Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{4}{-9}\right) -\left(\frac{8}{-9}\right) +\left(\frac{11}{12}\right)\\= \frac{-4}{9}+ \frac{8}{9}+\frac{11}{12}\\=\frac{-16}{36}+\frac{32}{36}+\frac{33}{36}\\=\frac{-16+32+33}{36}\\=\frac{49}{36}\)
2. \(-\left(\frac{4}{5}\right) +\left(\frac{-2}{-5}\right) -\left(\frac{-7}{11}\right)\\= \frac{-4}{5}+ \frac{2}{5}+\frac{7}{11}\\=\frac{-44}{55}+\frac{22}{55}+\frac{35}{55}\\=\frac{-44+22+35}{55}\\=\frac{13}{55}\)
3. \(+\left(\frac{4}{3}\right) +\left(\frac{6}{-5}\right) +\left(\frac{6}{-10}\right)\\= \frac{4}{3}- \frac{6}{5}-\frac{6}{10}\\=\frac{4}{3}-\frac{6}{5}-\frac{3}{5}\\=\frac{20}{15}-\frac{18}{15}-\frac{9}{15}\\=\frac{20-18-9}{15}\\=\frac{-7}{15}\)
4. \(+\left(\frac{8}{3}\right) -\left(\frac{-10}{-8}\right) +\left(\frac{3}{11}\right)\\= \frac{8}{3}- \frac{10}{8}+\frac{3}{11}\\=\frac{8}{3}-\frac{5}{4}+\frac{3}{11}\\=\frac{352}{132}-\frac{165}{132}+\frac{36}{132}\\=\frac{352-165+36}{132}\\=\frac{223}{132}\)
5. \(-\left(\frac{-3}{2}\right) -\left(\frac{-2}{4}\right) -\left(\frac{-11}{12}\right)\\= \frac{3}{2}+ \frac{2}{4}+\frac{11}{12}\\=\frac{3}{2}+\frac{1}{2}+\frac{11}{12}\\=\frac{18}{12}+\frac{6}{12}+\frac{11}{12}\\=\frac{18+6+11}{12}\\=\frac{35}{12}\)
6. \(+\left(\frac{4}{5}\right) +\left(\frac{-7}{4}\right) +\left(\frac{3}{5}\right)\\= \frac{4}{5}- \frac{7}{4}+\frac{3}{5}\\=\frac{16}{20}-\frac{35}{20}+\frac{12}{20}\\=\frac{16-35+12}{20}\\=\frac{-7}{20}\)
7. \(+\left(\frac{9}{-7}\right) -\left(\frac{-2}{9}\right) +\left(\frac{-7}{2}\right)\\= \frac{-9}{7}+ \frac{2}{9}-\frac{7}{2}\\=\frac{-162}{126}+\frac{28}{126}-\frac{441}{126}\\=\frac{-162+28-441}{126}\\=\frac{-575}{126}\)
8. \(-\left(\frac{2}{7}\right) +\left(\frac{2}{3}\right) +\left(\frac{2}{-6}\right)\\= \frac{-2}{7}+ \frac{2}{3}-\frac{2}{6}\\=\frac{-2}{7}+\frac{2}{3}-\frac{1}{3}\\=\frac{-6}{21}+\frac{14}{21}-\frac{7}{21}\\=\frac{-6+14-7}{21}\\=\frac{1}{21}\)
9. \(+\left(\frac{7}{-8}\right) +\left(\frac{-2}{-5}\right) -\left(\frac{-5}{7}\right)\\= \frac{-7}{8}+ \frac{2}{5}+\frac{5}{7}\\=\frac{-245}{280}+\frac{112}{280}+\frac{200}{280}\\=\frac{-245+112+200}{280}\\=\frac{67}{280}\)
10. \(+\left(\frac{-4}{5}\right) +\left(\frac{-8}{9}\right) +\left(\frac{-5}{11}\right)\\= \frac{-4}{5}- \frac{8}{9}-\frac{5}{11}\\=\frac{-396}{495}-\frac{440}{495}-\frac{225}{495}\\=\frac{-396-440-225}{495}\\=\frac{-1061}{495}\)
11. \(-\left(\frac{2}{-3}\right) +\left(\frac{-4}{-3}\right) -\left(\frac{-2}{2}\right)\\= \frac{2}{3}+ \frac{4}{3}+\frac{2}{2}\\=\frac{2}{3}+\frac{4}{3}+\frac{1}{1}\\=\frac{2+4+1}{3}\\=\frac{7}{3}\)
12. \(+\left(\frac{5}{9}\right) -\left(\frac{-9}{7}\right) -\left(\frac{4}{-6}\right)\\= \frac{5}{9}+ \frac{9}{7}+\frac{4}{6}\\=\frac{5}{9}+\frac{9}{7}+\frac{2}{3}\\=\frac{35}{63}+\frac{81}{63}+\frac{42}{63}\\=\frac{35+81+42}{63}\\=\frac{158}{63}\)