Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{2}\right) -\left(\frac{8}{-6}\right) +\left(\frac{4}{7}\right)\\= \frac{-9}{2}+ \frac{8}{6}+\frac{4}{7}\\=\frac{-9}{2}+\frac{4}{3}+\frac{4}{7}\\=\frac{-189}{42}+\frac{56}{42}+\frac{24}{42}\\=\frac{-189+56+24}{42}\\=\frac{-109}{42}\)
2. \(-\left(\frac{-9}{-2}\right) -\left(\frac{-5}{-7}\right) -\left(\frac{11}{6}\right)\\= \frac{-9}{2}- \frac{5}{7}-\frac{11}{6}\\=\frac{-189}{42}-\frac{30}{42}-\frac{77}{42}\\=\frac{-189-30-77}{42}\\=\frac{-296}{42}\\=\frac{-148}{21}\)
3. \(+\left(\frac{-7}{8}\right) -\left(\frac{8}{6}\right) +\left(\frac{7}{-7}\right)\\= \frac{-7}{8}- \frac{8}{6}-\frac{7}{7}\\=\frac{-7}{8}-\frac{4}{3}-\frac{1}{1}\\=\frac{-21}{24}-\frac{32}{24}-\frac{24}{24}\\=\frac{-21-32-24}{24}\\=\frac{-77}{24}\)
4. \(-\left(\frac{-7}{8}\right) -\left(\frac{-7}{-4}\right) -\left(\frac{-12}{10}\right)\\= \frac{7}{8}- \frac{7}{4}+\frac{12}{10}\\=\frac{7}{8}-\frac{7}{4}+\frac{6}{5}\\=\frac{35}{40}-\frac{70}{40}+\frac{48}{40}\\=\frac{35-70+48}{40}\\=\frac{13}{40}\)
5. \(-\left(\frac{-9}{-2}\right) +\left(\frac{-8}{-10}\right) +\left(\frac{-5}{-10}\right)\\= \frac{-9}{2}+ \frac{8}{10}+\frac{5}{10}\\=\frac{-9}{2}+\frac{4}{5}+\frac{1}{2}\\=\frac{-45}{10}+\frac{8}{10}+\frac{5}{10}\\=\frac{-45+8+5}{10}\\=\frac{-32}{10}\\=\frac{-16}{5}\)
6. \(+\left(\frac{-8}{3}\right) -\left(\frac{-9}{8}\right) -\left(\frac{-5}{-11}\right)\\= \frac{-8}{3}+ \frac{9}{8}-\frac{5}{11}\\=\frac{-704}{264}+\frac{297}{264}-\frac{120}{264}\\=\frac{-704+297-120}{264}\\=\frac{-527}{264}\)
7. \(+\left(\frac{-6}{5}\right) -\left(\frac{-4}{-6}\right) -\left(\frac{-11}{-4}\right)\\= \frac{-6}{5}- \frac{4}{6}-\frac{11}{4}\\=\frac{-6}{5}-\frac{2}{3}-\frac{11}{4}\\=\frac{-72}{60}-\frac{40}{60}-\frac{165}{60}\\=\frac{-72-40-165}{60}\\=\frac{-277}{60}\)
8. \(+\left(\frac{4}{-5}\right) -\left(\frac{-9}{6}\right) -\left(\frac{-2}{-11}\right)\\= \frac{-4}{5}+ \frac{9}{6}-\frac{2}{11}\\=\frac{-4}{5}+\frac{3}{2}-\frac{2}{11}\\=\frac{-88}{110}+\frac{165}{110}-\frac{20}{110}\\=\frac{-88+165-20}{110}\\=\frac{57}{110}\)
9. \(-\left(\frac{3}{-2}\right) +\left(\frac{8}{-5}\right) -\left(\frac{-5}{4}\right)\\= \frac{3}{2}- \frac{8}{5}+\frac{5}{4}\\=\frac{30}{20}-\frac{32}{20}+\frac{25}{20}\\=\frac{30-32+25}{20}\\=\frac{23}{20}\)
10. \(-\left(\frac{3}{-4}\right) -\left(\frac{2}{-3}\right) +\left(\frac{11}{11}\right)\\= \frac{3}{4}+ \frac{2}{3}+\frac{11}{11}\\=\frac{3}{4}+\frac{2}{3}+\frac{1}{1}\\=\frac{9}{12}+\frac{8}{12}+\frac{12}{12}\\=\frac{9+8+12}{12}\\=\frac{29}{12}\)
11. \(-\left(\frac{6}{-5}\right) -\left(\frac{-4}{-3}\right) -\left(\frac{-8}{2}\right)\\= \frac{6}{5}- \frac{4}{3}+\frac{8}{2}\\=\frac{6}{5}-\frac{4}{3}+\frac{4}{1}\\=\frac{18}{15}-\frac{20}{15}+\frac{60}{15}\\=\frac{18-20+60}{15}\\=\frac{58}{15}\)
12. \(+\left(\frac{4}{-9}\right) +\left(\frac{-2}{-8}\right) -\left(\frac{10}{-4}\right)\\= \frac{-4}{9}+ \frac{2}{8}+\frac{10}{4}\\=\frac{-4}{9}+\frac{1}{4}+\frac{5}{2}\\=\frac{-16}{36}+\frac{9}{36}+\frac{90}{36}\\=\frac{-16+9+90}{36}\\=\frac{83}{36}\)