Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{3}\right) +\left(\frac{4}{-8}\right) -\left(\frac{-11}{-7}\right)\\= \frac{10}{3}- \frac{4}{8}-\frac{11}{7}\\=\frac{10}{3}-\frac{1}{2}-\frac{11}{7}\\=\frac{140}{42}-\frac{21}{42}-\frac{66}{42}\\=\frac{140-21-66}{42}\\=\frac{53}{42}\)
2. \(-\left(\frac{10}{-7}\right) -\left(\frac{-4}{6}\right) +\left(\frac{11}{-7}\right)\\= \frac{10}{7}+ \frac{4}{6}-\frac{11}{7}\\=\frac{10}{7}+\frac{2}{3}-\frac{11}{7}\\=\frac{30}{21}+\frac{14}{21}-\frac{33}{21}\\=\frac{30+14-33}{21}\\=\frac{11}{21}\)
3. \(+\left(\frac{-10}{-3}\right) -\left(\frac{-7}{-5}\right) -\left(\frac{-5}{-6}\right)\\= \frac{10}{3}- \frac{7}{5}-\frac{5}{6}\\=\frac{100}{30}-\frac{42}{30}-\frac{25}{30}\\=\frac{100-42-25}{30}\\=\frac{33}{30}\\=\frac{11}{10}\)
4. \(-\left(\frac{9}{-4}\right) -\left(\frac{-3}{8}\right) -\left(\frac{12}{-3}\right)\\= \frac{9}{4}+ \frac{3}{8}+\frac{12}{3}\\=\frac{9}{4}+\frac{3}{8}+\frac{4}{1}\\=\frac{18}{8}+\frac{3}{8}+\frac{32}{8}\\=\frac{18+3+32}{8}\\=\frac{53}{8}\)
5. \(-\left(\frac{6}{5}\right) -\left(\frac{-8}{-3}\right) -\left(\frac{-10}{7}\right)\\= \frac{-6}{5}- \frac{8}{3}+\frac{10}{7}\\=\frac{-126}{105}-\frac{280}{105}+\frac{150}{105}\\=\frac{-126-280+150}{105}\\=\frac{-256}{105}\)
6. \(+\left(\frac{3}{-7}\right) +\left(\frac{-9}{-9}\right) +\left(\frac{2}{-3}\right)\\= \frac{-3}{7}+ \frac{9}{9}-\frac{2}{3}\\=\frac{-3}{7}+\frac{1}{1}-\frac{2}{3}\\=\frac{-9}{21}+\frac{21}{21}-\frac{14}{21}\\=\frac{-9+21-14}{21}\\=\frac{-2}{21}\)
7. \(-\left(\frac{7}{-4}\right) -\left(\frac{7}{-5}\right) -\left(\frac{5}{-8}\right)\\= \frac{7}{4}+ \frac{7}{5}+\frac{5}{8}\\=\frac{70}{40}+\frac{56}{40}+\frac{25}{40}\\=\frac{70+56+25}{40}\\=\frac{151}{40}\)
8. \(-\left(\frac{-7}{-2}\right) +\left(\frac{6}{-2}\right) -\left(\frac{-2}{-7}\right)\\= \frac{-7}{2}- \frac{6}{2}-\frac{2}{7}\\=\frac{-7}{2}-\frac{3}{1}-\frac{2}{7}\\=\frac{-49}{14}-\frac{42}{14}-\frac{4}{14}\\=\frac{-49-42-4}{14}\\=\frac{-95}{14}\)
9. \(+\left(\frac{-9}{4}\right) -\left(\frac{-9}{6}\right) +\left(\frac{2}{9}\right)\\= \frac{-9}{4}+ \frac{9}{6}+\frac{2}{9}\\=\frac{-9}{4}+\frac{3}{2}+\frac{2}{9}\\=\frac{-81}{36}+\frac{54}{36}+\frac{8}{36}\\=\frac{-81+54+8}{36}\\=\frac{-19}{36}\)
10. \(+\left(\frac{-5}{-6}\right) -\left(\frac{-7}{-6}\right) -\left(\frac{9}{7}\right)\\= \frac{5}{6}- \frac{7}{6}-\frac{9}{7}\\=\frac{35}{42}-\frac{49}{42}-\frac{54}{42}\\=\frac{35-49-54}{42}\\=\frac{-68}{42}\\=\frac{-34}{21}\)
11. \(+\left(\frac{-2}{-9}\right) +\left(\frac{-6}{-10}\right) -\left(\frac{3}{-5}\right)\\= \frac{2}{9}+ \frac{6}{10}+\frac{3}{5}\\=\frac{2}{9}+\frac{3}{5}+\frac{3}{5}\\=\frac{10}{45}+\frac{27}{45}+\frac{27}{45}\\=\frac{10+27+27}{45}\\=\frac{64}{45}\)
12. \(-\left(\frac{-5}{2}\right) +\left(\frac{4}{-5}\right) +\left(\frac{3}{-12}\right)\\= \frac{5}{2}- \frac{4}{5}-\frac{3}{12}\\=\frac{5}{2}-\frac{4}{5}-\frac{1}{4}\\=\frac{50}{20}-\frac{16}{20}-\frac{5}{20}\\=\frac{50-16-5}{20}\\=\frac{29}{20}\)