\(\dfrac{4}{7}\times\dfrac{21}{16}:\dfrac{5}{8}=\dfrac{4}{7}\times\dfrac{21}{16}\times\dfrac{8}{5}=\dfrac{6}{5}\)
\(\dfrac{15}{8}-\dfrac{4}{9}\times\dfrac{6}{8}+\dfrac{1}{6}=\dfrac{15}{8}-\dfrac{1}{3}+\dfrac{1}{6}=\dfrac{60}{24}-\dfrac{8}{24}+\dfrac{4}{24}=\dfrac{56}{24}=\dfrac{7}{3}\)
\(\dfrac{7}{15}+\left(\dfrac{5}{6}-\dfrac{1}{3}\right)=\dfrac{7}{15}+\dfrac{3}{6}=\dfrac{7}{15}+\dfrac{1}{2}=\dfrac{14}{30}+\dfrac{15}{30}=\dfrac{29}{30}\)
= 3/4 : 5/8 = 6/5
= 15/8 - 1/3 + 1/6 = 37/24 + 1/6 = 41/23
= 7/15 + 1/2 = 29/30
\(\dfrac{4}{7}\times\dfrac{21}{16}:\dfrac{5}{8}\)
\(=\dfrac{4}{7}\times\left(\dfrac{21}{16}:\dfrac{5}{8}\right)\)
\(=\dfrac{4}{7}\times\left(\dfrac{21}{16}\times\dfrac{8}{5}\right)\)
\(=\dfrac{4}{7}\times\dfrac{21}{10}=\dfrac{4\times21}{7\times10}=\dfrac{84}{70}=\dfrac{6}{5}\)
\(\dfrac{15}{8}-\dfrac{4}{9}\times\dfrac{6}{8}+\dfrac{1}{6}\)
\(=\dfrac{15}{8}-\dfrac{4}{9}\times\dfrac{3}{4}+\dfrac{1}{6}\)
\(=\dfrac{15}{8}-\dfrac{1}{3}+\dfrac{1}{6}\)
\(=\dfrac{15}{8}-\left(\dfrac{1}{3}-\dfrac{1}{6}\right)\)
\(=\dfrac{15}{8}-\left(\dfrac{2}{6}-\dfrac{1}{6}\right)\)
\(=\dfrac{15}{8}-\dfrac{1}{6}=\dfrac{45}{24}-\dfrac{4}{24}=\dfrac{41}{24}\)
\(\dfrac{7}{15}+\left(\dfrac{5}{6}-\dfrac{1}{3}\right)\)
\(=\dfrac{7}{15}+\dfrac{1}{2}=\dfrac{14}{30}+\dfrac{15}{30}=\dfrac{14+15}{30}=\dfrac{29}{30}\)