Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{8}\right) +\left(\frac{-10}{4}\right) +\left(\frac{8}{-4}\right)\\= \frac{9}{8}- \frac{10}{4}-\frac{8}{4}\\=\frac{9}{8}-\frac{5}{2}-\frac{2}{1}\\=\frac{9-5-2}{8}\\=\frac{2}{8}\\=\frac{1}{4}\)
2. \(-\left(\frac{-10}{7}\right) +\left(\frac{-4}{-6}\right) -\left(\frac{-2}{2}\right)\\= \frac{10}{7}+ \frac{4}{6}+\frac{2}{2}\\=\frac{10}{7}+\frac{2}{3}+\frac{1}{1}\\=\frac{30}{21}+\frac{14}{21}+\frac{21}{21}\\=\frac{30+14+21}{21}\\=\frac{65}{21}\)
3. \(-\left(\frac{2}{7}\right) -\left(\frac{-10}{2}\right) +\left(\frac{10}{-9}\right)\\= \frac{-2}{7}+ \frac{10}{2}-\frac{10}{9}\\=\frac{-2}{7}+\frac{5}{1}-\frac{10}{9}\\=\frac{-18}{63}+\frac{315}{63}-\frac{70}{63}\\=\frac{-18+315-70}{63}\\=\frac{227}{63}\)
4. \(+\left(\frac{6}{-5}\right) -\left(\frac{7}{3}\right) -\left(\frac{2}{6}\right)\\= \frac{-6}{5}- \frac{7}{3}-\frac{2}{6}\\=\frac{-6}{5}-\frac{7}{3}-\frac{1}{3}\\=\frac{-18}{15}-\frac{35}{15}-\frac{5}{15}\\=\frac{-18-35-5}{15}\\=\frac{-58}{15}\)
5. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-8}{-5}\right) -\left(\frac{-9}{-6}\right)\\= \frac{-6}{5}- \frac{8}{5}-\frac{9}{6}\\=\frac{-6}{5}-\frac{8}{5}-\frac{3}{2}\\=\frac{-12}{10}-\frac{16}{10}-\frac{15}{10}\\=\frac{-12-16-15}{10}\\=\frac{-43}{10}\)
6. \(+\left(\frac{9}{2}\right) -\left(\frac{3}{9}\right) -\left(\frac{-5}{6}\right)\\= \frac{9}{2}- \frac{3}{9}+\frac{5}{6}\\=\frac{9}{2}-\frac{1}{3}+\frac{5}{6}\\=\frac{27}{6}-\frac{2}{6}+\frac{5}{6}\\=\frac{27-2+5}{6}\\=\frac{30}{6}\\=\frac{5}{1}\)
7. \(-\left(\frac{-4}{-3}\right) -\left(\frac{-2}{2}\right) +\left(\frac{-6}{8}\right)\\= \frac{-4}{3}+ \frac{2}{2}-\frac{6}{8}\\=\frac{-4}{3}+\frac{1}{1}-\frac{3}{4}\\=\frac{-16}{12}+\frac{12}{12}-\frac{9}{12}\\=\frac{-16+12-9}{12}\\=\frac{-13}{12}\)
8. \(-\left(\frac{-10}{3}\right) +\left(\frac{2}{5}\right) +\left(\frac{4}{6}\right)\\= \frac{10}{3}+ \frac{2}{5}+\frac{4}{6}\\=\frac{10}{3}+\frac{2}{5}+\frac{2}{3}\\=\frac{50}{15}+\frac{6}{15}+\frac{10}{15}\\=\frac{50+6+10}{15}\\=\frac{66}{15}\\=\frac{22}{5}\)
9. \(-\left(\frac{-7}{8}\right) +\left(\frac{-8}{-9}\right) -\left(\frac{-3}{3}\right)\\= \frac{7}{8}+ \frac{8}{9}+\frac{3}{3}\\=\frac{7}{8}+\frac{8}{9}+\frac{1}{1}\\=\frac{63}{72}+\frac{64}{72}+\frac{72}{72}\\=\frac{63+64+72}{72}\\=\frac{199}{72}\)
10. \(-\left(\frac{4}{3}\right) -\left(\frac{5}{-6}\right) +\left(\frac{-7}{6}\right)\\= \frac{-4}{3}+ \frac{5}{6}-\frac{7}{6}\\=\frac{-8}{6}+\frac{5}{6}-\frac{7}{6}\\=\frac{-8+5-7}{6}\\=\frac{-10}{6}\\=\frac{-5}{3}\)
11. \(-\left(\frac{-7}{6}\right) -\left(\frac{10}{9}\right) +\left(\frac{-9}{7}\right)\\= \frac{7}{6}- \frac{10}{9}-\frac{9}{7}\\=\frac{147}{126}-\frac{140}{126}-\frac{162}{126}\\=\frac{147-140-162}{126}\\=\frac{-155}{126}\)
12. \(-\left(\frac{-2}{9}\right) +\left(\frac{-2}{-4}\right) +\left(\frac{8}{-7}\right)\\= \frac{2}{9}+ \frac{2}{4}-\frac{8}{7}\\=\frac{2}{9}+\frac{1}{2}-\frac{8}{7}\\=\frac{28}{126}+\frac{63}{126}-\frac{144}{126}\\=\frac{28+63-144}{126}\\=\frac{-53}{126}\)