Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{6}{5}\right) +\left(\frac{10}{4}\right) +\left(\frac{-6}{6}\right)\\= \frac{-6}{5}+ \frac{10}{4}-\frac{6}{6}\\=\frac{-6}{5}+\frac{5}{2}-\frac{1}{1}\\=\frac{-12}{10}+\frac{25}{10}-\frac{10}{10}\\=\frac{-12+25-10}{10}\\=\frac{3}{10}\)
2. \(-\left(\frac{8}{7}\right) -\left(\frac{-8}{-10}\right) +\left(\frac{2}{-11}\right)\\= \frac{-8}{7}- \frac{8}{10}-\frac{2}{11}\\=\frac{-8}{7}-\frac{4}{5}-\frac{2}{11}\\=\frac{-440}{385}-\frac{308}{385}-\frac{70}{385}\\=\frac{-440-308-70}{385}\\=\frac{-818}{385}\)
3. \(-\left(\frac{-9}{4}\right) +\left(\frac{-2}{-5}\right) +\left(\frac{9}{-12}\right)\\= \frac{9}{4}+ \frac{2}{5}-\frac{9}{12}\\=\frac{9}{4}+\frac{2}{5}-\frac{3}{4}\\=\frac{45}{20}+\frac{8}{20}-\frac{15}{20}\\=\frac{45+8-15}{20}\\=\frac{38}{20}\\=\frac{19}{10}\)
4. \(-\left(\frac{5}{-2}\right) +\left(\frac{3}{7}\right) +\left(\frac{9}{-2}\right)\\= \frac{5}{2}+ \frac{3}{7}-\frac{9}{2}\\=\frac{35}{14}+\frac{6}{14}-\frac{63}{14}\\=\frac{35+6-63}{14}\\=\frac{-22}{14}\\=\frac{-11}{7}\)
5. \(+\left(\frac{-4}{-9}\right) -\left(\frac{7}{4}\right) -\left(\frac{5}{2}\right)\\= \frac{4}{9}- \frac{7}{4}-\frac{5}{2}\\=\frac{16}{36}-\frac{63}{36}-\frac{90}{36}\\=\frac{16-63-90}{36}\\=\frac{-137}{36}\)
6. \(-\left(\frac{5}{3}\right) -\left(\frac{4}{-5}\right) -\left(\frac{8}{8}\right)\\= \frac{-5}{3}+ \frac{4}{5}-\frac{8}{8}\\=\frac{-5}{3}+\frac{4}{5}-\frac{1}{1}\\=\frac{-25}{15}+\frac{12}{15}-\frac{15}{15}\\=\frac{-25+12-15}{15}\\=\frac{-28}{15}\)
7. \(-\left(\frac{9}{5}\right) +\left(\frac{-10}{-9}\right) -\left(\frac{-3}{-5}\right)\\= \frac{-9}{5}+ \frac{10}{9}-\frac{3}{5}\\=\frac{-81}{45}+\frac{50}{45}-\frac{27}{45}\\=\frac{-81+50-27}{45}\\=\frac{-58}{45}\)
8. \(+\left(\frac{6}{-5}\right) +\left(\frac{10}{5}\right) -\left(\frac{11}{5}\right)\\= \frac{-6}{5}+ \frac{10}{5}-\frac{11}{5}\\=\frac{-6}{5}+\frac{2}{1}-\frac{11}{5}\\=\frac{-6+2-11}{5}\\=\frac{-15}{5}\\=\frac{-3}{1}\)
9. \(+\left(\frac{-8}{-7}\right) +\left(\frac{-9}{9}\right) +\left(\frac{-4}{2}\right)\\= \frac{8}{7}- \frac{9}{9}-\frac{4}{2}\\=\frac{8}{7}-\frac{1}{1}-\frac{2}{1}\\=\frac{8-1-2}{7}\\=\frac{5}{7}\)
10. \(-\left(\frac{-5}{8}\right) -\left(\frac{-10}{-7}\right) +\left(\frac{8}{-2}\right)\\= \frac{5}{8}- \frac{10}{7}-\frac{8}{2}\\=\frac{5}{8}-\frac{10}{7}-\frac{4}{1}\\=\frac{35}{56}-\frac{80}{56}-\frac{224}{56}\\=\frac{35-80-224}{56}\\=\frac{-269}{56}\)
11. \(-\left(\frac{-3}{-7}\right) -\left(\frac{-4}{4}\right) -\left(\frac{5}{8}\right)\\= \frac{-3}{7}+ \frac{4}{4}-\frac{5}{8}\\=\frac{-3}{7}+\frac{1}{1}-\frac{5}{8}\\=\frac{-24}{56}+\frac{56}{56}-\frac{35}{56}\\=\frac{-24+56-35}{56}\\=\frac{-3}{56}\)
12. \(+\left(\frac{2}{-3}\right) -\left(\frac{-2}{9}\right) -\left(\frac{11}{-3}\right)\\= \frac{-2}{3}+ \frac{2}{9}+\frac{11}{3}\\=\frac{-6}{9}+\frac{2}{9}+\frac{33}{9}\\=\frac{-6+2+33}{9}\\=\frac{29}{9}\)