Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{6}{5}\right) +\left(\frac{9}{5}\right) -\left(\frac{-6}{-11}\right)\\= \frac{-6}{5}+ \frac{9}{5}-\frac{6}{11}\\=\frac{-66}{55}+\frac{99}{55}-\frac{30}{55}\\=\frac{-66+99-30}{55}\\=\frac{3}{55}\)
2. \(-\left(\frac{-10}{3}\right) +\left(\frac{6}{2}\right) -\left(\frac{11}{11}\right)\\= \frac{10}{3}+ \frac{6}{2}-\frac{11}{11}\\=\frac{10}{3}+\frac{3}{1}-\frac{1}{1}\\=\frac{10+3-1}{3}\\=\frac{12}{3}\\=\frac{4}{1}\)
3. \(-\left(\frac{9}{-2}\right) -\left(\frac{-8}{4}\right) +\left(\frac{10}{2}\right)\\= \frac{9}{2}+ \frac{8}{4}+\frac{10}{2}\\=\frac{9}{2}+\frac{2}{1}+\frac{5}{1}\\=\frac{9+2+5}{2}\\=\frac{16}{2}\\=\frac{8}{1}\)
4. \(+\left(\frac{-7}{6}\right) +\left(\frac{-8}{-5}\right) +\left(\frac{-7}{7}\right)\\= \frac{-7}{6}+ \frac{8}{5}-\frac{7}{7}\\=\frac{-7}{6}+\frac{8}{5}-\frac{1}{1}\\=\frac{-35}{30}+\frac{48}{30}-\frac{30}{30}\\=\frac{-35+48-30}{30}\\=\frac{-17}{30}\)
5. \(-\left(\frac{8}{9}\right) +\left(\frac{8}{-9}\right) +\left(\frac{6}{-4}\right)\\= \frac{-8}{9}- \frac{8}{9}-\frac{6}{4}\\=\frac{-8}{9}-\frac{8}{9}-\frac{3}{2}\\=\frac{-16}{18}-\frac{16}{18}-\frac{27}{18}\\=\frac{-16-16-27}{18}\\=\frac{-59}{18}\)
6. \(-\left(\frac{2}{-9}\right) -\left(\frac{9}{-4}\right) +\left(\frac{2}{-12}\right)\\= \frac{2}{9}+ \frac{9}{4}-\frac{2}{12}\\=\frac{2}{9}+\frac{9}{4}-\frac{1}{6}\\=\frac{8}{36}+\frac{81}{36}-\frac{6}{36}\\=\frac{8+81-6}{36}\\=\frac{83}{36}\)
7. \(-\left(\frac{-10}{9}\right) -\left(\frac{-9}{2}\right) -\left(\frac{-7}{2}\right)\\= \frac{10}{9}+ \frac{9}{2}+\frac{7}{2}\\=\frac{20}{18}+\frac{81}{18}+\frac{63}{18}\\=\frac{20+81+63}{18}\\=\frac{164}{18}\\=\frac{82}{9}\)
8. \(-\left(\frac{5}{6}\right) +\left(\frac{8}{-4}\right) +\left(\frac{-7}{-6}\right)\\= \frac{-5}{6}- \frac{8}{4}+\frac{7}{6}\\=\frac{-5}{6}-\frac{2}{1}+\frac{7}{6}\\=\frac{-5-2+7}{6}\\=\frac{0}{6}\\=\frac{0}{1}\)
9. \(-\left(\frac{4}{-5}\right) -\left(\frac{5}{-10}\right) +\left(\frac{11}{-6}\right)\\= \frac{4}{5}+ \frac{5}{10}-\frac{11}{6}\\=\frac{4}{5}+\frac{1}{2}-\frac{11}{6}\\=\frac{24}{30}+\frac{15}{30}-\frac{55}{30}\\=\frac{24+15-55}{30}\\=\frac{-16}{30}\\=\frac{-8}{15}\)
10. \(+\left(\frac{3}{-2}\right) -\left(\frac{-10}{5}\right) -\left(\frac{-11}{7}\right)\\= \frac{-3}{2}+ \frac{10}{5}+\frac{11}{7}\\=\frac{-3}{2}+\frac{2}{1}+\frac{11}{7}\\=\frac{-21}{14}+\frac{28}{14}+\frac{22}{14}\\=\frac{-21+28+22}{14}\\=\frac{29}{14}\)
11. \(+\left(\frac{4}{-7}\right) +\left(\frac{8}{5}\right) -\left(\frac{11}{-7}\right)\\= \frac{-4}{7}+ \frac{8}{5}+\frac{11}{7}\\=\frac{-20}{35}+\frac{56}{35}+\frac{55}{35}\\=\frac{-20+56+55}{35}\\=\frac{91}{35}\\=\frac{13}{5}\)
12. \(-\left(\frac{-9}{5}\right) +\left(\frac{8}{7}\right) +\left(\frac{3}{-8}\right)\\= \frac{9}{5}+ \frac{8}{7}-\frac{3}{8}\\=\frac{504}{280}+\frac{320}{280}-\frac{105}{280}\\=\frac{504+320-105}{280}\\=\frac{719}{280}\)