Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{3}{4}\right) +\left(\frac{3}{3}\right) +\left(\frac{4}{-4}\right)\\= \frac{-3}{4}+ \frac{3}{3}-\frac{4}{4}\\=\frac{-3}{4}+\frac{1}{1}-\frac{1}{1}\\=\frac{-3+1-1}{4}\\=\frac{-3}{4}\)
2. \(+\left(\frac{-2}{-3}\right) +\left(\frac{-5}{-9}\right) +\left(\frac{-11}{5}\right)\\= \frac{2}{3}+ \frac{5}{9}-\frac{11}{5}\\=\frac{30}{45}+\frac{25}{45}-\frac{99}{45}\\=\frac{30+25-99}{45}\\=\frac{-44}{45}\)
3. \(-\left(\frac{3}{-5}\right) +\left(\frac{6}{10}\right) +\left(\frac{7}{6}\right)\\= \frac{3}{5}+ \frac{6}{10}+\frac{7}{6}\\=\frac{3}{5}+\frac{3}{5}+\frac{7}{6}\\=\frac{18}{30}+\frac{18}{30}+\frac{35}{30}\\=\frac{18+18+35}{30}\\=\frac{71}{30}\)
4. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-10}{10}\right) -\left(\frac{-7}{-6}\right)\\= \frac{6}{5}- \frac{10}{10}-\frac{7}{6}\\=\frac{6}{5}-\frac{1}{1}-\frac{7}{6}\\=\frac{36}{30}-\frac{30}{30}-\frac{35}{30}\\=\frac{36-30-35}{30}\\=\frac{-29}{30}\)
5. \(-\left(\frac{-7}{-3}\right) +\left(\frac{4}{-3}\right) +\left(\frac{9}{10}\right)\\= \frac{-7}{3}- \frac{4}{3}+\frac{9}{10}\\=\frac{-70}{30}-\frac{40}{30}+\frac{27}{30}\\=\frac{-70-40+27}{30}\\=\frac{-83}{30}\)
6. \(-\left(\frac{2}{3}\right) +\left(\frac{-7}{8}\right) -\left(\frac{-10}{8}\right)\\= \frac{-2}{3}- \frac{7}{8}+\frac{10}{8}\\=\frac{-2}{3}-\frac{7}{8}+\frac{5}{4}\\=\frac{-16}{24}-\frac{21}{24}+\frac{30}{24}\\=\frac{-16-21+30}{24}\\=\frac{-7}{24}\)
7. \(+\left(\frac{-9}{2}\right) -\left(\frac{-6}{-2}\right) +\left(\frac{9}{-5}\right)\\= \frac{-9}{2}- \frac{6}{2}-\frac{9}{5}\\=\frac{-9}{2}-\frac{3}{1}-\frac{9}{5}\\=\frac{-45}{10}-\frac{30}{10}-\frac{18}{10}\\=\frac{-45-30-18}{10}\\=\frac{-93}{10}\)
8. \(-\left(\frac{-4}{-3}\right) -\left(\frac{-6}{8}\right) -\left(\frac{-10}{3}\right)\\= \frac{-4}{3}+ \frac{6}{8}+\frac{10}{3}\\=\frac{-4}{3}+\frac{3}{4}+\frac{10}{3}\\=\frac{-16}{12}+\frac{9}{12}+\frac{40}{12}\\=\frac{-16+9+40}{12}\\=\frac{33}{12}\\=\frac{11}{4}\)
9. \(+\left(\frac{-8}{-7}\right) -\left(\frac{4}{7}\right) +\left(\frac{-3}{-6}\right)\\= \frac{8}{7}- \frac{4}{7}+\frac{3}{6}\\=\frac{8}{7}-\frac{4}{7}+\frac{1}{2}\\=\frac{16}{14}-\frac{8}{14}+\frac{7}{14}\\=\frac{16-8+7}{14}\\=\frac{15}{14}\)
10. \(+\left(\frac{9}{-2}\right) -\left(\frac{10}{9}\right) +\left(\frac{-12}{-5}\right)\\= \frac{-9}{2}- \frac{10}{9}+\frac{12}{5}\\=\frac{-405}{90}-\frac{100}{90}+\frac{216}{90}\\=\frac{-405-100+216}{90}\\=\frac{-289}{90}\)
11. \(+\left(\frac{-3}{7}\right) +\left(\frac{8}{3}\right) -\left(\frac{-8}{-9}\right)\\= \frac{-3}{7}+ \frac{8}{3}-\frac{8}{9}\\=\frac{-27}{63}+\frac{168}{63}-\frac{56}{63}\\=\frac{-27+168-56}{63}\\=\frac{85}{63}\)
12. \(-\left(\frac{10}{-7}\right) +\left(\frac{-8}{-8}\right) +\left(\frac{11}{2}\right)\\= \frac{10}{7}+ \frac{8}{8}+\frac{11}{2}\\=\frac{10}{7}+\frac{1}{1}+\frac{11}{2}\\=\frac{20}{14}+\frac{14}{14}+\frac{77}{14}\\=\frac{20+14+77}{14}\\=\frac{111}{14}\)