Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{-9}\right) -\left(\frac{3}{-10}\right) +\left(\frac{10}{-8}\right)\\= \frac{2}{9}+ \frac{3}{10}-\frac{10}{8}\\=\frac{2}{9}+\frac{3}{10}-\frac{5}{4}\\=\frac{40}{180}+\frac{54}{180}-\frac{225}{180}\\=\frac{40+54-225}{180}\\=\frac{-131}{180}\)
2. \(-\left(\frac{-8}{3}\right) +\left(\frac{-9}{7}\right) -\left(\frac{5}{-8}\right)\\= \frac{8}{3}- \frac{9}{7}+\frac{5}{8}\\=\frac{448}{168}-\frac{216}{168}+\frac{105}{168}\\=\frac{448-216+105}{168}\\=\frac{337}{168}\)
3. \(-\left(\frac{5}{8}\right) +\left(\frac{7}{-8}\right) +\left(\frac{4}{-12}\right)\\= \frac{-5}{8}- \frac{7}{8}-\frac{4}{12}\\=\frac{-5}{8}-\frac{7}{8}-\frac{1}{3}\\=\frac{-15}{24}-\frac{21}{24}-\frac{8}{24}\\=\frac{-15-21-8}{24}\\=\frac{-44}{24}\\=\frac{-11}{6}\)
4. \(-\left(\frac{5}{-2}\right) +\left(\frac{3}{2}\right) -\left(\frac{2}{-2}\right)\\= \frac{5}{2}+ \frac{3}{2}+\frac{2}{2}\\=\frac{5}{2}+\frac{3}{2}+\frac{1}{1}\\=\frac{5+3+1}{2}\\=\frac{9}{2}\)
5. \(+\left(\frac{9}{-4}\right) -\left(\frac{10}{4}\right) +\left(\frac{12}{-7}\right)\\= \frac{-9}{4}- \frac{10}{4}-\frac{12}{7}\\=\frac{-9}{4}-\frac{5}{2}-\frac{12}{7}\\=\frac{-63}{28}-\frac{70}{28}-\frac{48}{28}\\=\frac{-63-70-48}{28}\\=\frac{-181}{28}\)
6. \(-\left(\frac{7}{-4}\right) +\left(\frac{-4}{-6}\right) +\left(\frac{-2}{6}\right)\\= \frac{7}{4}+ \frac{4}{6}-\frac{2}{6}\\=\frac{7}{4}+\frac{2}{3}-\frac{1}{3}\\=\frac{21}{12}+\frac{8}{12}-\frac{4}{12}\\=\frac{21+8-4}{12}\\=\frac{25}{12}\)
7. \(+\left(\frac{-3}{-7}\right) +\left(\frac{-8}{-8}\right) -\left(\frac{-3}{-8}\right)\\= \frac{3}{7}+ \frac{8}{8}-\frac{3}{8}\\=\frac{3}{7}+\frac{1}{1}-\frac{3}{8}\\=\frac{24}{56}+\frac{56}{56}-\frac{21}{56}\\=\frac{24+56-21}{56}\\=\frac{59}{56}\)
8. \(-\left(\frac{-4}{7}\right) -\left(\frac{-8}{2}\right) +\left(\frac{5}{5}\right)\\= \frac{4}{7}+ \frac{8}{2}+\frac{5}{5}\\=\frac{4}{7}+\frac{4}{1}+\frac{1}{1}\\=\frac{4+4+1}{7}\\=\frac{9}{7}\)
9. \(-\left(\frac{-6}{5}\right) -\left(\frac{-3}{-9}\right) +\left(\frac{8}{-12}\right)\\= \frac{6}{5}- \frac{3}{9}-\frac{8}{12}\\=\frac{6}{5}-\frac{1}{3}-\frac{2}{3}\\=\frac{18}{15}-\frac{5}{15}-\frac{10}{15}\\=\frac{18-5-10}{15}\\=\frac{3}{15}\\=\frac{1}{5}\)
10. \(+\left(\frac{-4}{5}\right) -\left(\frac{-4}{-4}\right) -\left(\frac{-6}{12}\right)\\= \frac{-4}{5}- \frac{4}{4}+\frac{6}{12}\\=\frac{-4}{5}-\frac{1}{1}+\frac{1}{2}\\=\frac{-8}{10}-\frac{10}{10}+\frac{5}{10}\\=\frac{-8-10+5}{10}\\=\frac{-13}{10}\)
11. \(+\left(\frac{6}{5}\right) -\left(\frac{5}{9}\right) -\left(\frac{-5}{-4}\right)\\= \frac{6}{5}- \frac{5}{9}-\frac{5}{4}\\=\frac{216}{180}-\frac{100}{180}-\frac{225}{180}\\=\frac{216-100-225}{180}\\=\frac{-109}{180}\)
12. \(-\left(\frac{2}{7}\right) +\left(\frac{-3}{-2}\right) -\left(\frac{9}{8}\right)\\= \frac{-2}{7}+ \frac{3}{2}-\frac{9}{8}\\=\frac{-16}{56}+\frac{84}{56}-\frac{63}{56}\\=\frac{-16+84-63}{56}\\=\frac{5}{56}\)