Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{-8}\right) +\left(\frac{6}{-5}\right) +\left(\frac{11}{4}\right)\\= \frac{9}{8}- \frac{6}{5}+\frac{11}{4}\\=\frac{45}{40}-\frac{48}{40}+\frac{110}{40}\\=\frac{45-48+110}{40}\\=\frac{107}{40}\)
2. \(+\left(\frac{6}{-7}\right) +\left(\frac{-4}{-5}\right) -\left(\frac{-3}{7}\right)\\= \frac{-6}{7}+ \frac{4}{5}+\frac{3}{7}\\=\frac{-30}{35}+\frac{28}{35}+\frac{15}{35}\\=\frac{-30+28+15}{35}\\=\frac{13}{35}\)
3. \(-\left(\frac{2}{-7}\right) +\left(\frac{-6}{-2}\right) -\left(\frac{-3}{9}\right)\\= \frac{2}{7}+ \frac{6}{2}+\frac{3}{9}\\=\frac{2}{7}+\frac{3}{1}+\frac{1}{3}\\=\frac{6}{21}+\frac{63}{21}+\frac{7}{21}\\=\frac{6+63+7}{21}\\=\frac{76}{21}\)
4. \(-\left(\frac{7}{-8}\right) +\left(\frac{-9}{10}\right) +\left(\frac{-7}{-7}\right)\\= \frac{7}{8}- \frac{9}{10}+\frac{7}{7}\\=\frac{7}{8}-\frac{9}{10}+\frac{1}{1}\\=\frac{35}{40}-\frac{36}{40}+\frac{40}{40}\\=\frac{35-36+40}{40}\\=\frac{39}{40}\)
5. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-7}{-4}\right) +\left(\frac{-9}{6}\right)\\= \frac{6}{5}+ \frac{7}{4}-\frac{9}{6}\\=\frac{6}{5}+\frac{7}{4}-\frac{3}{2}\\=\frac{24}{20}+\frac{35}{20}-\frac{30}{20}\\=\frac{24+35-30}{20}\\=\frac{29}{20}\)
6. \(+\left(\frac{-9}{5}\right) +\left(\frac{-3}{-3}\right) -\left(\frac{5}{-10}\right)\\= \frac{-9}{5}+ \frac{3}{3}+\frac{5}{10}\\=\frac{-9}{5}+\frac{1}{1}+\frac{1}{2}\\=\frac{-18}{10}+\frac{10}{10}+\frac{5}{10}\\=\frac{-18+10+5}{10}\\=\frac{-3}{10}\)
7. \(-\left(\frac{-2}{-9}\right) -\left(\frac{4}{6}\right) -\left(\frac{5}{7}\right)\\= \frac{-2}{9}- \frac{4}{6}-\frac{5}{7}\\=\frac{-2}{9}-\frac{2}{3}-\frac{5}{7}\\=\frac{-14}{63}-\frac{42}{63}-\frac{45}{63}\\=\frac{-14-42-45}{63}\\=\frac{-101}{63}\)
8. \(-\left(\frac{-2}{-9}\right) -\left(\frac{6}{-10}\right) +\left(\frac{4}{-3}\right)\\= \frac{-2}{9}+ \frac{6}{10}-\frac{4}{3}\\=\frac{-2}{9}+\frac{3}{5}-\frac{4}{3}\\=\frac{-10}{45}+\frac{27}{45}-\frac{60}{45}\\=\frac{-10+27-60}{45}\\=\frac{-43}{45}\)
9. \(+\left(\frac{7}{-2}\right) -\left(\frac{-2}{-6}\right) -\left(\frac{11}{-2}\right)\\= \frac{-7}{2}- \frac{2}{6}+\frac{11}{2}\\=\frac{-7}{2}-\frac{1}{3}+\frac{11}{2}\\=\frac{-21}{6}-\frac{2}{6}+\frac{33}{6}\\=\frac{-21-2+33}{6}\\=\frac{10}{6}\\=\frac{5}{3}\)
10. \(-\left(\frac{3}{2}\right) -\left(\frac{3}{-3}\right) +\left(\frac{-12}{-11}\right)\\= \frac{-3}{2}+ \frac{3}{3}+\frac{12}{11}\\=\frac{-3}{2}+\frac{1}{1}+\frac{12}{11}\\=\frac{-33}{22}+\frac{22}{22}+\frac{24}{22}\\=\frac{-33+22+24}{22}\\=\frac{13}{22}\)
11. \(+\left(\frac{4}{-3}\right) +\left(\frac{-5}{-8}\right) -\left(\frac{10}{-4}\right)\\= \frac{-4}{3}+ \frac{5}{8}+\frac{10}{4}\\=\frac{-4}{3}+\frac{5}{8}+\frac{5}{2}\\=\frac{-32}{24}+\frac{15}{24}+\frac{60}{24}\\=\frac{-32+15+60}{24}\\=\frac{43}{24}\)
12. \(+\left(\frac{-6}{5}\right) +\left(\frac{-7}{8}\right) -\left(\frac{-6}{-2}\right)\\= \frac{-6}{5}- \frac{7}{8}-\frac{6}{2}\\=\frac{-6}{5}-\frac{7}{8}-\frac{3}{1}\\=\frac{-48}{40}-\frac{35}{40}-\frac{120}{40}\\=\frac{-48-35-120}{40}\\=\frac{-203}{40}\)