Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{9}\right) -\left(\frac{5}{9}\right) -\left(\frac{7}{-3}\right)\\= \frac{-10}{9}- \frac{5}{9}+\frac{7}{3}\\=\frac{-10-5+7}{9}\\=\frac{-8}{9}\)
2. \(+\left(\frac{-7}{-6}\right) -\left(\frac{-4}{-8}\right) -\left(\frac{-3}{11}\right)\\= \frac{7}{6}- \frac{4}{8}+\frac{3}{11}\\=\frac{7}{6}-\frac{1}{2}+\frac{3}{11}\\=\frac{77}{66}-\frac{33}{66}+\frac{18}{66}\\=\frac{77-33+18}{66}\\=\frac{62}{66}\\=\frac{31}{33}\)
3. \(-\left(\frac{-4}{-3}\right) +\left(\frac{8}{-8}\right) +\left(\frac{3}{-3}\right)\\= \frac{-4}{3}- \frac{8}{8}-\frac{3}{3}\\=\frac{-4}{3}-\frac{1}{1}-\frac{1}{1}\\=\frac{-4-1-1}{3}\\=\frac{-6}{3}\\=\frac{-2}{1}\)
4. \(-\left(\frac{4}{-5}\right) -\left(\frac{4}{-7}\right) +\left(\frac{-10}{5}\right)\\= \frac{4}{5}+ \frac{4}{7}-\frac{10}{5}\\=\frac{4}{5}+\frac{4}{7}-\frac{2}{1}\\=\frac{28}{35}+\frac{20}{35}-\frac{70}{35}\\=\frac{28+20-70}{35}\\=\frac{-22}{35}\)
5. \(-\left(\frac{-9}{-8}\right) -\left(\frac{3}{6}\right) -\left(\frac{-5}{3}\right)\\= \frac{-9}{8}- \frac{3}{6}+\frac{5}{3}\\=\frac{-9}{8}-\frac{1}{2}+\frac{5}{3}\\=\frac{-27}{24}-\frac{12}{24}+\frac{40}{24}\\=\frac{-27-12+40}{24}\\=\frac{1}{24}\)
6. \(+\left(\frac{-10}{-7}\right) -\left(\frac{3}{-6}\right) +\left(\frac{-2}{4}\right)\\= \frac{10}{7}+ \frac{3}{6}-\frac{2}{4}\\=\frac{10}{7}+\frac{1}{2}-\frac{1}{2}\\=\frac{20}{14}+\frac{7}{14}-\frac{7}{14}\\=\frac{20+7-7}{14}\\=\frac{20}{14}\\=\frac{10}{7}\)
7. \(-\left(\frac{-10}{7}\right) -\left(\frac{9}{-6}\right) -\left(\frac{2}{12}\right)\\= \frac{10}{7}+ \frac{9}{6}-\frac{2}{12}\\=\frac{10}{7}+\frac{3}{2}-\frac{1}{6}\\=\frac{60}{42}+\frac{63}{42}-\frac{7}{42}\\=\frac{60+63-7}{42}\\=\frac{116}{42}\\=\frac{58}{21}\)
8. \(-\left(\frac{8}{7}\right) +\left(\frac{-9}{-2}\right) +\left(\frac{4}{7}\right)\\= \frac{-8}{7}+ \frac{9}{2}+\frac{4}{7}\\=\frac{-16}{14}+\frac{63}{14}+\frac{8}{14}\\=\frac{-16+63+8}{14}\\=\frac{55}{14}\)
9. \(+\left(\frac{-5}{-7}\right) +\left(\frac{10}{-7}\right) +\left(\frac{-4}{6}\right)\\= \frac{5}{7}- \frac{10}{7}-\frac{4}{6}\\=\frac{5}{7}-\frac{10}{7}-\frac{2}{3}\\=\frac{15}{21}-\frac{30}{21}-\frac{14}{21}\\=\frac{15-30-14}{21}\\=\frac{-29}{21}\)
10. \(+\left(\frac{2}{7}\right) -\left(\frac{-8}{-6}\right) +\left(\frac{9}{12}\right)\\= \frac{2}{7}- \frac{8}{6}+\frac{9}{12}\\=\frac{2}{7}-\frac{4}{3}+\frac{3}{4}\\=\frac{24}{84}-\frac{112}{84}+\frac{63}{84}\\=\frac{24-112+63}{84}\\=\frac{-25}{84}\)
11. \(+\left(\frac{9}{-5}\right) +\left(\frac{9}{10}\right) -\left(\frac{-9}{-7}\right)\\= \frac{-9}{5}+ \frac{9}{10}-\frac{9}{7}\\=\frac{-126}{70}+\frac{63}{70}-\frac{90}{70}\\=\frac{-126+63-90}{70}\\=\frac{-153}{70}\)
12. \(-\left(\frac{-10}{9}\right) -\left(\frac{-10}{-4}\right) -\left(\frac{3}{10}\right)\\= \frac{10}{9}- \frac{10}{4}-\frac{3}{10}\\=\frac{10}{9}-\frac{5}{2}-\frac{3}{10}\\=\frac{100}{90}-\frac{225}{90}-\frac{27}{90}\\=\frac{100-225-27}{90}\\=\frac{-152}{90}\\=\frac{-76}{45}\)