\(\dfrac{5}{7}\cdot\dfrac{4}{15}+\dfrac{5}{7}\cdot\dfrac{11}{15}+\dfrac{2}{7}=\dfrac{5}{7}\cdot\left(\dfrac{4}{15}+\dfrac{11}{15}\right)+\dfrac{2}{7}\)
\(=\dfrac{5}{7}\cdot\dfrac{15}{15}+\dfrac{2}{7}=\dfrac{5}{7}\cdot1+\dfrac{2}{7}=\dfrac{5}{7}+\dfrac{2}{7}=\dfrac{7}{7}=1\)
\(\dfrac{5}{7}\cdot\dfrac{4}{15}+\dfrac{5}{7}\cdot\dfrac{11}{15}+\dfrac{2}{7}\)
\(=\dfrac{5}{7}\left(\dfrac{4}{15}+\dfrac{11}{15}\right)+\dfrac{2}{7}\)
\(=\dfrac{5}{7}.\dfrac{15}{15}+\dfrac{2}{7}\)
\(=\dfrac{5}{7}.1+\dfrac{2}{7}\)
\(=\dfrac{5}{7}+\dfrac{2}{7}\)
\(=\dfrac{7}{7}\)
\(=1\)
\(\dfrac{5}{7}\times\dfrac{4}{15}+\dfrac{5}{7}\times\dfrac{11}{15}+\dfrac{2}{7}\\ =\dfrac{5}{7}\times\left(\dfrac{4}{15}+\dfrac{11}{15}\right)+\dfrac{2}{7}\\ =\dfrac{5}{7}\times1+\dfrac{2}{7}\\ =\dfrac{5}{7}+\dfrac{2}{7}\\ =\dfrac{7}{7}\\ =1\)
