Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{-3}\right) +\left(\frac{4}{-2}\right) -\left(\frac{-10}{8}\right)\\= \frac{7}{3}- \frac{4}{2}+\frac{10}{8}\\=\frac{7}{3}-\frac{2}{1}+\frac{5}{4}\\=\frac{28}{12}-\frac{24}{12}+\frac{15}{12}\\=\frac{28-24+15}{12}\\=\frac{19}{12}\)
2. \(+\left(\frac{-5}{-9}\right) -\left(\frac{8}{2}\right) +\left(\frac{3}{-6}\right)\\= \frac{5}{9}- \frac{8}{2}-\frac{3}{6}\\=\frac{5}{9}-\frac{4}{1}-\frac{1}{2}\\=\frac{10}{18}-\frac{72}{18}-\frac{9}{18}\\=\frac{10-72-9}{18}\\=\frac{-71}{18}\)
3. \(-\left(\frac{-5}{6}\right) +\left(\frac{10}{-9}\right) +\left(\frac{12}{7}\right)\\= \frac{5}{6}- \frac{10}{9}+\frac{12}{7}\\=\frac{105}{126}-\frac{140}{126}+\frac{216}{126}\\=\frac{105-140+216}{126}\\=\frac{181}{126}\)
4. \(+\left(\frac{6}{-5}\right) +\left(\frac{5}{5}\right) -\left(\frac{-7}{3}\right)\\= \frac{-6}{5}+ \frac{5}{5}+\frac{7}{3}\\=\frac{-6}{5}+\frac{1}{1}+\frac{7}{3}\\=\frac{-18}{15}+\frac{15}{15}+\frac{35}{15}\\=\frac{-18+15+35}{15}\\=\frac{32}{15}\)
5. \(+\left(\frac{-5}{-8}\right) +\left(\frac{9}{-9}\right) -\left(\frac{-9}{-6}\right)\\= \frac{5}{8}- \frac{9}{9}-\frac{9}{6}\\=\frac{5}{8}-\frac{1}{1}-\frac{3}{2}\\=\frac{5-1-3}{8}\\=\frac{1}{8}\)
6. \(+\left(\frac{9}{-7}\right) +\left(\frac{-6}{4}\right) -\left(\frac{-9}{12}\right)\\= \frac{-9}{7}- \frac{6}{4}+\frac{9}{12}\\=\frac{-9}{7}-\frac{3}{2}+\frac{3}{4}\\=\frac{-36}{28}-\frac{42}{28}+\frac{21}{28}\\=\frac{-36-42+21}{28}\\=\frac{-57}{28}\)
7. \(+\left(\frac{4}{-7}\right) +\left(\frac{10}{9}\right) +\left(\frac{-4}{9}\right)\\= \frac{-4}{7}+ \frac{10}{9}-\frac{4}{9}\\=\frac{-36}{63}+\frac{70}{63}-\frac{28}{63}\\=\frac{-36+70-28}{63}\\=\frac{6}{63}\\=\frac{2}{21}\)
8. \(-\left(\frac{-3}{-2}\right) +\left(\frac{4}{-6}\right) +\left(\frac{-5}{9}\right)\\= \frac{-3}{2}- \frac{4}{6}-\frac{5}{9}\\=\frac{-3}{2}-\frac{2}{3}-\frac{5}{9}\\=\frac{-27}{18}-\frac{12}{18}-\frac{10}{18}\\=\frac{-27-12-10}{18}\\=\frac{-49}{18}\)
9. \(+\left(\frac{-6}{-5}\right) +\left(\frac{9}{9}\right) +\left(\frac{9}{9}\right)\\= \frac{6}{5}+ \frac{9}{9}+\frac{9}{9}\\=\frac{6}{5}+\frac{1}{1}+\frac{1}{1}\\=\frac{6+1+1}{5}\\=\frac{8}{5}\)
10. \(+\left(\frac{7}{-8}\right) +\left(\frac{5}{-8}\right) -\left(\frac{-6}{-5}\right)\\= \frac{-7}{8}- \frac{5}{8}-\frac{6}{5}\\=\frac{-35}{40}-\frac{25}{40}-\frac{48}{40}\\=\frac{-35-25-48}{40}\\=\frac{-108}{40}\\=\frac{-27}{10}\)
11. \(-\left(\frac{4}{3}\right) -\left(\frac{-3}{2}\right) -\left(\frac{6}{5}\right)\\= \frac{-4}{3}+ \frac{3}{2}-\frac{6}{5}\\=\frac{-40}{30}+\frac{45}{30}-\frac{36}{30}\\=\frac{-40+45-36}{30}\\=\frac{-31}{30}\)
12. \(-\left(\frac{-9}{-2}\right) +\left(\frac{-7}{-3}\right) -\left(\frac{-7}{-5}\right)\\= \frac{-9}{2}+ \frac{7}{3}-\frac{7}{5}\\=\frac{-135}{30}+\frac{70}{30}-\frac{42}{30}\\=\frac{-135+70-42}{30}\\=\frac{-107}{30}\)