Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{8}\right) -\left(\frac{-2}{7}\right) -\left(\frac{8}{-2}\right)\\= \frac{9}{8}+ \frac{2}{7}+\frac{8}{2}\\=\frac{9}{8}+\frac{2}{7}+\frac{4}{1}\\=\frac{63}{56}+\frac{16}{56}+\frac{224}{56}\\=\frac{63+16+224}{56}\\=\frac{303}{56}\)
2. \(+\left(\frac{10}{7}\right) -\left(\frac{9}{-10}\right) +\left(\frac{-8}{-9}\right)\\= \frac{10}{7}+ \frac{9}{10}+\frac{8}{9}\\=\frac{900}{630}+\frac{567}{630}+\frac{560}{630}\\=\frac{900+567+560}{630}\\=\frac{2027}{630}\)
3. \(+\left(\frac{-5}{7}\right) -\left(\frac{-5}{7}\right) -\left(\frac{-12}{5}\right)\\= \frac{-5}{7}+ \frac{5}{7}+\frac{12}{5}\\=\frac{-25}{35}+\frac{25}{35}+\frac{84}{35}\\=\frac{-25+25+84}{35}\\=\frac{84}{35}\\=\frac{12}{5}\)
4. \(-\left(\frac{9}{-4}\right) +\left(\frac{7}{-8}\right) -\left(\frac{6}{-9}\right)\\= \frac{9}{4}- \frac{7}{8}+\frac{6}{9}\\=\frac{9}{4}-\frac{7}{8}+\frac{2}{3}\\=\frac{54}{24}-\frac{21}{24}+\frac{16}{24}\\=\frac{54-21+16}{24}\\=\frac{49}{24}\)
5. \(-\left(\frac{-7}{-2}\right) -\left(\frac{-10}{8}\right) +\left(\frac{10}{9}\right)\\= \frac{-7}{2}+ \frac{10}{8}+\frac{10}{9}\\=\frac{-7}{2}+\frac{5}{4}+\frac{10}{9}\\=\frac{-126}{36}+\frac{45}{36}+\frac{40}{36}\\=\frac{-126+45+40}{36}\\=\frac{-41}{36}\)
6. \(-\left(\frac{-5}{-2}\right) +\left(\frac{4}{8}\right) +\left(\frac{-12}{-4}\right)\\= \frac{-5}{2}+ \frac{4}{8}+\frac{12}{4}\\=\frac{-5}{2}+\frac{1}{2}+\frac{3}{1}\\=\frac{-5+1+3}{2}\\=\frac{-1}{2}\)
7. \(+\left(\frac{5}{-7}\right) +\left(\frac{-7}{7}\right) -\left(\frac{8}{2}\right)\\= \frac{-5}{7}- \frac{7}{7}-\frac{8}{2}\\=\frac{-5}{7}-\frac{1}{1}-\frac{4}{1}\\=\frac{-5-1-4}{7}\\=\frac{-10}{7}\)
8. \(-\left(\frac{-10}{9}\right) -\left(\frac{-6}{-10}\right) +\left(\frac{-9}{-3}\right)\\= \frac{10}{9}- \frac{6}{10}+\frac{9}{3}\\=\frac{10}{9}-\frac{3}{5}+\frac{3}{1}\\=\frac{50}{45}-\frac{27}{45}+\frac{135}{45}\\=\frac{50-27+135}{45}\\=\frac{158}{45}\)
9. \(+\left(\frac{-7}{-2}\right) -\left(\frac{-3}{-3}\right) -\left(\frac{3}{-2}\right)\\= \frac{7}{2}- \frac{3}{3}+\frac{3}{2}\\=\frac{7}{2}-\frac{1}{1}+\frac{3}{2}\\=\frac{7-1+3}{2}\\=\frac{9}{2}\)
10. \(+\left(\frac{5}{-6}\right) -\left(\frac{9}{8}\right) -\left(\frac{9}{-10}\right)\\= \frac{-5}{6}- \frac{9}{8}+\frac{9}{10}\\=\frac{-100}{120}-\frac{135}{120}+\frac{108}{120}\\=\frac{-100-135+108}{120}\\=\frac{-127}{120}\)
11. \(-\left(\frac{6}{5}\right) +\left(\frac{-4}{6}\right) +\left(\frac{4}{-4}\right)\\= \frac{-6}{5}- \frac{4}{6}-\frac{4}{4}\\=\frac{-6}{5}-\frac{2}{3}-\frac{1}{1}\\=\frac{-18}{15}-\frac{10}{15}-\frac{15}{15}\\=\frac{-18-10-15}{15}\\=\frac{-43}{15}\)
12. \(-\left(\frac{9}{-2}\right) -\left(\frac{7}{3}\right) +\left(\frac{10}{-2}\right)\\= \frac{9}{2}- \frac{7}{3}-\frac{10}{2}\\=\frac{9}{2}-\frac{7}{3}-\frac{5}{1}\\=\frac{27}{6}-\frac{14}{6}-\frac{30}{6}\\=\frac{27-14-30}{6}\\=\frac{-17}{6}\)