Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{5}{8}\right) -\left(\frac{-8}{-8}\right) -\left(\frac{-4}{6}\right)\\= \frac{5}{8}- \frac{8}{8}+\frac{4}{6}\\=\frac{5}{8}-\frac{1}{1}+\frac{2}{3}\\=\frac{15}{24}-\frac{24}{24}+\frac{16}{24}\\=\frac{15-24+16}{24}\\=\frac{7}{24}\)
2. \(-\left(\frac{-10}{-9}\right) +\left(\frac{7}{-6}\right) +\left(\frac{-4}{-3}\right)\\= \frac{-10}{9}- \frac{7}{6}+\frac{4}{3}\\=\frac{-20}{18}-\frac{21}{18}+\frac{24}{18}\\=\frac{-20-21+24}{18}\\=\frac{-17}{18}\)
3. \(+\left(\frac{-4}{5}\right) -\left(\frac{7}{7}\right) -\left(\frac{-12}{-4}\right)\\= \frac{-4}{5}- \frac{7}{7}-\frac{12}{4}\\=\frac{-4}{5}-\frac{1}{1}-\frac{3}{1}\\=\frac{-4-1-3}{5}\\=\frac{-8}{5}\)
4. \(-\left(\frac{3}{2}\right) -\left(\frac{-8}{5}\right) -\left(\frac{4}{10}\right)\\= \frac{-3}{2}+ \frac{8}{5}-\frac{4}{10}\\=\frac{-3}{2}+\frac{8}{5}-\frac{2}{5}\\=\frac{-15}{10}+\frac{16}{10}-\frac{4}{10}\\=\frac{-15+16-4}{10}\\=\frac{-3}{10}\)
5. \(+\left(\frac{5}{-7}\right) -\left(\frac{-8}{-9}\right) +\left(\frac{11}{-6}\right)\\= \frac{-5}{7}- \frac{8}{9}-\frac{11}{6}\\=\frac{-90}{126}-\frac{112}{126}-\frac{231}{126}\\=\frac{-90-112-231}{126}\\=\frac{-433}{126}\)
6. \(-\left(\frac{2}{9}\right) +\left(\frac{-9}{8}\right) +\left(\frac{-6}{2}\right)\\= \frac{-2}{9}- \frac{9}{8}-\frac{6}{2}\\=\frac{-2}{9}-\frac{9}{8}-\frac{3}{1}\\=\frac{-16}{72}-\frac{81}{72}-\frac{216}{72}\\=\frac{-16-81-216}{72}\\=\frac{-313}{72}\)
7. \(+\left(\frac{9}{2}\right) +\left(\frac{-8}{-7}\right) -\left(\frac{4}{-11}\right)\\= \frac{9}{2}+ \frac{8}{7}+\frac{4}{11}\\=\frac{693}{154}+\frac{176}{154}+\frac{56}{154}\\=\frac{693+176+56}{154}\\=\frac{925}{154}\)
8. \(+\left(\frac{-7}{-4}\right) +\left(\frac{-8}{4}\right) +\left(\frac{4}{9}\right)\\= \frac{7}{4}- \frac{8}{4}+\frac{4}{9}\\=\frac{7}{4}-\frac{2}{1}+\frac{4}{9}\\=\frac{63}{36}-\frac{72}{36}+\frac{16}{36}\\=\frac{63-72+16}{36}\\=\frac{7}{36}\)
9. \(+\left(\frac{6}{5}\right) +\left(\frac{-4}{-8}\right) +\left(\frac{4}{4}\right)\\= \frac{6}{5}+ \frac{4}{8}+\frac{4}{4}\\=\frac{6}{5}+\frac{1}{2}+\frac{1}{1}\\=\frac{12}{10}+\frac{5}{10}+\frac{10}{10}\\=\frac{12+5+10}{10}\\=\frac{27}{10}\)
10. \(+\left(\frac{-2}{-9}\right) -\left(\frac{7}{-7}\right) -\left(\frac{12}{7}\right)\\= \frac{2}{9}+ \frac{7}{7}-\frac{12}{7}\\=\frac{2}{9}+\frac{1}{1}-\frac{12}{7}\\=\frac{14}{63}+\frac{63}{63}-\frac{108}{63}\\=\frac{14+63-108}{63}\\=\frac{-31}{63}\)
11. \(+\left(\frac{10}{-3}\right) -\left(\frac{-3}{-10}\right) -\left(\frac{10}{12}\right)\\= \frac{-10}{3}- \frac{3}{10}-\frac{10}{12}\\=\frac{-10}{3}-\frac{3}{10}-\frac{5}{6}\\=\frac{-100}{30}-\frac{9}{30}-\frac{25}{30}\\=\frac{-100-9-25}{30}\\=\frac{-134}{30}\\=\frac{-67}{15}\)
12. \(+\left(\frac{-3}{7}\right) -\left(\frac{9}{-2}\right) -\left(\frac{-9}{6}\right)\\= \frac{-3}{7}+ \frac{9}{2}+\frac{9}{6}\\=\frac{-3}{7}+\frac{9}{2}+\frac{3}{2}\\=\frac{-6}{14}+\frac{63}{14}+\frac{21}{14}\\=\frac{-6+63+21}{14}\\=\frac{78}{14}\\=\frac{39}{7}\)