Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{5}\right) -\left(\frac{5}{10}\right) -\left(\frac{12}{-11}\right)\\= \frac{4}{5}- \frac{5}{10}+\frac{12}{11}\\=\frac{4}{5}-\frac{1}{2}+\frac{12}{11}\\=\frac{88}{110}-\frac{55}{110}+\frac{120}{110}\\=\frac{88-55+120}{110}\\=\frac{153}{110}\)
2. \(-\left(\frac{-10}{9}\right) -\left(\frac{7}{-7}\right) +\left(\frac{5}{2}\right)\\= \frac{10}{9}+ \frac{7}{7}+\frac{5}{2}\\=\frac{10}{9}+\frac{1}{1}+\frac{5}{2}\\=\frac{20}{18}+\frac{18}{18}+\frac{45}{18}\\=\frac{20+18+45}{18}\\=\frac{83}{18}\)
3. \(+\left(\frac{-5}{6}\right) -\left(\frac{5}{-7}\right) +\left(\frac{9}{-12}\right)\\= \frac{-5}{6}+ \frac{5}{7}-\frac{9}{12}\\=\frac{-5}{6}+\frac{5}{7}-\frac{3}{4}\\=\frac{-70}{84}+\frac{60}{84}-\frac{63}{84}\\=\frac{-70+60-63}{84}\\=\frac{-73}{84}\)
4. \(-\left(\frac{-7}{8}\right) +\left(\frac{3}{-6}\right) +\left(\frac{11}{8}\right)\\= \frac{7}{8}- \frac{3}{6}+\frac{11}{8}\\=\frac{7}{8}-\frac{1}{2}+\frac{11}{8}\\=\frac{7-1+11}{8}\\=\frac{17}{8}\)
5. \(-\left(\frac{3}{4}\right) +\left(\frac{-8}{-8}\right) -\left(\frac{-2}{-8}\right)\\= \frac{-3}{4}+ \frac{8}{8}-\frac{2}{8}\\=\frac{-3}{4}+\frac{1}{1}-\frac{1}{4}\\=\frac{-3+1-1}{4}\\=\frac{-3}{4}\)
6. \(-\left(\frac{9}{5}\right) +\left(\frac{-4}{5}\right) -\left(\frac{3}{3}\right)\\= \frac{-9}{5}- \frac{4}{5}-\frac{3}{3}\\=\frac{-9}{5}-\frac{4}{5}-\frac{1}{1}\\=\frac{-9-4-1}{5}\\=\frac{-14}{5}\)
7. \(+\left(\frac{6}{5}\right) +\left(\frac{8}{7}\right) -\left(\frac{-4}{5}\right)\\= \frac{6}{5}+ \frac{8}{7}+\frac{4}{5}\\=\frac{42}{35}+\frac{40}{35}+\frac{28}{35}\\=\frac{42+40+28}{35}\\=\frac{110}{35}\\=\frac{22}{7}\)
8. \(-\left(\frac{4}{3}\right) -\left(\frac{-10}{5}\right) -\left(\frac{-9}{5}\right)\\= \frac{-4}{3}+ \frac{10}{5}+\frac{9}{5}\\=\frac{-4}{3}+\frac{2}{1}+\frac{9}{5}\\=\frac{-20}{15}+\frac{30}{15}+\frac{27}{15}\\=\frac{-20+30+27}{15}\\=\frac{37}{15}\)
9. \(-\left(\frac{2}{-5}\right) -\left(\frac{-5}{2}\right) +\left(\frac{-8}{-10}\right)\\= \frac{2}{5}+ \frac{5}{2}+\frac{8}{10}\\=\frac{2}{5}+\frac{5}{2}+\frac{4}{5}\\=\frac{4}{10}+\frac{25}{10}+\frac{8}{10}\\=\frac{4+25+8}{10}\\=\frac{37}{10}\)
10. \(-\left(\frac{-3}{-4}\right) -\left(\frac{7}{-2}\right) +\left(\frac{-10}{6}\right)\\= \frac{-3}{4}+ \frac{7}{2}-\frac{10}{6}\\=\frac{-3}{4}+\frac{7}{2}-\frac{5}{3}\\=\frac{-9}{12}+\frac{42}{12}-\frac{20}{12}\\=\frac{-9+42-20}{12}\\=\frac{13}{12}\)
11. \(-\left(\frac{2}{-3}\right) +\left(\frac{5}{-10}\right) +\left(\frac{-10}{-8}\right)\\= \frac{2}{3}- \frac{5}{10}+\frac{10}{8}\\=\frac{2}{3}-\frac{1}{2}+\frac{5}{4}\\=\frac{8}{12}-\frac{6}{12}+\frac{15}{12}\\=\frac{8-6+15}{12}\\=\frac{17}{12}\)
12. \(+\left(\frac{-2}{5}\right) -\left(\frac{-4}{-8}\right) +\left(\frac{7}{-3}\right)\\= \frac{-2}{5}- \frac{4}{8}-\frac{7}{3}\\=\frac{-2}{5}-\frac{1}{2}-\frac{7}{3}\\=\frac{-12}{30}-\frac{15}{30}-\frac{70}{30}\\=\frac{-12-15-70}{30}\\=\frac{-97}{30}\)