Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{7}\right) -\left(\frac{9}{5}\right) -\left(\frac{-11}{12}\right)\\= \frac{-6}{7}- \frac{9}{5}+\frac{11}{12}\\=\frac{-360}{420}-\frac{756}{420}+\frac{385}{420}\\=\frac{-360-756+385}{420}\\=\frac{-731}{420}\)
2. \(-\left(\frac{5}{-8}\right) +\left(\frac{2}{6}\right) +\left(\frac{11}{-4}\right)\\= \frac{5}{8}+ \frac{2}{6}-\frac{11}{4}\\=\frac{5}{8}+\frac{1}{3}-\frac{11}{4}\\=\frac{15}{24}+\frac{8}{24}-\frac{66}{24}\\=\frac{15+8-66}{24}\\=\frac{-43}{24}\)
3. \(+\left(\frac{9}{-2}\right) -\left(\frac{4}{8}\right) -\left(\frac{4}{-5}\right)\\= \frac{-9}{2}- \frac{4}{8}+\frac{4}{5}\\=\frac{-9}{2}-\frac{1}{2}+\frac{4}{5}\\=\frac{-45}{10}-\frac{5}{10}+\frac{8}{10}\\=\frac{-45-5+8}{10}\\=\frac{-42}{10}\\=\frac{-21}{5}\)
4. \(-\left(\frac{9}{4}\right) +\left(\frac{-10}{6}\right) -\left(\frac{-4}{-8}\right)\\= \frac{-9}{4}- \frac{10}{6}-\frac{4}{8}\\=\frac{-9}{4}-\frac{5}{3}-\frac{1}{2}\\=\frac{-27}{12}-\frac{20}{12}-\frac{6}{12}\\=\frac{-27-20-6}{12}\\=\frac{-53}{12}\)
5. \(-\left(\frac{8}{-3}\right) -\left(\frac{8}{-4}\right) -\left(\frac{7}{-4}\right)\\= \frac{8}{3}+ \frac{8}{4}+\frac{7}{4}\\=\frac{8}{3}+\frac{2}{1}+\frac{7}{4}\\=\frac{32}{12}+\frac{24}{12}+\frac{21}{12}\\=\frac{32+24+21}{12}\\=\frac{77}{12}\)
6. \(-\left(\frac{-8}{3}\right) -\left(\frac{10}{-2}\right) +\left(\frac{2}{5}\right)\\= \frac{8}{3}+ \frac{10}{2}+\frac{2}{5}\\=\frac{8}{3}+\frac{5}{1}+\frac{2}{5}\\=\frac{40}{15}+\frac{75}{15}+\frac{6}{15}\\=\frac{40+75+6}{15}\\=\frac{121}{15}\)
7. \(+\left(\frac{8}{-5}\right) +\left(\frac{-5}{-8}\right) -\left(\frac{-12}{-5}\right)\\= \frac{-8}{5}+ \frac{5}{8}-\frac{12}{5}\\=\frac{-64}{40}+\frac{25}{40}-\frac{96}{40}\\=\frac{-64+25-96}{40}\\=\frac{-135}{40}\\=\frac{-27}{8}\)
8. \(+\left(\frac{8}{-9}\right) -\left(\frac{-10}{7}\right) +\left(\frac{-11}{2}\right)\\= \frac{-8}{9}+ \frac{10}{7}-\frac{11}{2}\\=\frac{-112}{126}+\frac{180}{126}-\frac{693}{126}\\=\frac{-112+180-693}{126}\\=\frac{-625}{126}\)
9. \(+\left(\frac{4}{-9}\right) -\left(\frac{-7}{6}\right) -\left(\frac{4}{7}\right)\\= \frac{-4}{9}+ \frac{7}{6}-\frac{4}{7}\\=\frac{-56}{126}+\frac{147}{126}-\frac{72}{126}\\=\frac{-56+147-72}{126}\\=\frac{19}{126}\)
10. \(+\left(\frac{7}{3}\right) -\left(\frac{-10}{-9}\right) -\left(\frac{-11}{-3}\right)\\= \frac{7}{3}- \frac{10}{9}-\frac{11}{3}\\=\frac{21}{9}-\frac{10}{9}-\frac{33}{9}\\=\frac{21-10-33}{9}\\=\frac{-22}{9}\)
11. \(+\left(\frac{10}{3}\right) -\left(\frac{6}{-7}\right) -\left(\frac{8}{6}\right)\\= \frac{10}{3}+ \frac{6}{7}-\frac{8}{6}\\=\frac{10}{3}+\frac{6}{7}-\frac{4}{3}\\=\frac{70}{21}+\frac{18}{21}-\frac{28}{21}\\=\frac{70+18-28}{21}\\=\frac{60}{21}\\=\frac{20}{7}\)
12. \(-\left(\frac{10}{-9}\right) -\left(\frac{8}{3}\right) +\left(\frac{8}{9}\right)\\= \frac{10}{9}- \frac{8}{3}+\frac{8}{9}\\=\frac{10-8+8}{9}\\=\frac{10}{9}\)