Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{9}\right) -\left(\frac{3}{4}\right) +\left(\frac{-9}{-8}\right)\\= \frac{2}{9}- \frac{3}{4}+\frac{9}{8}\\=\frac{16}{72}-\frac{54}{72}+\frac{81}{72}\\=\frac{16-54+81}{72}\\=\frac{43}{72}\)
2. \(-\left(\frac{9}{2}\right) +\left(\frac{10}{5}\right) -\left(\frac{-8}{7}\right)\\= \frac{-9}{2}+ \frac{10}{5}+\frac{8}{7}\\=\frac{-9}{2}+\frac{2}{1}+\frac{8}{7}\\=\frac{-63}{14}+\frac{28}{14}+\frac{16}{14}\\=\frac{-63+28+16}{14}\\=\frac{-19}{14}\)
3. \(-\left(\frac{8}{9}\right) -\left(\frac{-2}{6}\right) +\left(\frac{6}{-7}\right)\\= \frac{-8}{9}+ \frac{2}{6}-\frac{6}{7}\\=\frac{-8}{9}+\frac{1}{3}-\frac{6}{7}\\=\frac{-56}{63}+\frac{21}{63}-\frac{54}{63}\\=\frac{-56+21-54}{63}\\=\frac{-89}{63}\)
4. \(-\left(\frac{-2}{3}\right) +\left(\frac{5}{-6}\right) +\left(\frac{-5}{-11}\right)\\= \frac{2}{3}- \frac{5}{6}+\frac{5}{11}\\=\frac{44}{66}-\frac{55}{66}+\frac{30}{66}\\=\frac{44-55+30}{66}\\=\frac{19}{66}\)
5. \(-\left(\frac{-9}{-4}\right) -\left(\frac{9}{8}\right) +\left(\frac{12}{5}\right)\\= \frac{-9}{4}- \frac{9}{8}+\frac{12}{5}\\=\frac{-90}{40}-\frac{45}{40}+\frac{96}{40}\\=\frac{-90-45+96}{40}\\=\frac{-39}{40}\)
6. \(+\left(\frac{7}{-6}\right) +\left(\frac{5}{-6}\right) +\left(\frac{-7}{12}\right)\\= \frac{-7}{6}- \frac{5}{6}-\frac{7}{12}\\=\frac{-14}{12}-\frac{10}{12}-\frac{7}{12}\\=\frac{-14-10-7}{12}\\=\frac{-31}{12}\)
7. \(+\left(\frac{-3}{-5}\right) -\left(\frac{3}{-8}\right) -\left(\frac{-10}{-10}\right)\\= \frac{3}{5}+ \frac{3}{8}-\frac{10}{10}\\=\frac{3}{5}+\frac{3}{8}-\frac{1}{1}\\=\frac{24}{40}+\frac{15}{40}-\frac{40}{40}\\=\frac{24+15-40}{40}\\=\frac{-1}{40}\)
8. \(-\left(\frac{5}{-9}\right) +\left(\frac{-9}{-8}\right) -\left(\frac{-8}{12}\right)\\= \frac{5}{9}+ \frac{9}{8}+\frac{8}{12}\\=\frac{5}{9}+\frac{9}{8}+\frac{2}{3}\\=\frac{40}{72}+\frac{81}{72}+\frac{48}{72}\\=\frac{40+81+48}{72}\\=\frac{169}{72}\)
9. \(-\left(\frac{4}{9}\right) +\left(\frac{-8}{8}\right) +\left(\frac{-2}{-4}\right)\\= \frac{-4}{9}- \frac{8}{8}+\frac{2}{4}\\=\frac{-4}{9}-\frac{1}{1}+\frac{1}{2}\\=\frac{-8}{18}-\frac{18}{18}+\frac{9}{18}\\=\frac{-8-18+9}{18}\\=\frac{-17}{18}\)
10. \(+\left(\frac{7}{8}\right) +\left(\frac{-10}{-8}\right) +\left(\frac{5}{-12}\right)\\= \frac{7}{8}+ \frac{10}{8}-\frac{5}{12}\\=\frac{7}{8}+\frac{5}{4}-\frac{5}{12}\\=\frac{21}{24}+\frac{30}{24}-\frac{10}{24}\\=\frac{21+30-10}{24}\\=\frac{41}{24}\)
11. \(+\left(\frac{-4}{-3}\right) -\left(\frac{-5}{-3}\right) -\left(\frac{-10}{-6}\right)\\= \frac{4}{3}- \frac{5}{3}-\frac{10}{6}\\=\frac{4}{3}-\frac{5}{3}-\frac{5}{3}\\=\frac{4-5-5}{3}\\=\frac{-6}{3}\\=\frac{-2}{1}\)
12. \(-\left(\frac{8}{3}\right) -\left(\frac{-2}{-2}\right) -\left(\frac{-7}{-3}\right)\\= \frac{-8}{3}- \frac{2}{2}-\frac{7}{3}\\=\frac{-8}{3}-\frac{1}{1}-\frac{7}{3}\\=\frac{-8-1-7}{3}\\=\frac{-16}{3}\)