Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{8}{-7}\right) -\left(\frac{6}{-3}\right) +\left(\frac{9}{3}\right)\\= \frac{-8}{7}+ \frac{6}{3}+\frac{9}{3}\\=\frac{-8}{7}+\frac{2}{1}+\frac{3}{1}\\=\frac{-8+2+3}{7}\\=\frac{-3}{7}\)
2. \(+\left(\frac{-8}{7}\right) +\left(\frac{7}{-9}\right) -\left(\frac{-3}{12}\right)\\= \frac{-8}{7}- \frac{7}{9}+\frac{3}{12}\\=\frac{-8}{7}-\frac{7}{9}+\frac{1}{4}\\=\frac{-288}{252}-\frac{196}{252}+\frac{63}{252}\\=\frac{-288-196+63}{252}\\=\frac{-421}{252}\)
3. \(-\left(\frac{-6}{-5}\right) +\left(\frac{3}{3}\right) -\left(\frac{7}{8}\right)\\= \frac{-6}{5}+ \frac{3}{3}-\frac{7}{8}\\=\frac{-6}{5}+\frac{1}{1}-\frac{7}{8}\\=\frac{-48}{40}+\frac{40}{40}-\frac{35}{40}\\=\frac{-48+40-35}{40}\\=\frac{-43}{40}\)
4. \(-\left(\frac{3}{7}\right) -\left(\frac{2}{5}\right) +\left(\frac{-2}{10}\right)\\= \frac{-3}{7}- \frac{2}{5}-\frac{2}{10}\\=\frac{-3}{7}-\frac{2}{5}-\frac{1}{5}\\=\frac{-15}{35}-\frac{14}{35}-\frac{7}{35}\\=\frac{-15-14-7}{35}\\=\frac{-36}{35}\)
5. \(-\left(\frac{2}{-3}\right) +\left(\frac{2}{-9}\right) +\left(\frac{-6}{-7}\right)\\= \frac{2}{3}- \frac{2}{9}+\frac{6}{7}\\=\frac{42}{63}-\frac{14}{63}+\frac{54}{63}\\=\frac{42-14+54}{63}\\=\frac{82}{63}\)
6. \(+\left(\frac{-4}{7}\right) -\left(\frac{10}{7}\right) -\left(\frac{8}{-2}\right)\\= \frac{-4}{7}- \frac{10}{7}+\frac{8}{2}\\=\frac{-4}{7}-\frac{10}{7}+\frac{4}{1}\\=\frac{-4-10+4}{7}\\=\frac{-10}{7}\)
7. \(+\left(\frac{-3}{7}\right) +\left(\frac{-2}{-6}\right) -\left(\frac{-2}{-8}\right)\\= \frac{-3}{7}+ \frac{2}{6}-\frac{2}{8}\\=\frac{-3}{7}+\frac{1}{3}-\frac{1}{4}\\=\frac{-36}{84}+\frac{28}{84}-\frac{21}{84}\\=\frac{-36+28-21}{84}\\=\frac{-29}{84}\)
8. \(-\left(\frac{-8}{5}\right) -\left(\frac{2}{5}\right) +\left(\frac{6}{7}\right)\\= \frac{8}{5}- \frac{2}{5}+\frac{6}{7}\\=\frac{56}{35}-\frac{14}{35}+\frac{30}{35}\\=\frac{56-14+30}{35}\\=\frac{72}{35}\)
9. \(-\left(\frac{5}{2}\right) +\left(\frac{-4}{9}\right) +\left(\frac{-12}{8}\right)\\= \frac{-5}{2}- \frac{4}{9}-\frac{12}{8}\\=\frac{-5}{2}-\frac{4}{9}-\frac{3}{2}\\=\frac{-45}{18}-\frac{8}{18}-\frac{27}{18}\\=\frac{-45-8-27}{18}\\=\frac{-80}{18}\\=\frac{-40}{9}\)
10. \(-\left(\frac{3}{2}\right) -\left(\frac{7}{-2}\right) -\left(\frac{-7}{-10}\right)\\= \frac{-3}{2}+ \frac{7}{2}-\frac{7}{10}\\=\frac{-15}{10}+\frac{35}{10}-\frac{7}{10}\\=\frac{-15+35-7}{10}\\=\frac{13}{10}\)
11. \(-\left(\frac{-10}{-3}\right) -\left(\frac{-2}{5}\right) -\left(\frac{9}{3}\right)\\= \frac{-10}{3}+ \frac{2}{5}-\frac{9}{3}\\=\frac{-10}{3}+\frac{2}{5}-\frac{3}{1}\\=\frac{-50}{15}+\frac{6}{15}-\frac{45}{15}\\=\frac{-50+6-45}{15}\\=\frac{-89}{15}\)
12. \(-\left(\frac{-7}{6}\right) +\left(\frac{4}{6}\right) -\left(\frac{10}{-11}\right)\\= \frac{7}{6}+ \frac{4}{6}+\frac{10}{11}\\=\frac{7}{6}+\frac{2}{3}+\frac{10}{11}\\=\frac{77}{66}+\frac{44}{66}+\frac{60}{66}\\=\frac{77+44+60}{66}\\=\frac{181}{66}\)