\(a.\dfrac{3}{4}+\left(\dfrac{-5}{4}\right)\cdot\left(\dfrac{-1}{5}\right)\\ =\dfrac{3}{4}+\dfrac{1}{4}\\ =\dfrac{4}{4}=1\\ b.\dfrac{7}{4}:\left(-\dfrac{7}{6}\right)\cdot\dfrac{2}{3}\\ =\dfrac{7}{4}\cdot\left(\dfrac{6}{-7}\right)\cdot\dfrac{2}{3}\\ =-\dfrac{6}{4}\cdot\dfrac{2}{3}\\ =-\dfrac{3}{2}\cdot\dfrac{2}{3}\\ =-1\\ c.\dfrac{47}{15}:\left(-4,7\right)\cdot\left(-\dfrac{3}{2}\right)\\ =\dfrac{47}{15}:\dfrac{-47}{10}\cdot\left(-\dfrac{3}{2}\right)\\ =\dfrac{47}{15}\cdot\dfrac{-10}{47}\cdot\left(-\dfrac{3}{2}\right)\\ =\dfrac{-2}{3}\cdot\left(-\dfrac{3}{2}\right)\\ =1\\ d.\dfrac{4}{9}\cdot\left(-7,5:\dfrac{25}{8}\right)\\ =\dfrac{4}{9}\cdot\left(-\dfrac{15}{2}\cdot\dfrac{8}{25}\right)\\ =\dfrac{4}{9}\cdot\dfrac{-3\cdot4}{5}\\ =\dfrac{4}{9}\cdot\dfrac{-12}{5}\\ =\dfrac{-16}{15}\)
a) \(\dfrac{3}{4}+\left(\dfrac{-5}{4}\right)\times\left(\dfrac{-1}{5}\right)\)= \(\dfrac{3}{4}+\dfrac{1}{4}\) = \(\dfrac{4}{4}=1\)
b) \(\dfrac{7}{4}:\left(\dfrac{-7}{6}\right)\times\dfrac{2}{3}=\dfrac{7}{4}\times\dfrac{-6}{7}\times\dfrac{2}{3}=\dfrac{1\times\left(-1\right)\times1}{1\times1\times1}=-1\)
c) \(\dfrac{47}{15}:\left(-4,7\right)\times\left(\dfrac{-3}{2}\right)\)
= \(\dfrac{47}{15}:\dfrac{-47}{10}\times\dfrac{-3}{2}\)
= \(\dfrac{47}{15}\times\dfrac{-10}{47}\times\dfrac{-3}{2}\)
= \(\dfrac{1\times\left(-1\right)\times\left(-1\right)}{1\times1\times1}=1\)
d) \(\dfrac{4}{9}\times\left(-7,5:\dfrac{25}{8}\right)\)
= \(\dfrac{4}{9}\times\left(\dfrac{-15}{2}.\dfrac{8}{25}\right)\)
= \(\dfrac{4}{9}\times\dfrac{-3\times4}{1\times5}\)
= \(\dfrac{4}{9}\times\dfrac{-12}{5}\)
= \(\dfrac{4\times\left(-4\right)}{3\times5}\)
= \(\dfrac{-16}{15}\)
