\(\dfrac{1}{7}.\dfrac{1}{5}+\dfrac{1}{7}.\dfrac{2}{5}+\dfrac{1}{7}.\dfrac{4}{5}\\ =\dfrac{1}{7}.\left(\dfrac{1}{5}+\dfrac{2}{5}+\dfrac{4}{5}\right)\\ =\dfrac{1}{7}.\dfrac{7}{5}\\ =\dfrac{1}{5}\)
b) \(\dfrac{4}{9}.-\dfrac{1}{19}+\dfrac{5}{9}.-\dfrac{1}{19}\)
= \(-\dfrac{1}{19}.\left(\dfrac{4}{9}+\dfrac{5}{9}\right)\)
= \(\dfrac{-1}{19}\) .\(1\)
= \(-\dfrac{1}{19}\)
c) \(\dfrac{8}{19}.\dfrac{5}{11}+\dfrac{7}{11}.\dfrac{8}{19}-\dfrac{1}{11}.\dfrac{8}{19}\)
= \(\dfrac{8}{19}.\left(\dfrac{5}{11}+\dfrac{7}{11}-\dfrac{1}{11}\right)\)
= \(\dfrac{8}{19}.1\)
= \(\dfrac{8}{19}\)
d) \(\left(\dfrac{17}{28}+\dfrac{18}{29}-\dfrac{19}{30}-\dfrac{20}{31}\right).\left(-\dfrac{5}{12}+\dfrac{1}{4}+\dfrac{1}{6}\right)\)
= x . 0
= 0
e) \(\dfrac{5.18-10.27+15.36}{10.36-20.54+30.72}\)
= \(\dfrac{5.18-10.27+15.36}{5.18-10.27+15.36}.\dfrac{1}{2}\)
= 1 . \(\dfrac{1}{2}\)
= \(\dfrac{1}{2}\)
