Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{4}{-9}\right) -\left(\frac{5}{-3}\right) -\left(\frac{-3}{-7}\right)\\= \frac{-4}{9}+ \frac{5}{3}-\frac{3}{7}\\=\frac{-28}{63}+\frac{105}{63}-\frac{27}{63}\\=\frac{-28+105-27}{63}\\=\frac{50}{63}\)
2. \(+\left(\frac{-2}{-3}\right) +\left(\frac{4}{-10}\right) +\left(\frac{7}{-4}\right)\\= \frac{2}{3}- \frac{4}{10}-\frac{7}{4}\\=\frac{2}{3}-\frac{2}{5}-\frac{7}{4}\\=\frac{40}{60}-\frac{24}{60}-\frac{105}{60}\\=\frac{40-24-105}{60}\\=\frac{-89}{60}\)
3. \(-\left(\frac{8}{9}\right) +\left(\frac{4}{-2}\right) +\left(\frac{-6}{-6}\right)\\= \frac{-8}{9}- \frac{4}{2}+\frac{6}{6}\\=\frac{-8}{9}-\frac{2}{1}+\frac{1}{1}\\=\frac{-8-2+1}{9}\\=\frac{-9}{9}\\=\frac{-1}{1}\)
4. \(-\left(\frac{-3}{2}\right) +\left(\frac{6}{6}\right) -\left(\frac{-10}{-4}\right)\\= \frac{3}{2}+ \frac{6}{6}-\frac{10}{4}\\=\frac{3}{2}+\frac{1}{1}-\frac{5}{2}\\=\frac{3+1-5}{2}\\=\frac{-1}{2}\)
5. \(-\left(\frac{-3}{-4}\right) +\left(\frac{4}{7}\right) +\left(\frac{12}{-12}\right)\\= \frac{-3}{4}+ \frac{4}{7}-\frac{12}{12}\\=\frac{-3}{4}+\frac{4}{7}-\frac{1}{1}\\=\frac{-21}{28}+\frac{16}{28}-\frac{28}{28}\\=\frac{-21+16-28}{28}\\=\frac{-33}{28}\)
6. \(-\left(\frac{9}{-8}\right) +\left(\frac{6}{2}\right) +\left(\frac{3}{11}\right)\\= \frac{9}{8}+ \frac{6}{2}+\frac{3}{11}\\=\frac{9}{8}+\frac{3}{1}+\frac{3}{11}\\=\frac{99}{88}+\frac{264}{88}+\frac{24}{88}\\=\frac{99+264+24}{88}\\=\frac{387}{88}\)
7. \(-\left(\frac{3}{5}\right) +\left(\frac{3}{3}\right) +\left(\frac{-6}{2}\right)\\= \frac{-3}{5}+ \frac{3}{3}-\frac{6}{2}\\=\frac{-3}{5}+\frac{1}{1}-\frac{3}{1}\\=\frac{-3+1-3}{5}\\=\frac{-5}{5}\\=\frac{-1}{1}\)
8. \(+\left(\frac{-4}{-9}\right) -\left(\frac{-8}{-10}\right) +\left(\frac{-12}{9}\right)\\= \frac{4}{9}- \frac{8}{10}-\frac{12}{9}\\=\frac{4}{9}-\frac{4}{5}-\frac{4}{3}\\=\frac{20}{45}-\frac{36}{45}-\frac{60}{45}\\=\frac{20-36-60}{45}\\=\frac{-76}{45}\)
9. \(-\left(\frac{-2}{5}\right) +\left(\frac{-3}{-2}\right) -\left(\frac{-11}{2}\right)\\= \frac{2}{5}+ \frac{3}{2}+\frac{11}{2}\\=\frac{4}{10}+\frac{15}{10}+\frac{55}{10}\\=\frac{4+15+55}{10}\\=\frac{74}{10}\\=\frac{37}{5}\)
10. \(+\left(\frac{-6}{-7}\right) -\left(\frac{-10}{-10}\right) +\left(\frac{-10}{-9}\right)\\= \frac{6}{7}- \frac{10}{10}+\frac{10}{9}\\=\frac{6}{7}-\frac{1}{1}+\frac{10}{9}\\=\frac{54}{63}-\frac{63}{63}+\frac{70}{63}\\=\frac{54-63+70}{63}\\=\frac{61}{63}\)
11. \(-\left(\frac{-7}{6}\right) -\left(\frac{4}{-2}\right) -\left(\frac{-9}{10}\right)\\= \frac{7}{6}+ \frac{4}{2}+\frac{9}{10}\\=\frac{7}{6}+\frac{2}{1}+\frac{9}{10}\\=\frac{35}{30}+\frac{60}{30}+\frac{27}{30}\\=\frac{35+60+27}{30}\\=\frac{122}{30}\\=\frac{61}{15}\)
12. \(-\left(\frac{-7}{3}\right) -\left(\frac{10}{-2}\right) +\left(\frac{-5}{2}\right)\\= \frac{7}{3}+ \frac{10}{2}-\frac{5}{2}\\=\frac{7}{3}+\frac{5}{1}-\frac{5}{2}\\=\frac{14}{6}+\frac{30}{6}-\frac{15}{6}\\=\frac{14+30-15}{6}\\=\frac{29}{6}\)