Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-8}{7}\right) +\left(\frac{-3}{8}\right) -\left(\frac{-11}{-2}\right)\\= \frac{8}{7}- \frac{3}{8}-\frac{11}{2}\\=\frac{64}{56}-\frac{21}{56}-\frac{308}{56}\\=\frac{64-21-308}{56}\\=\frac{-265}{56}\)
2. \(+\left(\frac{-2}{-7}\right) -\left(\frac{-7}{-7}\right) -\left(\frac{-3}{-4}\right)\\= \frac{2}{7}- \frac{7}{7}-\frac{3}{4}\\=\frac{2}{7}-\frac{1}{1}-\frac{3}{4}\\=\frac{8}{28}-\frac{28}{28}-\frac{21}{28}\\=\frac{8-28-21}{28}\\=\frac{-41}{28}\)
3. \(+\left(\frac{-5}{-7}\right) -\left(\frac{-7}{-7}\right) -\left(\frac{-5}{-2}\right)\\= \frac{5}{7}- \frac{7}{7}-\frac{5}{2}\\=\frac{5}{7}-\frac{1}{1}-\frac{5}{2}\\=\frac{10}{14}-\frac{14}{14}-\frac{35}{14}\\=\frac{10-14-35}{14}\\=\frac{-39}{14}\)
4. \(+\left(\frac{-8}{-3}\right) +\left(\frac{9}{9}\right) +\left(\frac{12}{-2}\right)\\= \frac{8}{3}+ \frac{9}{9}-\frac{12}{2}\\=\frac{8}{3}+\frac{1}{1}-\frac{6}{1}\\=\frac{8+1-6}{3}\\=\frac{3}{3}\\=\frac{1}{1}\)
5. \(-\left(\frac{-5}{-2}\right) -\left(\frac{-6}{-3}\right) -\left(\frac{9}{-10}\right)\\= \frac{-5}{2}- \frac{6}{3}+\frac{9}{10}\\=\frac{-5}{2}-\frac{2}{1}+\frac{9}{10}\\=\frac{-25}{10}-\frac{20}{10}+\frac{9}{10}\\=\frac{-25-20+9}{10}\\=\frac{-36}{10}\\=\frac{-18}{5}\)
6. \(+\left(\frac{-3}{-4}\right) +\left(\frac{-5}{5}\right) -\left(\frac{-9}{5}\right)\\= \frac{3}{4}- \frac{5}{5}+\frac{9}{5}\\=\frac{3}{4}-\frac{1}{1}+\frac{9}{5}\\=\frac{15}{20}-\frac{20}{20}+\frac{36}{20}\\=\frac{15-20+36}{20}\\=\frac{31}{20}\)
7. \(+\left(\frac{10}{3}\right) -\left(\frac{9}{-9}\right) +\left(\frac{10}{-8}\right)\\= \frac{10}{3}+ \frac{9}{9}-\frac{10}{8}\\=\frac{10}{3}+\frac{1}{1}-\frac{5}{4}\\=\frac{40}{12}+\frac{12}{12}-\frac{15}{12}\\=\frac{40+12-15}{12}\\=\frac{37}{12}\)
8. \(-\left(\frac{3}{-5}\right) +\left(\frac{6}{4}\right) -\left(\frac{12}{-6}\right)\\= \frac{3}{5}+ \frac{6}{4}+\frac{12}{6}\\=\frac{3}{5}+\frac{3}{2}+\frac{2}{1}\\=\frac{6}{10}+\frac{15}{10}+\frac{20}{10}\\=\frac{6+15+20}{10}\\=\frac{41}{10}\)
9. \(-\left(\frac{-7}{8}\right) +\left(\frac{-3}{3}\right) -\left(\frac{6}{10}\right)\\= \frac{7}{8}- \frac{3}{3}-\frac{6}{10}\\=\frac{7}{8}-\frac{1}{1}-\frac{3}{5}\\=\frac{35}{40}-\frac{40}{40}-\frac{24}{40}\\=\frac{35-40-24}{40}\\=\frac{-29}{40}\)
10. \(+\left(\frac{-4}{-7}\right) -\left(\frac{6}{6}\right) -\left(\frac{11}{6}\right)\\= \frac{4}{7}- \frac{6}{6}-\frac{11}{6}\\=\frac{4}{7}-\frac{1}{1}-\frac{11}{6}\\=\frac{24}{42}-\frac{42}{42}-\frac{77}{42}\\=\frac{24-42-77}{42}\\=\frac{-95}{42}\)
11. \(-\left(\frac{-7}{-9}\right) +\left(\frac{-7}{5}\right) -\left(\frac{-12}{6}\right)\\= \frac{-7}{9}- \frac{7}{5}+\frac{12}{6}\\=\frac{-7}{9}-\frac{7}{5}+\frac{2}{1}\\=\frac{-35}{45}-\frac{63}{45}+\frac{90}{45}\\=\frac{-35-63+90}{45}\\=\frac{-8}{45}\)
12. \(-\left(\frac{3}{-5}\right) +\left(\frac{-7}{-5}\right) +\left(\frac{-7}{-11}\right)\\= \frac{3}{5}+ \frac{7}{5}+\frac{7}{11}\\=\frac{33}{55}+\frac{77}{55}+\frac{35}{55}\\=\frac{33+77+35}{55}\\=\frac{145}{55}\\=\frac{29}{11}\)