Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{9}{-4}\right) -\left(\frac{6}{5}\right) -\left(\frac{-5}{9}\right)\\= \frac{9}{4}- \frac{6}{5}+\frac{5}{9}\\=\frac{405}{180}-\frac{216}{180}+\frac{100}{180}\\=\frac{405-216+100}{180}\\=\frac{289}{180}\)
2. \(+\left(\frac{8}{3}\right) -\left(\frac{-5}{-6}\right) -\left(\frac{-6}{-2}\right)\\= \frac{8}{3}- \frac{5}{6}-\frac{6}{2}\\=\frac{8}{3}-\frac{5}{6}-\frac{3}{1}\\=\frac{16}{6}-\frac{5}{6}-\frac{18}{6}\\=\frac{16-5-18}{6}\\=\frac{-7}{6}\)
3. \(+\left(\frac{-9}{-4}\right) -\left(\frac{-4}{-7}\right) +\left(\frac{6}{10}\right)\\= \frac{9}{4}- \frac{4}{7}+\frac{6}{10}\\=\frac{9}{4}-\frac{4}{7}+\frac{3}{5}\\=\frac{315}{140}-\frac{80}{140}+\frac{84}{140}\\=\frac{315-80+84}{140}\\=\frac{319}{140}\)
4. \(+\left(\frac{-2}{-5}\right) +\left(\frac{8}{-4}\right) -\left(\frac{-3}{8}\right)\\= \frac{2}{5}- \frac{8}{4}+\frac{3}{8}\\=\frac{2}{5}-\frac{2}{1}+\frac{3}{8}\\=\frac{16}{40}-\frac{80}{40}+\frac{15}{40}\\=\frac{16-80+15}{40}\\=\frac{-49}{40}\)
5. \(-\left(\frac{7}{8}\right) -\left(\frac{8}{-9}\right) +\left(\frac{-11}{-8}\right)\\= \frac{-7}{8}+ \frac{8}{9}+\frac{11}{8}\\=\frac{-63}{72}+\frac{64}{72}+\frac{99}{72}\\=\frac{-63+64+99}{72}\\=\frac{100}{72}\\=\frac{25}{18}\)
6. \(+\left(\frac{5}{-4}\right) +\left(\frac{-4}{-9}\right) +\left(\frac{5}{-7}\right)\\= \frac{-5}{4}+ \frac{4}{9}-\frac{5}{7}\\=\frac{-315}{252}+\frac{112}{252}-\frac{180}{252}\\=\frac{-315+112-180}{252}\\=\frac{-383}{252}\)
7. \(-\left(\frac{6}{-7}\right) +\left(\frac{-6}{-8}\right) -\left(\frac{2}{-4}\right)\\= \frac{6}{7}+ \frac{6}{8}+\frac{2}{4}\\=\frac{6}{7}+\frac{3}{4}+\frac{1}{2}\\=\frac{24}{28}+\frac{21}{28}+\frac{14}{28}\\=\frac{24+21+14}{28}\\=\frac{59}{28}\)
8. \(-\left(\frac{6}{-5}\right) -\left(\frac{10}{10}\right) -\left(\frac{10}{-11}\right)\\= \frac{6}{5}- \frac{10}{10}+\frac{10}{11}\\=\frac{6}{5}-\frac{1}{1}+\frac{10}{11}\\=\frac{66}{55}-\frac{55}{55}+\frac{50}{55}\\=\frac{66-55+50}{55}\\=\frac{61}{55}\)
9. \(+\left(\frac{9}{4}\right) -\left(\frac{-5}{3}\right) -\left(\frac{4}{6}\right)\\= \frac{9}{4}+ \frac{5}{3}-\frac{4}{6}\\=\frac{9}{4}+\frac{5}{3}-\frac{2}{3}\\=\frac{27}{12}+\frac{20}{12}-\frac{8}{12}\\=\frac{27+20-8}{12}\\=\frac{39}{12}\\=\frac{13}{4}\)
10. \(-\left(\frac{-2}{-3}\right) -\left(\frac{-8}{-10}\right) +\left(\frac{8}{6}\right)\\= \frac{-2}{3}- \frac{8}{10}+\frac{8}{6}\\=\frac{-2}{3}-\frac{4}{5}+\frac{4}{3}\\=\frac{-10}{15}-\frac{12}{15}+\frac{20}{15}\\=\frac{-10-12+20}{15}\\=\frac{-2}{15}\)
11. \(+\left(\frac{-7}{2}\right) +\left(\frac{-10}{-5}\right) +\left(\frac{-10}{-10}\right)\\= \frac{-7}{2}+ \frac{10}{5}+\frac{10}{10}\\=\frac{-7}{2}+\frac{2}{1}+\frac{1}{1}\\=\frac{-7+2+1}{2}\\=\frac{-4}{2}\\=\frac{-2}{1}\)
12. \(+\left(\frac{5}{-7}\right) -\left(\frac{8}{7}\right) -\left(\frac{6}{6}\right)\\= \frac{-5}{7}- \frac{8}{7}-\frac{6}{6}\\=\frac{-5}{7}-\frac{8}{7}-\frac{1}{1}\\=\frac{-5-8-1}{7}\\=\frac{-14}{7}\\=\frac{-2}{1}\)