{4} \times \dfrac{2}{5}=\dfrac{3 \times 2}{4 \times 5}=\dfrac{6}{20}=\dfrac{3}{10}\) ;
d) \( \dfrac{5}{8}:\dfrac{1}{2}\) \( =\dfrac{5}{8} \times \dfrac{2}{1}=\dfrac{5 \times 2}{8 \times 1}=\dfrac{10}{8}=\dfrac{5}{4}\) ;
e) \(4 \times \dfrac{3}{8} =\dfrac{4}{1} \times \dfrac{3}{8}=\dfrac{4 \times 3}{1 \times 8}=\dfrac{12}{8}=\dfrac{3}{2}\);
f) \( 3 :\dfrac{1}{2} =\dfrac{3}{1}:\dfrac{1}{2}=\dfrac{3}{1} \times \dfrac{2}{1}=\dfrac{6}{1}=6\) ;
g) \( \dfrac{1}{2}: 3 = \dfrac{1}{2}:\dfrac{3}{1}=\dfrac{1}{2} \times \dfrac{1}{3}=\dfrac{1}{6}\) .
