Question

Answer 1

19: \(15\dfrac{1}{4}:\dfrac{2}{5}-15\dfrac{1}{4}:\dfrac{2}{13}\)

\(=15\dfrac{1}{4}\cdot\dfrac{5}{2}-15\dfrac{1}{4}\cdot\dfrac{13}{2}\)

\(=\dfrac{61}{4}\left(\dfrac{5}{2}-\dfrac{13}{2}\right)=\dfrac{61}{4}\cdot\left(-\dfrac{8}{2}\right)=\dfrac{61}{4}\cdot\left(-4\right)=-61\)

20: \(\dfrac{5}{2}:\left(-\dfrac{5}{3}\right)-7\dfrac{1}{2}\cdot\dfrac{3}{5}\)

\(=\dfrac{5}{2}\cdot\dfrac{-3}{5}-\dfrac{15}{2}\cdot\dfrac{3}{5}\)

\(=\dfrac{-3}{2}-\dfrac{25}{2}=-\dfrac{28}{2}=-14\)

21: \(\dfrac{2}{3}:\dfrac{9}{17}-\dfrac{2}{3}:\dfrac{20}{17}\)

\(=\dfrac{2}{3}\cdot\dfrac{17}{9}-\dfrac{2}{3}\cdot\dfrac{17}{20}\)

\(=\dfrac{2}{3}\left(\dfrac{17}{9}-\dfrac{17}{20}\right)\)

\(=\dfrac{2}{3}\cdot\dfrac{187}{180}=\dfrac{187}{3\cdot90}=\dfrac{187}{270}\)

22: \(3,7+1,3\cdot\dfrac{10}{39}-\left(\dfrac{1}{3}-6,3\right)\)

\(=3,7+\dfrac{13}{39}-\dfrac{1}{3}+6,3\)

=3,7+6,3=10

Answer 2

\(19,15\dfrac{1}{4}:\left(\dfrac{2}{5}\right)-15\dfrac{1}{4}:\left(\dfrac{2}{13}\right)\)
\(=\dfrac{61}{4}.\dfrac{5}{2}-\dfrac{61}{4}.\dfrac{13}{2}\)
\(=\dfrac{61}{4}.\left(\dfrac{5}{2}-\dfrac{13}{2}\right)\)
\(=\dfrac{61}{4}.\dfrac{-8}{2}\)
\(=\dfrac{61}{4}.\left(-4\right)\)
\(=-61\)
\(20,\dfrac{5}{2}:\left(-\dfrac{5}{3}\right)-7\dfrac{1}{2}.\dfrac{3}{5}\)
\(=\dfrac{5}{2}.\dfrac{-3}{5}-\dfrac{15}{2}.\dfrac{3}{5}\)
\(=\dfrac{-5}{2}.\dfrac{3}{5}-\dfrac{15}{2}.\dfrac{3}{5}\)
\(=\dfrac{3}{5}.\left(\dfrac{-5}{2}-\dfrac{15}{2}\right)\)
\(=\dfrac{3}{5}.\dfrac{-20}{2}\)
\(=\dfrac{3}{5}.\left(-10\right)\)
\(=-6\)
\(21,\dfrac{2}{3}:\dfrac{9}{17}-\dfrac{2}{3}:\dfrac{20}{17}\)
\(=\dfrac{2}{3}.\dfrac{17}{9}-\dfrac{2}{3}.\dfrac{17}{20}\)
\(=\dfrac{2}{3}.\left(\dfrac{17}{9}-\dfrac{17}{20}\right)\)
\(=\dfrac{2}{3}.\left(\dfrac{340}{180}-\dfrac{153}{180}\right)\)
\(=\dfrac{2}{3}.\dfrac{187}{180}\)
\(=\dfrac{187}{270}\)
\(22,3,7+1,3.\dfrac{10}{39}-\left(\dfrac{1}{3}-6,3\right)\)
\(=\dfrac{37}{10}+\dfrac{13}{10}.\dfrac{10}{39}-\left(\dfrac{1}{3}-\dfrac{63}{10}\right)\)
\(=\dfrac{37}{10}+\dfrac{1}{3}+\left(\dfrac{10}{30}-\dfrac{189}{30}\right)\)
\(=\dfrac{37}{10}+\dfrac{1}{3}+\dfrac{179}{30}\)
\(=\dfrac{111}{30}+\dfrac{10}{30}+\dfrac{179}{30}\)
\(=\dfrac{300}{30}=10\)