Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{-3}\right) +\left(\frac{-3}{5}\right) -\left(\frac{-8}{9}\right)\\= \frac{-2}{3}- \frac{3}{5}+\frac{8}{9}\\=\frac{-30}{45}-\frac{27}{45}+\frac{40}{45}\\=\frac{-30-27+40}{45}\\=\frac{-17}{45}\)
2. \(-\left(\frac{-8}{-5}\right) +\left(\frac{7}{-8}\right) +\left(\frac{8}{-11}\right)\\= \frac{-8}{5}- \frac{7}{8}-\frac{8}{11}\\=\frac{-704}{440}-\frac{385}{440}-\frac{320}{440}\\=\frac{-704-385-320}{440}\\=\frac{-1409}{440}\)
3. \(-\left(\frac{-10}{-7}\right) -\left(\frac{5}{-4}\right) +\left(\frac{3}{-5}\right)\\= \frac{-10}{7}+ \frac{5}{4}-\frac{3}{5}\\=\frac{-200}{140}+\frac{175}{140}-\frac{84}{140}\\=\frac{-200+175-84}{140}\\=\frac{-109}{140}\)
4. \(+\left(\frac{-7}{-9}\right) +\left(\frac{-3}{-6}\right) -\left(\frac{12}{-8}\right)\\= \frac{7}{9}+ \frac{3}{6}+\frac{12}{8}\\=\frac{7}{9}+\frac{1}{2}+\frac{3}{2}\\=\frac{14}{18}+\frac{9}{18}+\frac{27}{18}\\=\frac{14+9+27}{18}\\=\frac{50}{18}\\=\frac{25}{9}\)
5. \(-\left(\frac{2}{7}\right) -\left(\frac{-6}{-8}\right) +\left(\frac{-3}{-8}\right)\\= \frac{-2}{7}- \frac{6}{8}+\frac{3}{8}\\=\frac{-2}{7}-\frac{3}{4}+\frac{3}{8}\\=\frac{-16}{56}-\frac{42}{56}+\frac{21}{56}\\=\frac{-16-42+21}{56}\\=\frac{-37}{56}\)
6. \(-\left(\frac{6}{5}\right) +\left(\frac{8}{8}\right) -\left(\frac{-4}{-8}\right)\\= \frac{-6}{5}+ \frac{8}{8}-\frac{4}{8}\\=\frac{-6}{5}+\frac{1}{1}-\frac{1}{2}\\=\frac{-12}{10}+\frac{10}{10}-\frac{5}{10}\\=\frac{-12+10-5}{10}\\=\frac{-7}{10}\)
7. \(-\left(\frac{-10}{-7}\right) +\left(\frac{7}{8}\right) -\left(\frac{-12}{-9}\right)\\= \frac{-10}{7}+ \frac{7}{8}-\frac{12}{9}\\=\frac{-10}{7}+\frac{7}{8}-\frac{4}{3}\\=\frac{-240}{168}+\frac{147}{168}-\frac{224}{168}\\=\frac{-240+147-224}{168}\\=\frac{-317}{168}\)
8. \(+\left(\frac{3}{-8}\right) -\left(\frac{-7}{-2}\right) -\left(\frac{10}{-3}\right)\\= \frac{-3}{8}- \frac{7}{2}+\frac{10}{3}\\=\frac{-9}{24}-\frac{84}{24}+\frac{80}{24}\\=\frac{-9-84+80}{24}\\=\frac{-13}{24}\)
9. \(-\left(\frac{6}{5}\right) -\left(\frac{4}{-3}\right) -\left(\frac{-11}{7}\right)\\= \frac{-6}{5}+ \frac{4}{3}+\frac{11}{7}\\=\frac{-126}{105}+\frac{140}{105}+\frac{165}{105}\\=\frac{-126+140+165}{105}\\=\frac{179}{105}\)
10. \(-\left(\frac{-4}{3}\right) +\left(\frac{5}{10}\right) -\left(\frac{3}{6}\right)\\= \frac{4}{3}+ \frac{5}{10}-\frac{3}{6}\\=\frac{4}{3}+\frac{1}{2}-\frac{1}{2}\\=\frac{8}{6}+\frac{3}{6}-\frac{3}{6}\\=\frac{8+3-3}{6}\\=\frac{8}{6}\\=\frac{4}{3}\)
11. \(+\left(\frac{2}{5}\right) -\left(\frac{10}{-10}\right) -\left(\frac{2}{11}\right)\\= \frac{2}{5}+ \frac{10}{10}-\frac{2}{11}\\=\frac{2}{5}+\frac{1}{1}-\frac{2}{11}\\=\frac{22}{55}+\frac{55}{55}-\frac{10}{55}\\=\frac{22+55-10}{55}\\=\frac{67}{55}\)
12. \(-\left(\frac{8}{-9}\right) +\left(\frac{-10}{-10}\right) +\left(\frac{-11}{9}\right)\\= \frac{8}{9}+ \frac{10}{10}-\frac{11}{9}\\=\frac{8}{9}+\frac{1}{1}-\frac{11}{9}\\=\frac{8+1-11}{9}\\=\frac{-2}{9}\)