Breuken haakjesregel (reeks 2)

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Bereken

1. \(+\left(\frac{-8}{-3}\right) -\left(\frac{9}{-6}\right) +\left(\frac{10}{-11}\right)\)
2. \(+\left(\frac{-8}{-9}\right) -\left(\frac{-9}{6}\right) +\left(\frac{11}{-5}\right)\)
3. \(-\left(\frac{5}{7}\right) -\left(\frac{7}{-2}\right) -\left(\frac{-7}{-11}\right)\)
4. \(-\left(\frac{-5}{-6}\right) -\left(\frac{7}{-4}\right) -\left(\frac{-10}{4}\right)\)
5. \(-\left(\frac{2}{-5}\right) -\left(\frac{-2}{6}\right) -\left(\frac{-3}{-8}\right)\)
6. \(+\left(\frac{9}{7}\right) -\left(\frac{-5}{-3}\right) -\left(\frac{9}{-12}\right)\)
7. \(-\left(\frac{-9}{2}\right) +\left(\frac{10}{7}\right) -\left(\frac{-6}{-8}\right)\)
8. \(+\left(\frac{6}{5}\right) -\left(\frac{6}{-2}\right) -\left(\frac{4}{-6}\right)\)
9. \(+\left(\frac{10}{-7}\right) +\left(\frac{-10}{6}\right) -\left(\frac{-11}{7}\right)\)
10. \(+\left(\frac{9}{7}\right) +\left(\frac{-9}{10}\right) -\left(\frac{-7}{-7}\right)\)
11. \(+\left(\frac{-7}{-3}\right) +\left(\frac{-2}{-6}\right) +\left(\frac{3}{5}\right)\)
12. \(+\left(\frac{10}{-9}\right) +\left(\frac{9}{-10}\right) +\left(\frac{4}{-10}\right)\)

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{-3}\right) -\left(\frac{9}{-6}\right) +\left(\frac{10}{-11}\right)\\= \frac{8}{3}+ \frac{9}{6}-\frac{10}{11}\\=\frac{8}{3}+\frac{3}{2}-\frac{10}{11}\\=\frac{176}{66}+\frac{99}{66}-\frac{60}{66}\\=\frac{176+99-60}{66}\\=\frac{215}{66}\)
2. \(+\left(\frac{-8}{-9}\right) -\left(\frac{-9}{6}\right) +\left(\frac{11}{-5}\right)\\= \frac{8}{9}+ \frac{9}{6}-\frac{11}{5}\\=\frac{8}{9}+\frac{3}{2}-\frac{11}{5}\\=\frac{80}{90}+\frac{135}{90}-\frac{198}{90}\\=\frac{80+135-198}{90}\\=\frac{17}{90}\)
3. \(-\left(\frac{5}{7}\right) -\left(\frac{7}{-2}\right) -\left(\frac{-7}{-11}\right)\\= \frac{-5}{7}+ \frac{7}{2}-\frac{7}{11}\\=\frac{-110}{154}+\frac{539}{154}-\frac{98}{154}\\=\frac{-110+539-98}{154}\\=\frac{331}{154}\)
4. \(-\left(\frac{-5}{-6}\right) -\left(\frac{7}{-4}\right) -\left(\frac{-10}{4}\right)\\= \frac{-5}{6}+ \frac{7}{4}+\frac{10}{4}\\=\frac{-5}{6}+\frac{7}{4}+\frac{5}{2}\\=\frac{-10}{12}+\frac{21}{12}+\frac{30}{12}\\=\frac{-10+21+30}{12}\\=\frac{41}{12}\)
5. \(-\left(\frac{2}{-5}\right) -\left(\frac{-2}{6}\right) -\left(\frac{-3}{-8}\right)\\= \frac{2}{5}+ \frac{2}{6}-\frac{3}{8}\\=\frac{2}{5}+\frac{1}{3}-\frac{3}{8}\\=\frac{48}{120}+\frac{40}{120}-\frac{45}{120}\\=\frac{48+40-45}{120}\\=\frac{43}{120}\)
6. \(+\left(\frac{9}{7}\right) -\left(\frac{-5}{-3}\right) -\left(\frac{9}{-12}\right)\\= \frac{9}{7}- \frac{5}{3}+\frac{9}{12}\\=\frac{9}{7}-\frac{5}{3}+\frac{3}{4}\\=\frac{108}{84}-\frac{140}{84}+\frac{63}{84}\\=\frac{108-140+63}{84}\\=\frac{31}{84}\)
7. \(-\left(\frac{-9}{2}\right) +\left(\frac{10}{7}\right) -\left(\frac{-6}{-8}\right)\\= \frac{9}{2}+ \frac{10}{7}-\frac{6}{8}\\=\frac{9}{2}+\frac{10}{7}-\frac{3}{4}\\=\frac{126}{28}+\frac{40}{28}-\frac{21}{28}\\=\frac{126+40-21}{28}\\=\frac{145}{28}\)
8. \(+\left(\frac{6}{5}\right) -\left(\frac{6}{-2}\right) -\left(\frac{4}{-6}\right)\\= \frac{6}{5}+ \frac{6}{2}+\frac{4}{6}\\=\frac{6}{5}+\frac{3}{1}+\frac{2}{3}\\=\frac{18}{15}+\frac{45}{15}+\frac{10}{15}\\=\frac{18+45+10}{15}\\=\frac{73}{15}\)
9. \(+\left(\frac{10}{-7}\right) +\left(\frac{-10}{6}\right) -\left(\frac{-11}{7}\right)\\= \frac{-10}{7}- \frac{10}{6}+\frac{11}{7}\\=\frac{-10}{7}-\frac{5}{3}+\frac{11}{7}\\=\frac{-30}{21}-\frac{35}{21}+\frac{33}{21}\\=\frac{-30-35+33}{21}\\=\frac{-32}{21}\)
10. \(+\left(\frac{9}{7}\right) +\left(\frac{-9}{10}\right) -\left(\frac{-7}{-7}\right)\\= \frac{9}{7}- \frac{9}{10}-\frac{7}{7}\\=\frac{9}{7}-\frac{9}{10}-\frac{1}{1}\\=\frac{90}{70}-\frac{63}{70}-\frac{70}{70}\\=\frac{90-63-70}{70}\\=\frac{-43}{70}\)
11. \(+\left(\frac{-7}{-3}\right) +\left(\frac{-2}{-6}\right) +\left(\frac{3}{5}\right)\\= \frac{7}{3}+ \frac{2}{6}+\frac{3}{5}\\=\frac{7}{3}+\frac{1}{3}+\frac{3}{5}\\=\frac{35}{15}+\frac{5}{15}+\frac{9}{15}\\=\frac{35+5+9}{15}\\=\frac{49}{15}\)
12. \(+\left(\frac{10}{-9}\right) +\left(\frac{9}{-10}\right) +\left(\frac{4}{-10}\right)\\= \frac{-10}{9}- \frac{9}{10}-\frac{4}{10}\\=\frac{-10}{9}-\frac{9}{10}-\frac{2}{5}\\=\frac{-100}{90}-\frac{81}{90}-\frac{36}{90}\\=\frac{-100-81-36}{90}\\=\frac{-217}{90}\)