Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{7}\right) -\left(\frac{-6}{-2}\right) +\left(\frac{-5}{12}\right)\\= \frac{-10}{7}- \frac{6}{2}-\frac{5}{12}\\=\frac{-10}{7}-\frac{3}{1}-\frac{5}{12}\\=\frac{-120}{84}-\frac{252}{84}-\frac{35}{84}\\=\frac{-120-252-35}{84}\\=\frac{-407}{84}\)
2. \(+\left(\frac{6}{5}\right) +\left(\frac{-2}{7}\right) -\left(\frac{-5}{7}\right)\\= \frac{6}{5}- \frac{2}{7}+\frac{5}{7}\\=\frac{42}{35}-\frac{10}{35}+\frac{25}{35}\\=\frac{42-10+25}{35}\\=\frac{57}{35}\)
3. \(-\left(\frac{-3}{2}\right) +\left(\frac{8}{-9}\right) -\left(\frac{-9}{9}\right)\\= \frac{3}{2}- \frac{8}{9}+\frac{9}{9}\\=\frac{3}{2}-\frac{8}{9}+\frac{1}{1}\\=\frac{27}{18}-\frac{16}{18}+\frac{18}{18}\\=\frac{27-16+18}{18}\\=\frac{29}{18}\)
4. \(+\left(\frac{7}{9}\right) +\left(\frac{4}{-7}\right) -\left(\frac{-2}{11}\right)\\= \frac{7}{9}- \frac{4}{7}+\frac{2}{11}\\=\frac{539}{693}-\frac{396}{693}+\frac{126}{693}\\=\frac{539-396+126}{693}\\=\frac{269}{693}\)
5. \(-\left(\frac{10}{7}\right) +\left(\frac{-5}{-2}\right) +\left(\frac{-3}{6}\right)\\= \frac{-10}{7}+ \frac{5}{2}-\frac{3}{6}\\=\frac{-10}{7}+\frac{5}{2}-\frac{1}{2}\\=\frac{-20}{14}+\frac{35}{14}-\frac{7}{14}\\=\frac{-20+35-7}{14}\\=\frac{8}{14}\\=\frac{4}{7}\)
6. \(+\left(\frac{7}{-5}\right) +\left(\frac{-8}{-10}\right) -\left(\frac{-8}{-10}\right)\\= \frac{-7}{5}+ \frac{8}{10}-\frac{8}{10}\\=\frac{-7}{5}+\frac{4}{5}-\frac{4}{5}\\=\frac{-7+4-4}{5}\\=\frac{-7}{5}\)
7. \(+\left(\frac{-3}{-8}\right) +\left(\frac{8}{6}\right) +\left(\frac{2}{-3}\right)\\= \frac{3}{8}+ \frac{8}{6}-\frac{2}{3}\\=\frac{3}{8}+\frac{4}{3}-\frac{2}{3}\\=\frac{9}{24}+\frac{32}{24}-\frac{16}{24}\\=\frac{9+32-16}{24}\\=\frac{25}{24}\)
8. \(-\left(\frac{-5}{-7}\right) -\left(\frac{-7}{3}\right) +\left(\frac{-11}{12}\right)\\= \frac{-5}{7}+ \frac{7}{3}-\frac{11}{12}\\=\frac{-60}{84}+\frac{196}{84}-\frac{77}{84}\\=\frac{-60+196-77}{84}\\=\frac{59}{84}\)
9. \(+\left(\frac{-7}{-8}\right) -\left(\frac{5}{-8}\right) -\left(\frac{5}{-4}\right)\\= \frac{7}{8}+ \frac{5}{8}+\frac{5}{4}\\=\frac{7+5+5}{8}\\=\frac{17}{8}\)
10. \(+\left(\frac{10}{7}\right) +\left(\frac{9}{6}\right) +\left(\frac{-11}{-11}\right)\\= \frac{10}{7}+ \frac{9}{6}+\frac{11}{11}\\=\frac{10}{7}+\frac{3}{2}+\frac{1}{1}\\=\frac{20}{14}+\frac{21}{14}+\frac{14}{14}\\=\frac{20+21+14}{14}\\=\frac{55}{14}\)
11. \(-\left(\frac{-10}{-9}\right) +\left(\frac{-6}{-3}\right) -\left(\frac{11}{7}\right)\\= \frac{-10}{9}+ \frac{6}{3}-\frac{11}{7}\\=\frac{-10}{9}+\frac{2}{1}-\frac{11}{7}\\=\frac{-70}{63}+\frac{126}{63}-\frac{99}{63}\\=\frac{-70+126-99}{63}\\=\frac{-43}{63}\)
12. \(-\left(\frac{9}{7}\right) +\left(\frac{8}{10}\right) +\left(\frac{3}{-12}\right)\\= \frac{-9}{7}+ \frac{8}{10}-\frac{3}{12}\\=\frac{-9}{7}+\frac{4}{5}-\frac{1}{4}\\=\frac{-180}{140}+\frac{112}{140}-\frac{35}{140}\\=\frac{-180+112-35}{140}\\=\frac{-103}{140}\)