Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{10}{-9}\right) +\left(\frac{-9}{6}\right) -\left(\frac{8}{-10}\right)\\= \frac{-10}{9}- \frac{9}{6}+\frac{8}{10}\\=\frac{-10}{9}-\frac{3}{2}+\frac{4}{5}\\=\frac{-100}{90}-\frac{135}{90}+\frac{72}{90}\\=\frac{-100-135+72}{90}\\=\frac{-163}{90}\)
2. \(+\left(\frac{3}{4}\right) -\left(\frac{-6}{-9}\right) -\left(\frac{-5}{-9}\right)\\= \frac{3}{4}- \frac{6}{9}-\frac{5}{9}\\=\frac{3}{4}-\frac{2}{3}-\frac{5}{9}\\=\frac{27}{36}-\frac{24}{36}-\frac{20}{36}\\=\frac{27-24-20}{36}\\=\frac{-17}{36}\)
3. \(-\left(\frac{-9}{4}\right) -\left(\frac{5}{8}\right) -\left(\frac{-11}{-11}\right)\\= \frac{9}{4}- \frac{5}{8}-\frac{11}{11}\\=\frac{9}{4}-\frac{5}{8}-\frac{1}{1}\\=\frac{18}{8}-\frac{5}{8}-\frac{8}{8}\\=\frac{18-5-8}{8}\\=\frac{5}{8}\)
4. \(-\left(\frac{3}{-8}\right) -\left(\frac{10}{-6}\right) -\left(\frac{-7}{-12}\right)\\= \frac{3}{8}+ \frac{10}{6}-\frac{7}{12}\\=\frac{3}{8}+\frac{5}{3}-\frac{7}{12}\\=\frac{9}{24}+\frac{40}{24}-\frac{14}{24}\\=\frac{9+40-14}{24}\\=\frac{35}{24}\)
5. \(+\left(\frac{10}{-7}\right) +\left(\frac{4}{-10}\right) +\left(\frac{6}{5}\right)\\= \frac{-10}{7}- \frac{4}{10}+\frac{6}{5}\\=\frac{-10}{7}-\frac{2}{5}+\frac{6}{5}\\=\frac{-50}{35}-\frac{14}{35}+\frac{42}{35}\\=\frac{-50-14+42}{35}\\=\frac{-22}{35}\)
6. \(-\left(\frac{3}{-8}\right) -\left(\frac{-9}{-10}\right) +\left(\frac{-11}{11}\right)\\= \frac{3}{8}- \frac{9}{10}-\frac{11}{11}\\=\frac{3}{8}-\frac{9}{10}-\frac{1}{1}\\=\frac{15}{40}-\frac{36}{40}-\frac{40}{40}\\=\frac{15-36-40}{40}\\=\frac{-61}{40}\)
7. \(-\left(\frac{-10}{-3}\right) +\left(\frac{-3}{-4}\right) +\left(\frac{-6}{-12}\right)\\= \frac{-10}{3}+ \frac{3}{4}+\frac{6}{12}\\=\frac{-10}{3}+\frac{3}{4}+\frac{1}{2}\\=\frac{-40}{12}+\frac{9}{12}+\frac{6}{12}\\=\frac{-40+9+6}{12}\\=\frac{-25}{12}\)
8. \(-\left(\frac{-7}{6}\right) -\left(\frac{-9}{-6}\right) +\left(\frac{-5}{-4}\right)\\= \frac{7}{6}- \frac{9}{6}+\frac{5}{4}\\=\frac{7}{6}-\frac{3}{2}+\frac{5}{4}\\=\frac{14}{12}-\frac{18}{12}+\frac{15}{12}\\=\frac{14-18+15}{12}\\=\frac{11}{12}\)
9. \(+\left(\frac{2}{5}\right) +\left(\frac{2}{4}\right) -\left(\frac{6}{2}\right)\\= \frac{2}{5}+ \frac{2}{4}-\frac{6}{2}\\=\frac{2}{5}+\frac{1}{2}-\frac{3}{1}\\=\frac{4}{10}+\frac{5}{10}-\frac{30}{10}\\=\frac{4+5-30}{10}\\=\frac{-21}{10}\)
10. \(+\left(\frac{-2}{9}\right) +\left(\frac{-7}{-5}\right) +\left(\frac{-4}{-7}\right)\\= \frac{-2}{9}+ \frac{7}{5}+\frac{4}{7}\\=\frac{-70}{315}+\frac{441}{315}+\frac{180}{315}\\=\frac{-70+441+180}{315}\\=\frac{551}{315}\)
11. \(+\left(\frac{-8}{-3}\right) -\left(\frac{9}{-7}\right) -\left(\frac{5}{5}\right)\\= \frac{8}{3}+ \frac{9}{7}-\frac{5}{5}\\=\frac{8}{3}+\frac{9}{7}-\frac{1}{1}\\=\frac{56}{21}+\frac{27}{21}-\frac{21}{21}\\=\frac{56+27-21}{21}\\=\frac{62}{21}\)
12. \(-\left(\frac{-10}{3}\right) +\left(\frac{8}{3}\right) -\left(\frac{-6}{10}\right)\\= \frac{10}{3}+ \frac{8}{3}+\frac{6}{10}\\=\frac{10}{3}+\frac{8}{3}+\frac{3}{5}\\=\frac{50}{15}+\frac{40}{15}+\frac{9}{15}\\=\frac{50+40+9}{15}\\=\frac{99}{15}\\=\frac{33}{5}\)