Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{-2}\right) -\left(\frac{-10}{-6}\right) -\left(\frac{4}{-4}\right)\\= \frac{9}{2}- \frac{10}{6}+\frac{4}{4}\\=\frac{9}{2}-\frac{5}{3}+\frac{1}{1}\\=\frac{27}{6}-\frac{10}{6}+\frac{6}{6}\\=\frac{27-10+6}{6}\\=\frac{23}{6}\)
2. \(-\left(\frac{10}{-7}\right) +\left(\frac{-5}{-3}\right) -\left(\frac{11}{-9}\right)\\= \frac{10}{7}+ \frac{5}{3}+\frac{11}{9}\\=\frac{90}{63}+\frac{105}{63}+\frac{77}{63}\\=\frac{90+105+77}{63}\\=\frac{272}{63}\)
3. \(+\left(\frac{-8}{5}\right) +\left(\frac{-4}{-3}\right) -\left(\frac{6}{-3}\right)\\= \frac{-8}{5}+ \frac{4}{3}+\frac{6}{3}\\=\frac{-8}{5}+\frac{4}{3}+\frac{2}{1}\\=\frac{-24}{15}+\frac{20}{15}+\frac{30}{15}\\=\frac{-24+20+30}{15}\\=\frac{26}{15}\)
4. \(+\left(\frac{-7}{8}\right) -\left(\frac{-3}{4}\right) +\left(\frac{-2}{6}\right)\\= \frac{-7}{8}+ \frac{3}{4}-\frac{2}{6}\\=\frac{-7}{8}+\frac{3}{4}-\frac{1}{3}\\=\frac{-21}{24}+\frac{18}{24}-\frac{8}{24}\\=\frac{-21+18-8}{24}\\=\frac{-11}{24}\)
5. \(+\left(\frac{2}{3}\right) -\left(\frac{2}{-4}\right) +\left(\frac{-3}{-8}\right)\\= \frac{2}{3}+ \frac{2}{4}+\frac{3}{8}\\=\frac{2}{3}+\frac{1}{2}+\frac{3}{8}\\=\frac{16}{24}+\frac{12}{24}+\frac{9}{24}\\=\frac{16+12+9}{24}\\=\frac{37}{24}\)
6. \(-\left(\frac{-9}{-7}\right) +\left(\frac{-3}{-7}\right) -\left(\frac{2}{-12}\right)\\= \frac{-9}{7}+ \frac{3}{7}+\frac{2}{12}\\=\frac{-9}{7}+\frac{3}{7}+\frac{1}{6}\\=\frac{-54}{42}+\frac{18}{42}+\frac{7}{42}\\=\frac{-54+18+7}{42}\\=\frac{-29}{42}\)
7. \(+\left(\frac{-5}{6}\right) -\left(\frac{10}{-8}\right) +\left(\frac{-10}{-6}\right)\\= \frac{-5}{6}+ \frac{10}{8}+\frac{10}{6}\\=\frac{-5}{6}+\frac{5}{4}+\frac{5}{3}\\=\frac{-10}{12}+\frac{15}{12}+\frac{20}{12}\\=\frac{-10+15+20}{12}\\=\frac{25}{12}\)
8. \(+\left(\frac{5}{-7}\right) -\left(\frac{-2}{-9}\right) +\left(\frac{3}{-6}\right)\\= \frac{-5}{7}- \frac{2}{9}-\frac{3}{6}\\=\frac{-5}{7}-\frac{2}{9}-\frac{1}{2}\\=\frac{-90}{126}-\frac{28}{126}-\frac{63}{126}\\=\frac{-90-28-63}{126}\\=\frac{-181}{126}\)
9. \(-\left(\frac{10}{9}\right) -\left(\frac{10}{10}\right) +\left(\frac{-5}{-2}\right)\\= \frac{-10}{9}- \frac{10}{10}+\frac{5}{2}\\=\frac{-10}{9}-\frac{1}{1}+\frac{5}{2}\\=\frac{-20}{18}-\frac{18}{18}+\frac{45}{18}\\=\frac{-20-18+45}{18}\\=\frac{7}{18}\)
10. \(-\left(\frac{-10}{7}\right) -\left(\frac{-6}{-8}\right) +\left(\frac{12}{6}\right)\\= \frac{10}{7}- \frac{6}{8}+\frac{12}{6}\\=\frac{10}{7}-\frac{3}{4}+\frac{2}{1}\\=\frac{40}{28}-\frac{21}{28}+\frac{56}{28}\\=\frac{40-21+56}{28}\\=\frac{75}{28}\)
11. \(-\left(\frac{5}{3}\right) -\left(\frac{-9}{-6}\right) -\left(\frac{2}{9}\right)\\= \frac{-5}{3}- \frac{9}{6}-\frac{2}{9}\\=\frac{-5}{3}-\frac{3}{2}-\frac{2}{9}\\=\frac{-30}{18}-\frac{27}{18}-\frac{4}{18}\\=\frac{-30-27-4}{18}\\=\frac{-61}{18}\)
12. \(-\left(\frac{8}{9}\right) -\left(\frac{-9}{-8}\right) -\left(\frac{-5}{6}\right)\\= \frac{-8}{9}- \frac{9}{8}+\frac{5}{6}\\=\frac{-64}{72}-\frac{81}{72}+\frac{60}{72}\\=\frac{-64-81+60}{72}\\=\frac{-85}{72}\)