Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-7}\right) +\left(\frac{-2}{9}\right) -\left(\frac{-11}{-2}\right)\\= \frac{10}{7}- \frac{2}{9}-\frac{11}{2}\\=\frac{180}{126}-\frac{28}{126}-\frac{693}{126}\\=\frac{180-28-693}{126}\\=\frac{-541}{126}\)
2. \(+\left(\frac{6}{-7}\right) +\left(\frac{7}{10}\right) -\left(\frac{7}{-12}\right)\\= \frac{-6}{7}+ \frac{7}{10}+\frac{7}{12}\\=\frac{-360}{420}+\frac{294}{420}+\frac{245}{420}\\=\frac{-360+294+245}{420}\\=\frac{179}{420}\)
3. \(-\left(\frac{-9}{5}\right) +\left(\frac{-3}{8}\right) +\left(\frac{11}{-6}\right)\\= \frac{9}{5}- \frac{3}{8}-\frac{11}{6}\\=\frac{216}{120}-\frac{45}{120}-\frac{220}{120}\\=\frac{216-45-220}{120}\\=\frac{-49}{120}\)
4. \(+\left(\frac{8}{-7}\right) +\left(\frac{5}{9}\right) +\left(\frac{8}{-4}\right)\\= \frac{-8}{7}+ \frac{5}{9}-\frac{8}{4}\\=\frac{-8}{7}+\frac{5}{9}-\frac{2}{1}\\=\frac{-72}{63}+\frac{35}{63}-\frac{126}{63}\\=\frac{-72+35-126}{63}\\=\frac{-163}{63}\)
5. \(-\left(\frac{-2}{-3}\right) -\left(\frac{2}{2}\right) +\left(\frac{12}{-11}\right)\\= \frac{-2}{3}- \frac{2}{2}-\frac{12}{11}\\=\frac{-2}{3}-\frac{1}{1}-\frac{12}{11}\\=\frac{-22}{33}-\frac{33}{33}-\frac{36}{33}\\=\frac{-22-33-36}{33}\\=\frac{-91}{33}\)
6. \(-\left(\frac{-9}{2}\right) -\left(\frac{7}{-9}\right) -\left(\frac{11}{3}\right)\\= \frac{9}{2}+ \frac{7}{9}-\frac{11}{3}\\=\frac{81}{18}+\frac{14}{18}-\frac{66}{18}\\=\frac{81+14-66}{18}\\=\frac{29}{18}\)
7. \(+\left(\frac{7}{5}\right) -\left(\frac{-7}{8}\right) -\left(\frac{-6}{7}\right)\\= \frac{7}{5}+ \frac{7}{8}+\frac{6}{7}\\=\frac{392}{280}+\frac{245}{280}+\frac{240}{280}\\=\frac{392+245+240}{280}\\=\frac{877}{280}\)
8. \(+\left(\frac{-5}{3}\right) +\left(\frac{-6}{8}\right) +\left(\frac{12}{8}\right)\\= \frac{-5}{3}- \frac{6}{8}+\frac{12}{8}\\=\frac{-5}{3}-\frac{3}{4}+\frac{3}{2}\\=\frac{-20}{12}-\frac{9}{12}+\frac{18}{12}\\=\frac{-20-9+18}{12}\\=\frac{-11}{12}\)
9. \(-\left(\frac{-5}{-2}\right) -\left(\frac{-5}{2}\right) +\left(\frac{2}{6}\right)\\= \frac{-5}{2}+ \frac{5}{2}+\frac{2}{6}\\=\frac{-5}{2}+\frac{5}{2}+\frac{1}{3}\\=\frac{-15}{6}+\frac{15}{6}+\frac{2}{6}\\=\frac{-15+15+2}{6}\\=\frac{2}{6}\\=\frac{1}{3}\)
10. \(-\left(\frac{3}{-2}\right) +\left(\frac{-2}{2}\right) -\left(\frac{5}{-9}\right)\\= \frac{3}{2}- \frac{2}{2}+\frac{5}{9}\\=\frac{3}{2}-\frac{1}{1}+\frac{5}{9}\\=\frac{27}{18}-\frac{18}{18}+\frac{10}{18}\\=\frac{27-18+10}{18}\\=\frac{19}{18}\)
11. \(+\left(\frac{-7}{4}\right) -\left(\frac{-9}{4}\right) +\left(\frac{7}{-7}\right)\\= \frac{-7}{4}+ \frac{9}{4}-\frac{7}{7}\\=\frac{-7}{4}+\frac{9}{4}-\frac{1}{1}\\=\frac{-7+9-1}{4}\\=\frac{1}{4}\)
12. \(+\left(\frac{6}{-5}\right) +\left(\frac{-4}{-3}\right) +\left(\frac{-7}{12}\right)\\= \frac{-6}{5}+ \frac{4}{3}-\frac{7}{12}\\=\frac{-72}{60}+\frac{80}{60}-\frac{35}{60}\\=\frac{-72+80-35}{60}\\=\frac{-27}{60}\\=\frac{-9}{20}\)