a) \(\dfrac{-7}{5}\) . \(\dfrac{4}{23}\) + \(\dfrac{4}{23}\) . \(\dfrac{2}{5}\)
= \(\dfrac{4}{23}\) . ( \(\dfrac{-7}{5}\) + \(\dfrac{2}{5}\) )
= \(\dfrac{4}{23}\) . -1
= \(\dfrac{-4}{23}\)
b) \(\dfrac{-6}{7}\) . \(\dfrac{3}{5}\) +\(\dfrac{-6}{7}\) .\(\dfrac{2}{5}\) - \(1\dfrac{1}{3}\)
= \(\dfrac{-6}{7}\) . \(\dfrac{3}{5}\) +\(\dfrac{-6}{7}\) .\(\dfrac{2}{5}\) - \(\dfrac{4}{3}\)
= \(\dfrac{-6}{7}\) . (\(\dfrac{3}{5}\) + \(\dfrac{2}{5}\) ) - \(\dfrac{4}{3}\)
= \(\dfrac{-6}{7}\) . 1 - \(\dfrac{4}{3}\)
= \(\dfrac{-6}{7}\) - \(\dfrac{4}{3}\)
= \(\dfrac{-18}{21}\) - \(\dfrac{28}{21}\)
= \(\dfrac{-18}{21}\) + \(\dfrac{-28}{21}\)
= \(\dfrac{-46}{21}\)
c) \(\dfrac{4}{21}\) . \(\dfrac{-5}{7}\) + \(\dfrac{-5}{7}\) . \(\dfrac{15}{21}\) + \(\dfrac{-5}{7}\) . \(\dfrac{2}{21}\)
= \(\dfrac{-5}{7}\) . ( \(\dfrac{4}{21}\) + \(\dfrac{15}{21}\) + \(\dfrac{2}{21}\) )
= \(\dfrac{-5}{7}\) . 1
= \(\dfrac{-5}{7}\)
d) \(\dfrac{6}{11}\) . \(\dfrac{-4}{5}\) + \(\dfrac{4}{5}\) . \(\dfrac{-5}{11}\) + \(1\dfrac{1}{2}\)
= \(\dfrac{6}{11}\) . \(\dfrac{-4}{5}\) - \(\dfrac{-4}{5}\) . \(\dfrac{-5}{11}\) + \(\dfrac{3}{2}\)
= \(\dfrac{-4}{5}\) . ( \(\dfrac{6}{11}\) - \(\dfrac{-5}{11}\) ) + \(\dfrac{3}{2}\)
= \(\dfrac{-4}{5}\) . ( \(\dfrac{6}{11}\) + \(\dfrac{5}{11}\) ) + \(\dfrac{3}{2}\)
= \(\dfrac{-4}{5}\) . 1 + \(\dfrac{3}{2}\)
= \(\dfrac{-4}{5}\) + \(\dfrac{3}{2}\)
= \(\dfrac{-8}{10}\) + \(\dfrac{15}{10}\)
= \(\dfrac{7}{10}\)
e) \(\dfrac{-3}{7}\) . \(\dfrac{8}{19}\) + \(\dfrac{3}{7}\) . \(\dfrac{-11}{19}\) - \(3\dfrac{1}{3}\)
= \(\dfrac{-3}{7}\) . \(\dfrac{8}{19}\) - \(\dfrac{-3}{7}\) . \(\dfrac{-11}{19}\) - \(\dfrac{10}{3}\)
= \(\dfrac{-3}{7}\) . ( \(\dfrac{8}{19}\) - \(\dfrac{-11}{19}\) ) - \(\dfrac{10}{3}\)
= \(\dfrac{-3}{7}\) . ( \(\dfrac{8}{19}\) + \(\dfrac{11}{19}\) ) - \(\dfrac{10}{3}\)
= \(\dfrac{-3}{7}\) . 1 - \(\dfrac{10}{3}\)
= \(\dfrac{-3}{7}\) - \(\dfrac{10}{3}\)
= \(\dfrac{-9}{21}\) - \(\dfrac{70}{21}\)
= \(\dfrac{-9}{21}\) + \(\dfrac{-70}{21}\)
= \(\dfrac{-79}{21}\)
f) \(\dfrac{-6}{17}\) . \(\dfrac{3}{5}\) + \(\dfrac{-3}{5}\) . \(\dfrac{10}{17}\) + \(\dfrac{3}{5}\) . \(\dfrac{-1}{17}\)
= \(\dfrac{-6}{17}\) . \(\dfrac{3}{5}\) - \(\dfrac{3}{5}\) . \(\dfrac{10}{17}\) + \(\dfrac{3}{5}\) . \(\dfrac{-1}{17}\)
= \(\dfrac{3}{5}\) . ( \(\dfrac{-6}{17}\) - \(\dfrac{10}{17}\) + \(\dfrac{-1}{17}\) )
= \(\dfrac{3}{5}\) . ( \(\dfrac{-6}{17}\) + \(\dfrac{-10}{17}\) + \(\dfrac{-1}{17}\) )
= \(\dfrac{3}{5}\) . -1
= \(\dfrac{-3}{5}\)
g) \(\dfrac{-3}{20}\) . \(\dfrac{2}{5}\) + \(\dfrac{3}{20}\) . \(\dfrac{-1}{5}\) + \(\dfrac{3}{5}\) . \(\dfrac{-17}{20}\)
= \(\dfrac{-3}{20}\) . \(\dfrac{2}{5}\) - \(\dfrac{-3}{20}\) . \(\dfrac{-1}{5}\) - \(\dfrac{-3}{20}\) . \(\dfrac{-17}{5}\)
= \(\dfrac{-3}{20}\) . ( \(\dfrac{2}{5}\) - \(\dfrac{-1}{5}\) - \(\dfrac{-17}{5}\) )
= \(\dfrac{-3}{20}\) . ( \(\dfrac{2}{5}\) + \(\dfrac{1}{5}\) + \(\dfrac{17}{5}\) )
= \(\dfrac{-3}{20}\) . 4
= \(\dfrac{-3.4}{20}\)
= \(\dfrac{-3.1}{5}\)
= \(\dfrac{-3}{5}\)
h) \(\dfrac{-8}{15}\) . \(\dfrac{4}{9}\) + \(\dfrac{-4}{9}\) . \(\dfrac{4}{15}\) + \(\dfrac{12}{15}\) . \(\dfrac{-5}{9}\)
= \(\dfrac{-8}{15}\) . \(\dfrac{4}{9}\) - \(\dfrac{4}{9}\) . \(\dfrac{4}{15}\) + \(\dfrac{4}{5}\) . \(\dfrac{-5}{9}\)
= \(\dfrac{-8}{15}\) . \(\dfrac{4}{9}\) - \(\dfrac{4}{9}\) . \(\dfrac{4}{15}\) + \(\dfrac{4}{9}\) . -1
= \(\dfrac{4}{9}\) . [\(\dfrac{-8}{15}\) - \(\dfrac{4}{15}\) + (-1) ]
= \(\dfrac{4}{9}\) . [\(\dfrac{-8}{15}\) + \(\dfrac{-4}{15}\) + (-1) ]
= \(\dfrac{4}{9}\) . \(\dfrac{-9}{5}\)
= \(\dfrac{4.\left(-9\right)}{9.5}\)
= \(\dfrac{4.\left(-1\right)}{1.5}\)
= \(\dfrac{-4}{5}\)
