Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{8}\right) -\left(\frac{-7}{4}\right) -\left(\frac{6}{8}\right)\\= \frac{5}{8}+ \frac{7}{4}-\frac{6}{8}\\=\frac{5}{8}+\frac{7}{4}-\frac{3}{4}\\=\frac{5+7-3}{8}\\=\frac{9}{8}\)
2. \(-\left(\frac{8}{9}\right) +\left(\frac{-10}{-5}\right) +\left(\frac{9}{10}\right)\\= \frac{-8}{9}+ \frac{10}{5}+\frac{9}{10}\\=\frac{-8}{9}+\frac{2}{1}+\frac{9}{10}\\=\frac{-80}{90}+\frac{180}{90}+\frac{81}{90}\\=\frac{-80+180+81}{90}\\=\frac{181}{90}\)
3. \(-\left(\frac{-8}{5}\right) -\left(\frac{-9}{-6}\right) +\left(\frac{-6}{-11}\right)\\= \frac{8}{5}- \frac{9}{6}+\frac{6}{11}\\=\frac{8}{5}-\frac{3}{2}+\frac{6}{11}\\=\frac{176}{110}-\frac{165}{110}+\frac{60}{110}\\=\frac{176-165+60}{110}\\=\frac{71}{110}\)
4. \(-\left(\frac{3}{8}\right) +\left(\frac{-9}{-3}\right) +\left(\frac{9}{2}\right)\\= \frac{-3}{8}+ \frac{9}{3}+\frac{9}{2}\\=\frac{-3}{8}+\frac{3}{1}+\frac{9}{2}\\=\frac{-3+3+9}{8}\\=\frac{9}{8}\)
5. \(+\left(\frac{8}{7}\right) +\left(\frac{-8}{10}\right) +\left(\frac{-11}{7}\right)\\= \frac{8}{7}- \frac{8}{10}-\frac{11}{7}\\=\frac{8}{7}-\frac{4}{5}-\frac{11}{7}\\=\frac{40}{35}-\frac{28}{35}-\frac{55}{35}\\=\frac{40-28-55}{35}\\=\frac{-43}{35}\)
6. \(+\left(\frac{-4}{-9}\right) +\left(\frac{-7}{-4}\right) -\left(\frac{12}{6}\right)\\= \frac{4}{9}+ \frac{7}{4}-\frac{12}{6}\\=\frac{4}{9}+\frac{7}{4}-\frac{2}{1}\\=\frac{16}{36}+\frac{63}{36}-\frac{72}{36}\\=\frac{16+63-72}{36}\\=\frac{7}{36}\)
7. \(-\left(\frac{3}{7}\right) -\left(\frac{-9}{10}\right) -\left(\frac{11}{3}\right)\\= \frac{-3}{7}+ \frac{9}{10}-\frac{11}{3}\\=\frac{-90}{210}+\frac{189}{210}-\frac{770}{210}\\=\frac{-90+189-770}{210}\\=\frac{-671}{210}\)
8. \(+\left(\frac{-6}{5}\right) -\left(\frac{9}{2}\right) +\left(\frac{-2}{-5}\right)\\= \frac{-6}{5}- \frac{9}{2}+\frac{2}{5}\\=\frac{-12}{10}-\frac{45}{10}+\frac{4}{10}\\=\frac{-12-45+4}{10}\\=\frac{-53}{10}\)
9. \(-\left(\frac{10}{9}\right) +\left(\frac{-9}{-4}\right) +\left(\frac{-5}{4}\right)\\= \frac{-10}{9}+ \frac{9}{4}-\frac{5}{4}\\=\frac{-40}{36}+\frac{81}{36}-\frac{45}{36}\\=\frac{-40+81-45}{36}\\=\frac{-4}{36}\\=\frac{-1}{9}\)
10. \(-\left(\frac{-10}{7}\right) -\left(\frac{-2}{9}\right) +\left(\frac{12}{7}\right)\\= \frac{10}{7}+ \frac{2}{9}+\frac{12}{7}\\=\frac{90}{63}+\frac{14}{63}+\frac{108}{63}\\=\frac{90+14+108}{63}\\=\frac{212}{63}\)
11. \(-\left(\frac{-10}{9}\right) -\left(\frac{-4}{7}\right) +\left(\frac{7}{4}\right)\\= \frac{10}{9}+ \frac{4}{7}+\frac{7}{4}\\=\frac{280}{252}+\frac{144}{252}+\frac{441}{252}\\=\frac{280+144+441}{252}\\=\frac{865}{252}\)
12. \(-\left(\frac{10}{-3}\right) +\left(\frac{10}{-3}\right) +\left(\frac{-7}{4}\right)\\= \frac{10}{3}- \frac{10}{3}-\frac{7}{4}\\=\frac{40}{12}-\frac{40}{12}-\frac{21}{12}\\=\frac{40-40-21}{12}\\=\frac{-21}{12}\\=\frac{-7}{4}\)