Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{4}\right) -\left(\frac{-4}{8}\right) +\left(\frac{6}{8}\right)\\= \frac{-3}{4}+ \frac{4}{8}+\frac{6}{8}\\=\frac{-3}{4}+\frac{1}{2}+\frac{3}{4}\\=\frac{-3+1+3}{4}\\=\frac{1}{4}\)
2. \(-\left(\frac{5}{-3}\right) +\left(\frac{-8}{10}\right) -\left(\frac{-2}{8}\right)\\= \frac{5}{3}- \frac{8}{10}+\frac{2}{8}\\=\frac{5}{3}-\frac{4}{5}+\frac{1}{4}\\=\frac{100}{60}-\frac{48}{60}+\frac{15}{60}\\=\frac{100-48+15}{60}\\=\frac{67}{60}\)
3. \(+\left(\frac{10}{3}\right) +\left(\frac{5}{7}\right) +\left(\frac{6}{-12}\right)\\= \frac{10}{3}+ \frac{5}{7}-\frac{6}{12}\\=\frac{10}{3}+\frac{5}{7}-\frac{1}{2}\\=\frac{140}{42}+\frac{30}{42}-\frac{21}{42}\\=\frac{140+30-21}{42}\\=\frac{149}{42}\)
4. \(-\left(\frac{-4}{7}\right) -\left(\frac{-8}{-2}\right) +\left(\frac{-5}{10}\right)\\= \frac{4}{7}- \frac{8}{2}-\frac{5}{10}\\=\frac{4}{7}-\frac{4}{1}-\frac{1}{2}\\=\frac{8}{14}-\frac{56}{14}-\frac{7}{14}\\=\frac{8-56-7}{14}\\=\frac{-55}{14}\)
5. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-8}{-6}\right) +\left(\frac{10}{-9}\right)\\= \frac{6}{5}- \frac{8}{6}-\frac{10}{9}\\=\frac{6}{5}-\frac{4}{3}-\frac{10}{9}\\=\frac{54}{45}-\frac{60}{45}-\frac{50}{45}\\=\frac{54-60-50}{45}\\=\frac{-56}{45}\)
6. \(+\left(\frac{-6}{7}\right) +\left(\frac{10}{8}\right) -\left(\frac{4}{7}\right)\\= \frac{-6}{7}+ \frac{10}{8}-\frac{4}{7}\\=\frac{-6}{7}+\frac{5}{4}-\frac{4}{7}\\=\frac{-24}{28}+\frac{35}{28}-\frac{16}{28}\\=\frac{-24+35-16}{28}\\=\frac{-5}{28}\)
7. \(-\left(\frac{-2}{-9}\right) -\left(\frac{-7}{4}\right) -\left(\frac{5}{-11}\right)\\= \frac{-2}{9}+ \frac{7}{4}+\frac{5}{11}\\=\frac{-88}{396}+\frac{693}{396}+\frac{180}{396}\\=\frac{-88+693+180}{396}\\=\frac{785}{396}\)
8. \(-\left(\frac{8}{-3}\right) +\left(\frac{3}{5}\right) +\left(\frac{9}{-4}\right)\\= \frac{8}{3}+ \frac{3}{5}-\frac{9}{4}\\=\frac{160}{60}+\frac{36}{60}-\frac{135}{60}\\=\frac{160+36-135}{60}\\=\frac{61}{60}\)
9. \(+\left(\frac{10}{-3}\right) +\left(\frac{-2}{8}\right) +\left(\frac{10}{8}\right)\\= \frac{-10}{3}- \frac{2}{8}+\frac{10}{8}\\=\frac{-10}{3}-\frac{1}{4}+\frac{5}{4}\\=\frac{-40}{12}-\frac{3}{12}+\frac{15}{12}\\=\frac{-40-3+15}{12}\\=\frac{-28}{12}\\=\frac{-7}{3}\)
10. \(-\left(\frac{-7}{-8}\right) +\left(\frac{-10}{3}\right) -\left(\frac{11}{7}\right)\\= \frac{-7}{8}- \frac{10}{3}-\frac{11}{7}\\=\frac{-147}{168}-\frac{560}{168}-\frac{264}{168}\\=\frac{-147-560-264}{168}\\=\frac{-971}{168}\)
11. \(-\left(\frac{-6}{-5}\right) -\left(\frac{2}{2}\right) -\left(\frac{5}{10}\right)\\= \frac{-6}{5}- \frac{2}{2}-\frac{5}{10}\\=\frac{-6}{5}-\frac{1}{1}-\frac{1}{2}\\=\frac{-12}{10}-\frac{10}{10}-\frac{5}{10}\\=\frac{-12-10-5}{10}\\=\frac{-27}{10}\)
12. \(-\left(\frac{10}{7}\right) +\left(\frac{-4}{-9}\right) -\left(\frac{6}{2}\right)\\= \frac{-10}{7}+ \frac{4}{9}-\frac{6}{2}\\=\frac{-10}{7}+\frac{4}{9}-\frac{3}{1}\\=\frac{-90}{63}+\frac{28}{63}-\frac{189}{63}\\=\frac{-90+28-189}{63}\\=\frac{-251}{63}\)