Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{6}{5}\right) +\left(\frac{6}{-6}\right) -\left(\frac{-2}{5}\right)\\= \frac{-6}{5}- \frac{6}{6}+\frac{2}{5}\\=\frac{-6}{5}-\frac{1}{1}+\frac{2}{5}\\=\frac{-6-1+2}{5}\\=\frac{-5}{5}\\=\frac{-1}{1}\)
2. \(-\left(\frac{-5}{-4}\right) -\left(\frac{10}{9}\right) +\left(\frac{-5}{6}\right)\\= \frac{-5}{4}- \frac{10}{9}-\frac{5}{6}\\=\frac{-45}{36}-\frac{40}{36}-\frac{30}{36}\\=\frac{-45-40-30}{36}\\=\frac{-115}{36}\)
3. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-3}{-7}\right) -\left(\frac{4}{9}\right)\\= \frac{-6}{5}- \frac{3}{7}-\frac{4}{9}\\=\frac{-378}{315}-\frac{135}{315}-\frac{140}{315}\\=\frac{-378-135-140}{315}\\=\frac{-653}{315}\)
4. \(+\left(\frac{2}{9}\right) -\left(\frac{-3}{-6}\right) -\left(\frac{12}{-12}\right)\\= \frac{2}{9}- \frac{3}{6}+\frac{12}{12}\\=\frac{2}{9}-\frac{1}{2}+\frac{1}{1}\\=\frac{4}{18}-\frac{9}{18}+\frac{18}{18}\\=\frac{4-9+18}{18}\\=\frac{13}{18}\)
5. \(-\left(\frac{-8}{-9}\right) -\left(\frac{6}{9}\right) -\left(\frac{-4}{-7}\right)\\= \frac{-8}{9}- \frac{6}{9}-\frac{4}{7}\\=\frac{-8}{9}-\frac{2}{3}-\frac{4}{7}\\=\frac{-56}{63}-\frac{42}{63}-\frac{36}{63}\\=\frac{-56-42-36}{63}\\=\frac{-134}{63}\)
6. \(-\left(\frac{6}{-7}\right) +\left(\frac{-10}{6}\right) +\left(\frac{-6}{-2}\right)\\= \frac{6}{7}- \frac{10}{6}+\frac{6}{2}\\=\frac{6}{7}-\frac{5}{3}+\frac{3}{1}\\=\frac{18}{21}-\frac{35}{21}+\frac{63}{21}\\=\frac{18-35+63}{21}\\=\frac{46}{21}\)
7. \(+\left(\frac{3}{-2}\right) -\left(\frac{-7}{-7}\right) +\left(\frac{-6}{11}\right)\\= \frac{-3}{2}- \frac{7}{7}-\frac{6}{11}\\=\frac{-3}{2}-\frac{1}{1}-\frac{6}{11}\\=\frac{-33}{22}-\frac{22}{22}-\frac{12}{22}\\=\frac{-33-22-12}{22}\\=\frac{-67}{22}\)
8. \(-\left(\frac{2}{9}\right) +\left(\frac{9}{5}\right) -\left(\frac{2}{-6}\right)\\= \frac{-2}{9}+ \frac{9}{5}+\frac{2}{6}\\=\frac{-2}{9}+\frac{9}{5}+\frac{1}{3}\\=\frac{-10}{45}+\frac{81}{45}+\frac{15}{45}\\=\frac{-10+81+15}{45}\\=\frac{86}{45}\)
9. \(-\left(\frac{-3}{-4}\right) +\left(\frac{7}{-6}\right) -\left(\frac{11}{-12}\right)\\= \frac{-3}{4}- \frac{7}{6}+\frac{11}{12}\\=\frac{-9}{12}-\frac{14}{12}+\frac{11}{12}\\=\frac{-9-14+11}{12}\\=\frac{-12}{12}\\=\frac{-1}{1}\)
10. \(+\left(\frac{-9}{7}\right) -\left(\frac{-2}{-7}\right) -\left(\frac{-4}{-11}\right)\\= \frac{-9}{7}- \frac{2}{7}-\frac{4}{11}\\=\frac{-99}{77}-\frac{22}{77}-\frac{28}{77}\\=\frac{-99-22-28}{77}\\=\frac{-149}{77}\)
11. \(+\left(\frac{-5}{-6}\right) +\left(\frac{5}{-3}\right) -\left(\frac{9}{10}\right)\\= \frac{5}{6}- \frac{5}{3}-\frac{9}{10}\\=\frac{25}{30}-\frac{50}{30}-\frac{27}{30}\\=\frac{25-50-27}{30}\\=\frac{-52}{30}\\=\frac{-26}{15}\)
12. \(-\left(\frac{-3}{4}\right) +\left(\frac{-10}{-3}\right) +\left(\frac{-9}{7}\right)\\= \frac{3}{4}+ \frac{10}{3}-\frac{9}{7}\\=\frac{63}{84}+\frac{280}{84}-\frac{108}{84}\\=\frac{63+280-108}{84}\\=\frac{235}{84}\)