Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{4}{3}\right) -\left(\frac{2}{-7}\right) -\left(\frac{-3}{-7}\right)\\= \frac{4}{3}+ \frac{2}{7}-\frac{3}{7}\\=\frac{28}{21}+\frac{6}{21}-\frac{9}{21}\\=\frac{28+6-9}{21}\\=\frac{25}{21}\)
2. \(-\left(\frac{-8}{-9}\right) -\left(\frac{9}{-3}\right) -\left(\frac{-9}{-7}\right)\\= \frac{-8}{9}+ \frac{9}{3}-\frac{9}{7}\\=\frac{-8}{9}+\frac{3}{1}-\frac{9}{7}\\=\frac{-56}{63}+\frac{189}{63}-\frac{81}{63}\\=\frac{-56+189-81}{63}\\=\frac{52}{63}\)
3. \(-\left(\frac{-10}{-3}\right) -\left(\frac{3}{9}\right) +\left(\frac{4}{8}\right)\\= \frac{-10}{3}- \frac{3}{9}+\frac{4}{8}\\=\frac{-10}{3}-\frac{1}{3}+\frac{1}{2}\\=\frac{-20}{6}-\frac{2}{6}+\frac{3}{6}\\=\frac{-20-2+3}{6}\\=\frac{-19}{6}\)
4. \(-\left(\frac{-10}{-9}\right) -\left(\frac{4}{-9}\right) -\left(\frac{8}{4}\right)\\= \frac{-10}{9}+ \frac{4}{9}-\frac{8}{4}\\=\frac{-10}{9}+\frac{4}{9}-\frac{2}{1}\\=\frac{-10+4-2}{9}\\=\frac{-8}{9}\)
5. \(+\left(\frac{5}{-7}\right) +\left(\frac{2}{-5}\right) -\left(\frac{10}{7}\right)\\= \frac{-5}{7}- \frac{2}{5}-\frac{10}{7}\\=\frac{-25}{35}-\frac{14}{35}-\frac{50}{35}\\=\frac{-25-14-50}{35}\\=\frac{-89}{35}\)
6. \(+\left(\frac{-3}{2}\right) +\left(\frac{3}{-4}\right) +\left(\frac{-10}{8}\right)\\= \frac{-3}{2}- \frac{3}{4}-\frac{10}{8}\\=\frac{-3}{2}-\frac{3}{4}-\frac{5}{4}\\=\frac{-6}{4}-\frac{3}{4}-\frac{5}{4}\\=\frac{-6-3-5}{4}\\=\frac{-14}{4}\\=\frac{-7}{2}\)
7. \(-\left(\frac{-5}{-2}\right) -\left(\frac{4}{-3}\right) +\left(\frac{2}{12}\right)\\= \frac{-5}{2}+ \frac{4}{3}+\frac{2}{12}\\=\frac{-5}{2}+\frac{4}{3}+\frac{1}{6}\\=\frac{-15}{6}+\frac{8}{6}+\frac{1}{6}\\=\frac{-15+8+1}{6}\\=\frac{-6}{6}\\=\frac{-1}{1}\)
8. \(-\left(\frac{4}{7}\right) +\left(\frac{-10}{2}\right) +\left(\frac{-5}{9}\right)\\= \frac{-4}{7}- \frac{10}{2}-\frac{5}{9}\\=\frac{-4}{7}-\frac{5}{1}-\frac{5}{9}\\=\frac{-36}{63}-\frac{315}{63}-\frac{35}{63}\\=\frac{-36-315-35}{63}\\=\frac{-386}{63}\)
9. \(+\left(\frac{10}{7}\right) +\left(\frac{7}{-5}\right) -\left(\frac{-10}{12}\right)\\= \frac{10}{7}- \frac{7}{5}+\frac{10}{12}\\=\frac{10}{7}-\frac{7}{5}+\frac{5}{6}\\=\frac{300}{210}-\frac{294}{210}+\frac{175}{210}\\=\frac{300-294+175}{210}\\=\frac{181}{210}\)
10. \(-\left(\frac{10}{-3}\right) +\left(\frac{2}{-8}\right) +\left(\frac{-9}{-2}\right)\\= \frac{10}{3}- \frac{2}{8}+\frac{9}{2}\\=\frac{10}{3}-\frac{1}{4}+\frac{9}{2}\\=\frac{40}{12}-\frac{3}{12}+\frac{54}{12}\\=\frac{40-3+54}{12}\\=\frac{91}{12}\)
11. \(+\left(\frac{-2}{9}\right) -\left(\frac{9}{10}\right) +\left(\frac{7}{5}\right)\\= \frac{-2}{9}- \frac{9}{10}+\frac{7}{5}\\=\frac{-20}{90}-\frac{81}{90}+\frac{126}{90}\\=\frac{-20-81+126}{90}\\=\frac{25}{90}\\=\frac{5}{18}\)
12. \(+\left(\frac{-9}{8}\right) +\left(\frac{-5}{5}\right) +\left(\frac{-3}{-10}\right)\\= \frac{-9}{8}- \frac{5}{5}+\frac{3}{10}\\=\frac{-9}{8}-\frac{1}{1}+\frac{3}{10}\\=\frac{-45}{40}-\frac{40}{40}+\frac{12}{40}\\=\frac{-45-40+12}{40}\\=\frac{-73}{40}\)