Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{2}\right) -\left(\frac{-10}{4}\right) -\left(\frac{-3}{-12}\right)\\= \frac{9}{2}+ \frac{10}{4}-\frac{3}{12}\\=\frac{9}{2}+\frac{5}{2}-\frac{1}{4}\\=\frac{18}{4}+\frac{10}{4}-\frac{1}{4}\\=\frac{18+10-1}{4}\\=\frac{27}{4}\)
2. \(-\left(\frac{-10}{-3}\right) -\left(\frac{9}{-6}\right) +\left(\frac{3}{-3}\right)\\= \frac{-10}{3}+ \frac{9}{6}-\frac{3}{3}\\=\frac{-10}{3}+\frac{3}{2}-\frac{1}{1}\\=\frac{-20}{6}+\frac{9}{6}-\frac{6}{6}\\=\frac{-20+9-6}{6}\\=\frac{-17}{6}\)
3. \(+\left(\frac{-3}{-2}\right) +\left(\frac{9}{-3}\right) -\left(\frac{-3}{-10}\right)\\= \frac{3}{2}- \frac{9}{3}-\frac{3}{10}\\=\frac{3}{2}-\frac{3}{1}-\frac{3}{10}\\=\frac{15}{10}-\frac{30}{10}-\frac{3}{10}\\=\frac{15-30-3}{10}\\=\frac{-18}{10}\\=\frac{-9}{5}\)
4. \(+\left(\frac{-7}{-8}\right) +\left(\frac{8}{6}\right) -\left(\frac{-11}{11}\right)\\= \frac{7}{8}+ \frac{8}{6}+\frac{11}{11}\\=\frac{7}{8}+\frac{4}{3}+\frac{1}{1}\\=\frac{21}{24}+\frac{32}{24}+\frac{24}{24}\\=\frac{21+32+24}{24}\\=\frac{77}{24}\)
5. \(-\left(\frac{7}{-4}\right) -\left(\frac{-8}{-10}\right) -\left(\frac{11}{8}\right)\\= \frac{7}{4}- \frac{8}{10}-\frac{11}{8}\\=\frac{7}{4}-\frac{4}{5}-\frac{11}{8}\\=\frac{70}{40}-\frac{32}{40}-\frac{55}{40}\\=\frac{70-32-55}{40}\\=\frac{-17}{40}\)
6. \(-\left(\frac{9}{-7}\right) +\left(\frac{-6}{-5}\right) -\left(\frac{4}{-8}\right)\\= \frac{9}{7}+ \frac{6}{5}+\frac{4}{8}\\=\frac{9}{7}+\frac{6}{5}+\frac{1}{2}\\=\frac{90}{70}+\frac{84}{70}+\frac{35}{70}\\=\frac{90+84+35}{70}\\=\frac{209}{70}\)
7. \(-\left(\frac{-4}{-7}\right) -\left(\frac{-7}{-4}\right) -\left(\frac{-11}{9}\right)\\= \frac{-4}{7}- \frac{7}{4}+\frac{11}{9}\\=\frac{-144}{252}-\frac{441}{252}+\frac{308}{252}\\=\frac{-144-441+308}{252}\\=\frac{-277}{252}\)
8. \(-\left(\frac{-5}{-8}\right) -\left(\frac{-8}{-4}\right) +\left(\frac{9}{-8}\right)\\= \frac{-5}{8}- \frac{8}{4}-\frac{9}{8}\\=\frac{-5}{8}-\frac{2}{1}-\frac{9}{8}\\=\frac{-5-2-9}{8}\\=\frac{-16}{8}\\=\frac{-2}{1}\)
9. \(-\left(\frac{6}{5}\right) +\left(\frac{-8}{3}\right) -\left(\frac{-11}{-6}\right)\\= \frac{-6}{5}- \frac{8}{3}-\frac{11}{6}\\=\frac{-36}{30}-\frac{80}{30}-\frac{55}{30}\\=\frac{-36-80-55}{30}\\=\frac{-171}{30}\\=\frac{-57}{10}\)
10. \(-\left(\frac{-2}{-7}\right) -\left(\frac{-9}{8}\right) +\left(\frac{-11}{-9}\right)\\= \frac{-2}{7}+ \frac{9}{8}+\frac{11}{9}\\=\frac{-144}{504}+\frac{567}{504}+\frac{616}{504}\\=\frac{-144+567+616}{504}\\=\frac{1039}{504}\)
11. \(+\left(\frac{10}{-7}\right) +\left(\frac{5}{8}\right) -\left(\frac{-12}{5}\right)\\= \frac{-10}{7}+ \frac{5}{8}+\frac{12}{5}\\=\frac{-400}{280}+\frac{175}{280}+\frac{672}{280}\\=\frac{-400+175+672}{280}\\=\frac{447}{280}\)
12. \(-\left(\frac{-5}{6}\right) +\left(\frac{-4}{4}\right) -\left(\frac{6}{-12}\right)\\= \frac{5}{6}- \frac{4}{4}+\frac{6}{12}\\=\frac{5}{6}-\frac{1}{1}+\frac{1}{2}\\=\frac{5-1+1}{6}\\=\frac{5}{6}\)