17:
a: \(\dfrac{2}{3}+\dfrac{1}{5}\cdot\dfrac{10}{7}=\dfrac{2}{3}+\dfrac{2}{7}=\dfrac{14}{21}+\dfrac{6}{21}=\dfrac{20}{21}\)
b: \(\dfrac{2}{7}+\dfrac{5}{7}\cdot\dfrac{14}{25}=\dfrac{2}{7}+\dfrac{2}{5}=\dfrac{10}{35}+\dfrac{14}{35}=\dfrac{24}{35}\)
c: \(\dfrac{7}{12}-\dfrac{27}{7}\cdot\dfrac{1}{18}\)
\(=\dfrac{7}{12}-\dfrac{3}{2\cdot7}=\dfrac{7}{12}-\dfrac{3}{14}\)
\(=\dfrac{49}{84}-\dfrac{18}{84}=\dfrac{31}{84}\)
d: \(\dfrac{3}{10}\cdot\dfrac{-5}{6}-\dfrac{1}{8}=\dfrac{-15}{60}-\dfrac{1}{8}\)
\(=-\dfrac{1}{4}-\dfrac{1}{8}=-\dfrac{3}{8}\)
e: \(\left(\dfrac{7}{6}-0,75\right):1\dfrac{1}{2}\)
\(=\left(\dfrac{14}{12}-\dfrac{9}{12}\right):\dfrac{3}{2}=\dfrac{5}{12}\cdot\dfrac{2}{3}=\dfrac{10}{36}=\dfrac{5}{18}\)
f: \(\dfrac{1}{2}-\dfrac{1}{3}:\dfrac{2}{3}+0,25\)
\(=\dfrac{1}{2}-\dfrac{1}{3}\cdot\dfrac{3}{2}+\dfrac{1}{4}\)
\(=\dfrac{1}{2}-\dfrac{1}{2}+\dfrac{1}{4}=\dfrac{1}{4}\)
18:
a: \(\dfrac{1}{7}\cdot\dfrac{1}{5}+\dfrac{1}{7}\cdot\dfrac{4}{5}=\dfrac{1}{7}\left(\dfrac{1}{5}+\dfrac{4}{5}\right)=\dfrac{1}{7}\cdot\dfrac{5}{5}=\dfrac{1}{7}\)
b: \(\dfrac{6}{7}+\dfrac{8}{7}\cdot\dfrac{2}{5}+\dfrac{8}{7}\cdot\dfrac{3}{5}\)
\(=\dfrac{6}{7}+\dfrac{8}{7}\left(\dfrac{2}{5}+\dfrac{3}{5}\right)\)
\(=\dfrac{6}{7}+\dfrac{8}{7}=\dfrac{14}{7}=2\)
c: \(\dfrac{4}{9}\cdot\dfrac{13}{3}-\dfrac{4}{9}\cdot\dfrac{40}{3}-\dfrac{4}{9}\)
\(=\dfrac{4}{9}\left(\dfrac{13}{3}-\dfrac{40}{3}-1\right)\)
\(=\dfrac{4}{9}\cdot\left(-\dfrac{27}{3}-1\right)=\dfrac{4}{9}\cdot\left(-10\right)=-\dfrac{40}{9}\)
d: \(\dfrac{4}{9}\cdot\dfrac{13}{17}+\dfrac{2}{17}\cdot\dfrac{4}{9}+\dfrac{2}{9}\cdot\dfrac{4}{17}\)
\(=\dfrac{4}{9}\left(\dfrac{13}{17}+\dfrac{2}{17}+\dfrac{2}{17}\right)\)
\(=\dfrac{4}{9}\cdot\dfrac{17}{17}=\dfrac{4}{9}\)
e: \(\dfrac{6}{7}\cdot\left(-\dfrac{1}{8}\right)+\dfrac{6}{7}\cdot\left(-\dfrac{3}{4}\right)\)
\(=\dfrac{6}{7}\left(-\dfrac{1}{8}-\dfrac{3}{4}\right)\)
\(=\dfrac{6}{7}\left(-\dfrac{1}{8}-\dfrac{6}{8}\right)=\dfrac{6}{7}\cdot\dfrac{-7}{8}=\dfrac{-6}{8}=-\dfrac{3}{4}\)
f: \(\dfrac{-7}{17}\cdot\dfrac{5}{12}+\dfrac{-7}{17}\cdot\dfrac{7}{12}+\dfrac{-10}{17}\)
\(=-\dfrac{7}{17}\left(\dfrac{5}{12}+\dfrac{7}{12}\right)+\dfrac{-10}{17}\)
\(=-\dfrac{7}{17}-\dfrac{10}{17}=-\dfrac{17}{17}\)
=-1
Bài 17:
\(a,\dfrac{2}{3}+\dfrac{1}{5}.\dfrac{10}{7}\)
\(=\dfrac{2}{3}+\dfrac{1.2}{7}\)
\(=\dfrac{2}{3}+\dfrac{2}{7}\)
\(=\dfrac{14}{21}+\dfrac{6}{21}\)
\(=\dfrac{20}{21}\)
\(b,\dfrac{2}{7}+\dfrac{5}{7}.\dfrac{14}{25}\)
\(=\dfrac{2}{7}+\dfrac{1.2}{5}\)
\(=\dfrac{2}{7}+\dfrac{2}{5}\)
\(=\dfrac{10}{35}+\dfrac{14}{35}\)
\(=\dfrac{24}{35}\)
\(c,\dfrac{7}{12}-\dfrac{27}{7}.\dfrac{1}{18}\)
\(=\dfrac{7}{12}-\dfrac{3.1}{7.2}\)
\(=\dfrac{7}{12}-\dfrac{3}{14}\)
\(=\dfrac{49}{84}-\dfrac{18}{84}\)
\(=\dfrac{31}{84}\)
\(d,\dfrac{3}{10}.\left(\dfrac{-5}{6}\right)-\dfrac{1}{8}\)
\(=\dfrac{1.\left(-1\right)}{2.2}-\dfrac{1}{8}\)
\(=\dfrac{-1}{4}-\dfrac{1}{8}\)
\(=\dfrac{-2}{8}-\dfrac{1}{8}\)
\(=\dfrac{-3}{8}\)
\(e,\left(\dfrac{7}{6}-0,75\right):2\dfrac{1}{2}\)
\(=\left(\dfrac{7}{6}-\dfrac{3}{4}\right):\dfrac{5}{2}\)
\(=\left(\dfrac{14}{12}-\dfrac{9}{12}\right).\dfrac{2}{5}\)
\(=\dfrac{5}{12}.\dfrac{2}{5}\)
\(=\dfrac{1}{6}\)
\(f,\dfrac{1}{2}-\dfrac{1}{3}:\dfrac{2}{3}+0,25\)
\(=\dfrac{1}{2}-\dfrac{1}{3}.\dfrac{3}{2}+\dfrac{1}{4}\)
\(=\dfrac{1}{2}-\dfrac{1}{2}+\dfrac{1}{4}\)
\(=0+\dfrac{1}{4}\)
\(=\dfrac{1}{4}\)
