Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{-7}\right) +\left(\frac{3}{-7}\right) -\left(\frac{8}{-11}\right)\\= \frac{-10}{7}- \frac{3}{7}+\frac{8}{11}\\=\frac{-110}{77}-\frac{33}{77}+\frac{56}{77}\\=\frac{-110-33+56}{77}\\=\frac{-87}{77}\)
2. \(-\left(\frac{-8}{-7}\right) -\left(\frac{-5}{2}\right) -\left(\frac{3}{-5}\right)\\= \frac{-8}{7}+ \frac{5}{2}+\frac{3}{5}\\=\frac{-80}{70}+\frac{175}{70}+\frac{42}{70}\\=\frac{-80+175+42}{70}\\=\frac{137}{70}\)
3. \(-\left(\frac{-4}{-7}\right) +\left(\frac{-5}{6}\right) +\left(\frac{-8}{-8}\right)\\= \frac{-4}{7}- \frac{5}{6}+\frac{8}{8}\\=\frac{-4}{7}-\frac{5}{6}+\frac{1}{1}\\=\frac{-24}{42}-\frac{35}{42}+\frac{42}{42}\\=\frac{-24-35+42}{42}\\=\frac{-17}{42}\)
4. \(-\left(\frac{-8}{-3}\right) -\left(\frac{6}{8}\right) +\left(\frac{-3}{-9}\right)\\= \frac{-8}{3}- \frac{6}{8}+\frac{3}{9}\\=\frac{-8}{3}-\frac{3}{4}+\frac{1}{3}\\=\frac{-32}{12}-\frac{9}{12}+\frac{4}{12}\\=\frac{-32-9+4}{12}\\=\frac{-37}{12}\)
5. \(+\left(\frac{-6}{5}\right) +\left(\frac{-8}{6}\right) -\left(\frac{10}{5}\right)\\= \frac{-6}{5}- \frac{8}{6}-\frac{10}{5}\\=\frac{-6}{5}-\frac{4}{3}-\frac{2}{1}\\=\frac{-18}{15}-\frac{20}{15}-\frac{30}{15}\\=\frac{-18-20-30}{15}\\=\frac{-68}{15}\)
6. \(-\left(\frac{-5}{3}\right) -\left(\frac{4}{7}\right) +\left(\frac{11}{-8}\right)\\= \frac{5}{3}- \frac{4}{7}-\frac{11}{8}\\=\frac{280}{168}-\frac{96}{168}-\frac{231}{168}\\=\frac{280-96-231}{168}\\=\frac{-47}{168}\)
7. \(-\left(\frac{-4}{3}\right) -\left(\frac{-4}{-3}\right) +\left(\frac{9}{-3}\right)\\= \frac{4}{3}- \frac{4}{3}-\frac{9}{3}\\=\frac{4}{3}-\frac{4}{3}-\frac{3}{1}\\=\frac{4-4-3}{3}\\=\frac{-3}{3}\\=\frac{-1}{1}\)
8. \(+\left(\frac{-3}{-5}\right) +\left(\frac{8}{-8}\right) -\left(\frac{-8}{7}\right)\\= \frac{3}{5}- \frac{8}{8}+\frac{8}{7}\\=\frac{3}{5}-\frac{1}{1}+\frac{8}{7}\\=\frac{21}{35}-\frac{35}{35}+\frac{40}{35}\\=\frac{21-35+40}{35}\\=\frac{26}{35}\)
9. \(+\left(\frac{6}{5}\right) -\left(\frac{5}{8}\right) +\left(\frac{11}{-5}\right)\\= \frac{6}{5}- \frac{5}{8}-\frac{11}{5}\\=\frac{48}{40}-\frac{25}{40}-\frac{88}{40}\\=\frac{48-25-88}{40}\\=\frac{-65}{40}\\=\frac{-13}{8}\)
10. \(+\left(\frac{-6}{-7}\right) +\left(\frac{-3}{-3}\right) +\left(\frac{6}{-2}\right)\\= \frac{6}{7}+ \frac{3}{3}-\frac{6}{2}\\=\frac{6}{7}+\frac{1}{1}-\frac{3}{1}\\=\frac{6+1-3}{7}\\=\frac{4}{7}\)
11. \(+\left(\frac{-3}{4}\right) -\left(\frac{5}{5}\right) +\left(\frac{7}{-10}\right)\\= \frac{-3}{4}- \frac{5}{5}-\frac{7}{10}\\=\frac{-3}{4}-\frac{1}{1}-\frac{7}{10}\\=\frac{-15}{20}-\frac{20}{20}-\frac{14}{20}\\=\frac{-15-20-14}{20}\\=\frac{-49}{20}\)
12. \(-\left(\frac{-6}{7}\right) +\left(\frac{3}{4}\right) +\left(\frac{-5}{-9}\right)\\= \frac{6}{7}+ \frac{3}{4}+\frac{5}{9}\\=\frac{216}{252}+\frac{189}{252}+\frac{140}{252}\\=\frac{216+189+140}{252}\\=\frac{545}{252}\)