Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{-5}\right) +\left(\frac{10}{6}\right) -\left(\frac{-9}{-7}\right)\\= \frac{-9}{5}+ \frac{10}{6}-\frac{9}{7}\\=\frac{-9}{5}+\frac{5}{3}-\frac{9}{7}\\=\frac{-189}{105}+\frac{175}{105}-\frac{135}{105}\\=\frac{-189+175-135}{105}\\=\frac{-149}{105}\)
2. \(-\left(\frac{-10}{7}\right) -\left(\frac{-4}{-2}\right) -\left(\frac{-5}{11}\right)\\= \frac{10}{7}- \frac{4}{2}+\frac{5}{11}\\=\frac{10}{7}-\frac{2}{1}+\frac{5}{11}\\=\frac{110}{77}-\frac{154}{77}+\frac{35}{77}\\=\frac{110-154+35}{77}\\=\frac{-9}{77}\)
3. \(-\left(\frac{9}{-4}\right) +\left(\frac{-10}{-8}\right) -\left(\frac{-5}{6}\right)\\= \frac{9}{4}+ \frac{10}{8}+\frac{5}{6}\\=\frac{9}{4}+\frac{5}{4}+\frac{5}{6}\\=\frac{27}{12}+\frac{15}{12}+\frac{10}{12}\\=\frac{27+15+10}{12}\\=\frac{52}{12}\\=\frac{13}{3}\)
4. \(+\left(\frac{-4}{5}\right) +\left(\frac{-10}{9}\right) -\left(\frac{12}{4}\right)\\= \frac{-4}{5}- \frac{10}{9}-\frac{12}{4}\\=\frac{-4}{5}-\frac{10}{9}-\frac{3}{1}\\=\frac{-36}{45}-\frac{50}{45}-\frac{135}{45}\\=\frac{-36-50-135}{45}\\=\frac{-221}{45}\)
5. \(-\left(\frac{-8}{-3}\right) -\left(\frac{-4}{-6}\right) +\left(\frac{-7}{10}\right)\\= \frac{-8}{3}- \frac{4}{6}-\frac{7}{10}\\=\frac{-8}{3}-\frac{2}{3}-\frac{7}{10}\\=\frac{-80}{30}-\frac{20}{30}-\frac{21}{30}\\=\frac{-80-20-21}{30}\\=\frac{-121}{30}\)
6. \(-\left(\frac{-8}{-7}\right) -\left(\frac{8}{-7}\right) +\left(\frac{-6}{-6}\right)\\= \frac{-8}{7}+ \frac{8}{7}+\frac{6}{6}\\=\frac{-8}{7}+\frac{8}{7}+\frac{1}{1}\\=\frac{-8+8+1}{7}\\=\frac{1}{7}\)
7. \(-\left(\frac{9}{-7}\right) -\left(\frac{10}{-2}\right) -\left(\frac{9}{11}\right)\\= \frac{9}{7}+ \frac{10}{2}-\frac{9}{11}\\=\frac{9}{7}+\frac{5}{1}-\frac{9}{11}\\=\frac{99}{77}+\frac{385}{77}-\frac{63}{77}\\=\frac{99+385-63}{77}\\=\frac{421}{77}\)
8. \(-\left(\frac{3}{-7}\right) -\left(\frac{9}{10}\right) -\left(\frac{9}{-11}\right)\\= \frac{3}{7}- \frac{9}{10}+\frac{9}{11}\\=\frac{330}{770}-\frac{693}{770}+\frac{630}{770}\\=\frac{330-693+630}{770}\\=\frac{267}{770}\)
9. \(-\left(\frac{5}{-3}\right) -\left(\frac{10}{-4}\right) +\left(\frac{-6}{-11}\right)\\= \frac{5}{3}+ \frac{10}{4}+\frac{6}{11}\\=\frac{5}{3}+\frac{5}{2}+\frac{6}{11}\\=\frac{110}{66}+\frac{165}{66}+\frac{36}{66}\\=\frac{110+165+36}{66}\\=\frac{311}{66}\)
10. \(-\left(\frac{-8}{-5}\right) +\left(\frac{2}{4}\right) -\left(\frac{-7}{-8}\right)\\= \frac{-8}{5}+ \frac{2}{4}-\frac{7}{8}\\=\frac{-8}{5}+\frac{1}{2}-\frac{7}{8}\\=\frac{-64}{40}+\frac{20}{40}-\frac{35}{40}\\=\frac{-64+20-35}{40}\\=\frac{-79}{40}\)
11. \(+\left(\frac{-6}{-7}\right) +\left(\frac{-5}{8}\right) -\left(\frac{-10}{10}\right)\\= \frac{6}{7}- \frac{5}{8}+\frac{10}{10}\\=\frac{6}{7}-\frac{5}{8}+\frac{1}{1}\\=\frac{48}{56}-\frac{35}{56}+\frac{56}{56}\\=\frac{48-35+56}{56}\\=\frac{69}{56}\)
12. \(+\left(\frac{5}{-6}\right) -\left(\frac{6}{4}\right) -\left(\frac{9}{12}\right)\\= \frac{-5}{6}- \frac{6}{4}-\frac{9}{12}\\=\frac{-5}{6}-\frac{3}{2}-\frac{3}{4}\\=\frac{-10}{12}-\frac{18}{12}-\frac{9}{12}\\=\frac{-10-18-9}{12}\\=\frac{-37}{12}\)