Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{7}\right) +\left(\frac{2}{-9}\right) -\left(\frac{-12}{12}\right)\\= \frac{-8}{7}- \frac{2}{9}+\frac{12}{12}\\=\frac{-8}{7}-\frac{2}{9}+\frac{1}{1}\\=\frac{-72}{63}-\frac{14}{63}+\frac{63}{63}\\=\frac{-72-14+63}{63}\\=\frac{-23}{63}\)
2. \(-\left(\frac{6}{5}\right) -\left(\frac{-3}{9}\right) +\left(\frac{-3}{-6}\right)\\= \frac{-6}{5}+ \frac{3}{9}+\frac{3}{6}\\=\frac{-6}{5}+\frac{1}{3}+\frac{1}{2}\\=\frac{-36}{30}+\frac{10}{30}+\frac{15}{30}\\=\frac{-36+10+15}{30}\\=\frac{-11}{30}\)
3. \(-\left(\frac{-8}{9}\right) +\left(\frac{10}{7}\right) -\left(\frac{-2}{5}\right)\\= \frac{8}{9}+ \frac{10}{7}+\frac{2}{5}\\=\frac{280}{315}+\frac{450}{315}+\frac{126}{315}\\=\frac{280+450+126}{315}\\=\frac{856}{315}\)
4. \(+\left(\frac{-5}{-4}\right) -\left(\frac{4}{10}\right) +\left(\frac{7}{9}\right)\\= \frac{5}{4}- \frac{4}{10}+\frac{7}{9}\\=\frac{5}{4}-\frac{2}{5}+\frac{7}{9}\\=\frac{225}{180}-\frac{72}{180}+\frac{140}{180}\\=\frac{225-72+140}{180}\\=\frac{293}{180}\)
5. \(-\left(\frac{-7}{-6}\right) +\left(\frac{6}{6}\right) -\left(\frac{-2}{-9}\right)\\= \frac{-7}{6}+ \frac{6}{6}-\frac{2}{9}\\=\frac{-7}{6}+\frac{1}{1}-\frac{2}{9}\\=\frac{-21}{18}+\frac{18}{18}-\frac{4}{18}\\=\frac{-21+18-4}{18}\\=\frac{-7}{18}\)
6. \(-\left(\frac{-3}{-4}\right) +\left(\frac{5}{5}\right) +\left(\frac{-11}{12}\right)\\= \frac{-3}{4}+ \frac{5}{5}-\frac{11}{12}\\=\frac{-3}{4}+\frac{1}{1}-\frac{11}{12}\\=\frac{-9}{12}+\frac{12}{12}-\frac{11}{12}\\=\frac{-9+12-11}{12}\\=\frac{-8}{12}\\=\frac{-2}{3}\)
7. \(+\left(\frac{-5}{-2}\right) +\left(\frac{-2}{-7}\right) -\left(\frac{-5}{-12}\right)\\= \frac{5}{2}+ \frac{2}{7}-\frac{5}{12}\\=\frac{210}{84}+\frac{24}{84}-\frac{35}{84}\\=\frac{210+24-35}{84}\\=\frac{199}{84}\)
8. \(+\left(\frac{-8}{5}\right) -\left(\frac{10}{-5}\right) +\left(\frac{3}{7}\right)\\= \frac{-8}{5}+ \frac{10}{5}+\frac{3}{7}\\=\frac{-8}{5}+\frac{2}{1}+\frac{3}{7}\\=\frac{-56}{35}+\frac{70}{35}+\frac{15}{35}\\=\frac{-56+70+15}{35}\\=\frac{29}{35}\)
9. \(-\left(\frac{-5}{6}\right) -\left(\frac{8}{6}\right) -\left(\frac{9}{10}\right)\\= \frac{5}{6}- \frac{8}{6}-\frac{9}{10}\\=\frac{5}{6}-\frac{4}{3}-\frac{9}{10}\\=\frac{25}{30}-\frac{40}{30}-\frac{27}{30}\\=\frac{25-40-27}{30}\\=\frac{-42}{30}\\=\frac{-7}{5}\)
10. \(-\left(\frac{6}{7}\right) -\left(\frac{2}{-10}\right) +\left(\frac{-8}{-6}\right)\\= \frac{-6}{7}+ \frac{2}{10}+\frac{8}{6}\\=\frac{-6}{7}+\frac{1}{5}+\frac{4}{3}\\=\frac{-90}{105}+\frac{21}{105}+\frac{140}{105}\\=\frac{-90+21+140}{105}\\=\frac{71}{105}\)
11. \(+\left(\frac{-8}{-7}\right) +\left(\frac{-4}{-3}\right) -\left(\frac{2}{-11}\right)\\= \frac{8}{7}+ \frac{4}{3}+\frac{2}{11}\\=\frac{264}{231}+\frac{308}{231}+\frac{42}{231}\\=\frac{264+308+42}{231}\\=\frac{614}{231}\)
12. \(-\left(\frac{-10}{-3}\right) -\left(\frac{6}{3}\right) -\left(\frac{-7}{7}\right)\\= \frac{-10}{3}- \frac{6}{3}+\frac{7}{7}\\=\frac{-10}{3}-\frac{2}{1}+\frac{1}{1}\\=\frac{-10-2+1}{3}\\=\frac{-11}{3}\)