Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{6}{-5}\right) +\left(\frac{-5}{10}\right) -\left(\frac{-2}{2}\right)\\= \frac{6}{5}- \frac{5}{10}+\frac{2}{2}\\=\frac{6}{5}-\frac{1}{2}+\frac{1}{1}\\=\frac{12}{10}-\frac{5}{10}+\frac{10}{10}\\=\frac{12-5+10}{10}\\=\frac{17}{10}\)
2. \(-\left(\frac{2}{9}\right) -\left(\frac{-10}{-6}\right) -\left(\frac{-2}{-8}\right)\\= \frac{-2}{9}- \frac{10}{6}-\frac{2}{8}\\=\frac{-2}{9}-\frac{5}{3}-\frac{1}{4}\\=\frac{-8}{36}-\frac{60}{36}-\frac{9}{36}\\=\frac{-8-60-9}{36}\\=\frac{-77}{36}\)
3. \(+\left(\frac{2}{9}\right) +\left(\frac{10}{-4}\right) -\left(\frac{10}{4}\right)\\= \frac{2}{9}- \frac{10}{4}-\frac{10}{4}\\=\frac{2}{9}-\frac{5}{2}-\frac{5}{2}\\=\frac{4}{18}-\frac{45}{18}-\frac{45}{18}\\=\frac{4-45-45}{18}\\=\frac{-86}{18}\\=\frac{-43}{9}\)
4. \(-\left(\frac{-10}{7}\right) -\left(\frac{9}{-2}\right) +\left(\frac{-10}{-8}\right)\\= \frac{10}{7}+ \frac{9}{2}+\frac{10}{8}\\=\frac{10}{7}+\frac{9}{2}+\frac{5}{4}\\=\frac{40}{28}+\frac{126}{28}+\frac{35}{28}\\=\frac{40+126+35}{28}\\=\frac{201}{28}\)
5. \(+\left(\frac{-8}{-3}\right) +\left(\frac{-10}{8}\right) +\left(\frac{9}{3}\right)\\= \frac{8}{3}- \frac{10}{8}+\frac{9}{3}\\=\frac{8}{3}-\frac{5}{4}+\frac{3}{1}\\=\frac{32}{12}-\frac{15}{12}+\frac{36}{12}\\=\frac{32-15+36}{12}\\=\frac{53}{12}\)
6. \(-\left(\frac{5}{-6}\right) -\left(\frac{-6}{-7}\right) +\left(\frac{-4}{11}\right)\\= \frac{5}{6}- \frac{6}{7}-\frac{4}{11}\\=\frac{385}{462}-\frac{396}{462}-\frac{168}{462}\\=\frac{385-396-168}{462}\\=\frac{-179}{462}\)
7. \(+\left(\frac{3}{7}\right) -\left(\frac{-4}{-2}\right) -\left(\frac{-2}{2}\right)\\= \frac{3}{7}- \frac{4}{2}+\frac{2}{2}\\=\frac{3}{7}-\frac{2}{1}+\frac{1}{1}\\=\frac{3-2+1}{7}\\=\frac{2}{7}\)
8. \(+\left(\frac{-9}{-4}\right) +\left(\frac{-10}{4}\right) -\left(\frac{-7}{2}\right)\\= \frac{9}{4}- \frac{10}{4}+\frac{7}{2}\\=\frac{9}{4}-\frac{5}{2}+\frac{7}{2}\\=\frac{9-5+7}{4}\\=\frac{11}{4}\)
9. \(+\left(\frac{-5}{-3}\right) +\left(\frac{-5}{2}\right) -\left(\frac{6}{8}\right)\\= \frac{5}{3}- \frac{5}{2}-\frac{6}{8}\\=\frac{5}{3}-\frac{5}{2}-\frac{3}{4}\\=\frac{20}{12}-\frac{30}{12}-\frac{9}{12}\\=\frac{20-30-9}{12}\\=\frac{-19}{12}\)
10. \(-\left(\frac{3}{-7}\right) -\left(\frac{-6}{3}\right) +\left(\frac{-3}{-12}\right)\\= \frac{3}{7}+ \frac{6}{3}+\frac{3}{12}\\=\frac{3}{7}+\frac{2}{1}+\frac{1}{4}\\=\frac{12}{28}+\frac{56}{28}+\frac{7}{28}\\=\frac{12+56+7}{28}\\=\frac{75}{28}\)
11. \(-\left(\frac{6}{5}\right) +\left(\frac{2}{-3}\right) +\left(\frac{6}{-12}\right)\\= \frac{-6}{5}- \frac{2}{3}-\frac{6}{12}\\=\frac{-6}{5}-\frac{2}{3}-\frac{1}{2}\\=\frac{-36}{30}-\frac{20}{30}-\frac{15}{30}\\=\frac{-36-20-15}{30}\\=\frac{-71}{30}\)
12. \(+\left(\frac{10}{-7}\right) +\left(\frac{-7}{10}\right) +\left(\frac{-5}{-2}\right)\\= \frac{-10}{7}- \frac{7}{10}+\frac{5}{2}\\=\frac{-100}{70}-\frac{49}{70}+\frac{175}{70}\\=\frac{-100-49+175}{70}\\=\frac{26}{70}\\=\frac{13}{35}\)