Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{7}\right) -\left(\frac{-2}{-9}\right) +\left(\frac{3}{9}\right)\\= \frac{4}{7}- \frac{2}{9}+\frac{3}{9}\\=\frac{4}{7}-\frac{2}{9}+\frac{1}{3}\\=\frac{36}{63}-\frac{14}{63}+\frac{21}{63}\\=\frac{36-14+21}{63}\\=\frac{43}{63}\)
2. \(-\left(\frac{4}{-9}\right) -\left(\frac{3}{-7}\right) +\left(\frac{-2}{6}\right)\\= \frac{4}{9}+ \frac{3}{7}-\frac{2}{6}\\=\frac{4}{9}+\frac{3}{7}-\frac{1}{3}\\=\frac{28}{63}+\frac{27}{63}-\frac{21}{63}\\=\frac{28+27-21}{63}\\=\frac{34}{63}\)
3. \(+\left(\frac{10}{-7}\right) -\left(\frac{10}{9}\right) -\left(\frac{-11}{-7}\right)\\= \frac{-10}{7}- \frac{10}{9}-\frac{11}{7}\\=\frac{-90}{63}-\frac{70}{63}-\frac{99}{63}\\=\frac{-90-70-99}{63}\\=\frac{-259}{63}\\=\frac{-37}{9}\)
4. \(+\left(\frac{-6}{-5}\right) +\left(\frac{10}{9}\right) +\left(\frac{11}{-12}\right)\\= \frac{6}{5}+ \frac{10}{9}-\frac{11}{12}\\=\frac{216}{180}+\frac{200}{180}-\frac{165}{180}\\=\frac{216+200-165}{180}\\=\frac{251}{180}\)
5. \(+\left(\frac{8}{3}\right) +\left(\frac{3}{3}\right) +\left(\frac{-6}{6}\right)\\= \frac{8}{3}+ \frac{3}{3}-\frac{6}{6}\\=\frac{8}{3}+\frac{1}{1}-\frac{1}{1}\\=\frac{8+1-1}{3}\\=\frac{8}{3}\)
6. \(+\left(\frac{3}{2}\right) +\left(\frac{9}{5}\right) +\left(\frac{6}{6}\right)\\= \frac{3}{2}+ \frac{9}{5}+\frac{6}{6}\\=\frac{3}{2}+\frac{9}{5}+\frac{1}{1}\\=\frac{15}{10}+\frac{18}{10}+\frac{10}{10}\\=\frac{15+18+10}{10}\\=\frac{43}{10}\)
7. \(+\left(\frac{8}{-7}\right) +\left(\frac{3}{2}\right) +\left(\frac{10}{12}\right)\\= \frac{-8}{7}+ \frac{3}{2}+\frac{10}{12}\\=\frac{-8}{7}+\frac{3}{2}+\frac{5}{6}\\=\frac{-48}{42}+\frac{63}{42}+\frac{35}{42}\\=\frac{-48+63+35}{42}\\=\frac{50}{42}\\=\frac{25}{21}\)
8. \(+\left(\frac{-4}{3}\right) -\left(\frac{3}{-9}\right) -\left(\frac{-2}{-5}\right)\\= \frac{-4}{3}+ \frac{3}{9}-\frac{2}{5}\\=\frac{-4}{3}+\frac{1}{3}-\frac{2}{5}\\=\frac{-20}{15}+\frac{5}{15}-\frac{6}{15}\\=\frac{-20+5-6}{15}\\=\frac{-21}{15}\\=\frac{-7}{5}\)
9. \(+\left(\frac{-7}{-8}\right) +\left(\frac{9}{-7}\right) -\left(\frac{9}{5}\right)\\= \frac{7}{8}- \frac{9}{7}-\frac{9}{5}\\=\frac{245}{280}-\frac{360}{280}-\frac{504}{280}\\=\frac{245-360-504}{280}\\=\frac{-619}{280}\)
10. \(+\left(\frac{6}{-5}\right) -\left(\frac{-4}{10}\right) -\left(\frac{-12}{7}\right)\\= \frac{-6}{5}+ \frac{4}{10}+\frac{12}{7}\\=\frac{-6}{5}+\frac{2}{5}+\frac{12}{7}\\=\frac{-42}{35}+\frac{14}{35}+\frac{60}{35}\\=\frac{-42+14+60}{35}\\=\frac{32}{35}\)
11. \(-\left(\frac{-8}{-9}\right) -\left(\frac{-4}{2}\right) +\left(\frac{-2}{-2}\right)\\= \frac{-8}{9}+ \frac{4}{2}+\frac{2}{2}\\=\frac{-8}{9}+\frac{2}{1}+\frac{1}{1}\\=\frac{-8+2+1}{9}\\=\frac{-5}{9}\)
12. \(-\left(\frac{3}{5}\right) -\left(\frac{-9}{-8}\right) +\left(\frac{-7}{11}\right)\\= \frac{-3}{5}- \frac{9}{8}-\frac{7}{11}\\=\frac{-264}{440}-\frac{495}{440}-\frac{280}{440}\\=\frac{-264-495-280}{440}\\=\frac{-1039}{440}\)