Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{10}{9}\right) +\left(\frac{9}{4}\right) +\left(\frac{-5}{8}\right)\\= \frac{-10}{9}+ \frac{9}{4}-\frac{5}{8}\\=\frac{-80}{72}+\frac{162}{72}-\frac{45}{72}\\=\frac{-80+162-45}{72}\\=\frac{37}{72}\)
2. \(-\left(\frac{-6}{-7}\right) -\left(\frac{2}{-5}\right) -\left(\frac{4}{2}\right)\\= \frac{-6}{7}+ \frac{2}{5}-\frac{4}{2}\\=\frac{-6}{7}+\frac{2}{5}-\frac{2}{1}\\=\frac{-30}{35}+\frac{14}{35}-\frac{70}{35}\\=\frac{-30+14-70}{35}\\=\frac{-86}{35}\)
3. \(+\left(\frac{5}{7}\right) -\left(\frac{-7}{-6}\right) -\left(\frac{6}{-5}\right)\\= \frac{5}{7}- \frac{7}{6}+\frac{6}{5}\\=\frac{150}{210}-\frac{245}{210}+\frac{252}{210}\\=\frac{150-245+252}{210}\\=\frac{157}{210}\)
4. \(-\left(\frac{3}{2}\right) -\left(\frac{5}{-9}\right) +\left(\frac{11}{12}\right)\\= \frac{-3}{2}+ \frac{5}{9}+\frac{11}{12}\\=\frac{-54}{36}+\frac{20}{36}+\frac{33}{36}\\=\frac{-54+20+33}{36}\\=\frac{-1}{36}\)
5. \(+\left(\frac{2}{7}\right) -\left(\frac{-9}{7}\right) -\left(\frac{4}{11}\right)\\= \frac{2}{7}+ \frac{9}{7}-\frac{4}{11}\\=\frac{22}{77}+\frac{99}{77}-\frac{28}{77}\\=\frac{22+99-28}{77}\\=\frac{93}{77}\)
6. \(+\left(\frac{-8}{-3}\right) -\left(\frac{6}{2}\right) +\left(\frac{-2}{9}\right)\\= \frac{8}{3}- \frac{6}{2}-\frac{2}{9}\\=\frac{8}{3}-\frac{3}{1}-\frac{2}{9}\\=\frac{24}{9}-\frac{27}{9}-\frac{2}{9}\\=\frac{24-27-2}{9}\\=\frac{-5}{9}\)
7. \(+\left(\frac{-10}{3}\right) +\left(\frac{5}{-2}\right) +\left(\frac{-6}{-2}\right)\\= \frac{-10}{3}- \frac{5}{2}+\frac{6}{2}\\=\frac{-10}{3}-\frac{5}{2}+\frac{3}{1}\\=\frac{-20}{6}-\frac{15}{6}+\frac{18}{6}\\=\frac{-20-15+18}{6}\\=\frac{-17}{6}\)
8. \(+\left(\frac{-6}{5}\right) -\left(\frac{2}{6}\right) -\left(\frac{-7}{11}\right)\\= \frac{-6}{5}- \frac{2}{6}+\frac{7}{11}\\=\frac{-6}{5}-\frac{1}{3}+\frac{7}{11}\\=\frac{-198}{165}-\frac{55}{165}+\frac{105}{165}\\=\frac{-198-55+105}{165}\\=\frac{-148}{165}\)
9. \(+\left(\frac{-6}{7}\right) +\left(\frac{-9}{2}\right) -\left(\frac{-10}{11}\right)\\= \frac{-6}{7}- \frac{9}{2}+\frac{10}{11}\\=\frac{-132}{154}-\frac{693}{154}+\frac{140}{154}\\=\frac{-132-693+140}{154}\\=\frac{-685}{154}\)
10. \(+\left(\frac{-9}{2}\right) +\left(\frac{-5}{-4}\right) -\left(\frac{2}{5}\right)\\= \frac{-9}{2}+ \frac{5}{4}-\frac{2}{5}\\=\frac{-90}{20}+\frac{25}{20}-\frac{8}{20}\\=\frac{-90+25-8}{20}\\=\frac{-73}{20}\)
11. \(+\left(\frac{-6}{5}\right) -\left(\frac{10}{5}\right) -\left(\frac{-5}{-4}\right)\\= \frac{-6}{5}- \frac{10}{5}-\frac{5}{4}\\=\frac{-6}{5}-\frac{2}{1}-\frac{5}{4}\\=\frac{-24}{20}-\frac{40}{20}-\frac{25}{20}\\=\frac{-24-40-25}{20}\\=\frac{-89}{20}\)
12. \(-\left(\frac{-4}{5}\right) +\left(\frac{-5}{7}\right) +\left(\frac{5}{8}\right)\\= \frac{4}{5}- \frac{5}{7}+\frac{5}{8}\\=\frac{224}{280}-\frac{200}{280}+\frac{175}{280}\\=\frac{224-200+175}{280}\\=\frac{199}{280}\)