Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{-5}\right) +\left(\frac{9}{4}\right) -\left(\frac{-7}{-7}\right)\\= \frac{-9}{5}+ \frac{9}{4}-\frac{7}{7}\\=\frac{-9}{5}+\frac{9}{4}-\frac{1}{1}\\=\frac{-36}{20}+\frac{45}{20}-\frac{20}{20}\\=\frac{-36+45-20}{20}\\=\frac{-11}{20}\)
2. \(+\left(\frac{3}{7}\right) +\left(\frac{6}{-6}\right) +\left(\frac{10}{-10}\right)\\= \frac{3}{7}- \frac{6}{6}-\frac{10}{10}\\=\frac{3}{7}-\frac{1}{1}-\frac{1}{1}\\=\frac{3-1-1}{7}\\=\frac{1}{7}\)
3. \(+\left(\frac{-4}{-5}\right) -\left(\frac{-9}{6}\right) +\left(\frac{2}{-6}\right)\\= \frac{4}{5}+ \frac{9}{6}-\frac{2}{6}\\=\frac{4}{5}+\frac{3}{2}-\frac{1}{3}\\=\frac{24}{30}+\frac{45}{30}-\frac{10}{30}\\=\frac{24+45-10}{30}\\=\frac{59}{30}\)
4. \(+\left(\frac{7}{9}\right) +\left(\frac{-8}{-6}\right) +\left(\frac{-8}{7}\right)\\= \frac{7}{9}+ \frac{8}{6}-\frac{8}{7}\\=\frac{7}{9}+\frac{4}{3}-\frac{8}{7}\\=\frac{49}{63}+\frac{84}{63}-\frac{72}{63}\\=\frac{49+84-72}{63}\\=\frac{61}{63}\)
5. \(-\left(\frac{-8}{-9}\right) -\left(\frac{10}{4}\right) -\left(\frac{11}{-4}\right)\\= \frac{-8}{9}- \frac{10}{4}+\frac{11}{4}\\=\frac{-8}{9}-\frac{5}{2}+\frac{11}{4}\\=\frac{-32}{36}-\frac{90}{36}+\frac{99}{36}\\=\frac{-32-90+99}{36}\\=\frac{-23}{36}\)
6. \(-\left(\frac{-3}{2}\right) +\left(\frac{-7}{-5}\right) +\left(\frac{8}{12}\right)\\= \frac{3}{2}+ \frac{7}{5}+\frac{8}{12}\\=\frac{3}{2}+\frac{7}{5}+\frac{2}{3}\\=\frac{45}{30}+\frac{42}{30}+\frac{20}{30}\\=\frac{45+42+20}{30}\\=\frac{107}{30}\)
7. \(+\left(\frac{3}{-4}\right) -\left(\frac{-4}{10}\right) -\left(\frac{-6}{-5}\right)\\= \frac{-3}{4}+ \frac{4}{10}-\frac{6}{5}\\=\frac{-3}{4}+\frac{2}{5}-\frac{6}{5}\\=\frac{-15}{20}+\frac{8}{20}-\frac{24}{20}\\=\frac{-15+8-24}{20}\\=\frac{-31}{20}\)
8. \(+\left(\frac{8}{-5}\right) +\left(\frac{-2}{6}\right) +\left(\frac{-7}{12}\right)\\= \frac{-8}{5}- \frac{2}{6}-\frac{7}{12}\\=\frac{-8}{5}-\frac{1}{3}-\frac{7}{12}\\=\frac{-96}{60}-\frac{20}{60}-\frac{35}{60}\\=\frac{-96-20-35}{60}\\=\frac{-151}{60}\)
9. \(+\left(\frac{2}{-9}\right) +\left(\frac{-8}{-2}\right) +\left(\frac{7}{9}\right)\\= \frac{-2}{9}+ \frac{8}{2}+\frac{7}{9}\\=\frac{-2}{9}+\frac{4}{1}+\frac{7}{9}\\=\frac{-2+4+7}{9}\\=\frac{9}{9}\\=\frac{1}{1}\)
10. \(+\left(\frac{8}{7}\right) -\left(\frac{10}{9}\right) +\left(\frac{-7}{-3}\right)\\= \frac{8}{7}- \frac{10}{9}+\frac{7}{3}\\=\frac{72}{63}-\frac{70}{63}+\frac{147}{63}\\=\frac{72-70+147}{63}\\=\frac{149}{63}\)
11. \(+\left(\frac{7}{-6}\right) +\left(\frac{8}{-8}\right) +\left(\frac{-10}{2}\right)\\= \frac{-7}{6}- \frac{8}{8}-\frac{10}{2}\\=\frac{-7}{6}-\frac{1}{1}-\frac{5}{1}\\=\frac{-7-1-5}{6}\\=\frac{-13}{6}\)
12. \(-\left(\frac{3}{5}\right) -\left(\frac{6}{-3}\right) +\left(\frac{6}{11}\right)\\= \frac{-3}{5}+ \frac{6}{3}+\frac{6}{11}\\=\frac{-3}{5}+\frac{2}{1}+\frac{6}{11}\\=\frac{-33}{55}+\frac{110}{55}+\frac{30}{55}\\=\frac{-33+110+30}{55}\\=\frac{107}{55}\)