Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{-7}\right) -\left(\frac{8}{10}\right) -\left(\frac{-11}{11}\right)\\= \frac{-3}{7}- \frac{8}{10}+\frac{11}{11}\\=\frac{-3}{7}-\frac{4}{5}+\frac{1}{1}\\=\frac{-15}{35}-\frac{28}{35}+\frac{35}{35}\\=\frac{-15-28+35}{35}\\=\frac{-8}{35}\)
2. \(+\left(\frac{-2}{3}\right) -\left(\frac{10}{-9}\right) -\left(\frac{-6}{6}\right)\\= \frac{-2}{3}+ \frac{10}{9}+\frac{6}{6}\\=\frac{-2}{3}+\frac{10}{9}+\frac{1}{1}\\=\frac{-6}{9}+\frac{10}{9}+\frac{9}{9}\\=\frac{-6+10+9}{9}\\=\frac{13}{9}\)
3. \(-\left(\frac{5}{6}\right) -\left(\frac{-2}{-8}\right) -\left(\frac{-3}{-2}\right)\\= \frac{-5}{6}- \frac{2}{8}-\frac{3}{2}\\=\frac{-5}{6}-\frac{1}{4}-\frac{3}{2}\\=\frac{-10}{12}-\frac{3}{12}-\frac{18}{12}\\=\frac{-10-3-18}{12}\\=\frac{-31}{12}\)
4. \(+\left(\frac{-5}{6}\right) -\left(\frac{-8}{-9}\right) -\left(\frac{-4}{-9}\right)\\= \frac{-5}{6}- \frac{8}{9}-\frac{4}{9}\\=\frac{-15}{18}-\frac{16}{18}-\frac{8}{18}\\=\frac{-15-16-8}{18}\\=\frac{-39}{18}\\=\frac{-13}{6}\)
5. \(+\left(\frac{9}{-4}\right) -\left(\frac{-7}{-4}\right) -\left(\frac{9}{10}\right)\\= \frac{-9}{4}- \frac{7}{4}-\frac{9}{10}\\=\frac{-45}{20}-\frac{35}{20}-\frac{18}{20}\\=\frac{-45-35-18}{20}\\=\frac{-98}{20}\\=\frac{-49}{10}\)
6. \(-\left(\frac{-5}{9}\right) -\left(\frac{2}{4}\right) +\left(\frac{-6}{-4}\right)\\= \frac{5}{9}- \frac{2}{4}+\frac{6}{4}\\=\frac{5}{9}-\frac{1}{2}+\frac{3}{2}\\=\frac{10}{18}-\frac{9}{18}+\frac{27}{18}\\=\frac{10-9+27}{18}\\=\frac{28}{18}\\=\frac{14}{9}\)
7. \(-\left(\frac{-7}{-9}\right) +\left(\frac{8}{10}\right) -\left(\frac{-11}{-6}\right)\\= \frac{-7}{9}+ \frac{8}{10}-\frac{11}{6}\\=\frac{-7}{9}+\frac{4}{5}-\frac{11}{6}\\=\frac{-70}{90}+\frac{72}{90}-\frac{165}{90}\\=\frac{-70+72-165}{90}\\=\frac{-163}{90}\)
8. \(+\left(\frac{5}{-6}\right) -\left(\frac{5}{-7}\right) +\left(\frac{-2}{-7}\right)\\= \frac{-5}{6}+ \frac{5}{7}+\frac{2}{7}\\=\frac{-35}{42}+\frac{30}{42}+\frac{12}{42}\\=\frac{-35+30+12}{42}\\=\frac{7}{42}\\=\frac{1}{6}\)
9. \(+\left(\frac{-9}{8}\right) +\left(\frac{3}{-3}\right) +\left(\frac{-2}{9}\right)\\= \frac{-9}{8}- \frac{3}{3}-\frac{2}{9}\\=\frac{-9}{8}-\frac{1}{1}-\frac{2}{9}\\=\frac{-81}{72}-\frac{72}{72}-\frac{16}{72}\\=\frac{-81-72-16}{72}\\=\frac{-169}{72}\)
10. \(-\left(\frac{-7}{4}\right) -\left(\frac{-5}{-6}\right) -\left(\frac{-11}{-4}\right)\\= \frac{7}{4}- \frac{5}{6}-\frac{11}{4}\\=\frac{21}{12}-\frac{10}{12}-\frac{33}{12}\\=\frac{21-10-33}{12}\\=\frac{-22}{12}\\=\frac{-11}{6}\)
11. \(-\left(\frac{-2}{5}\right) -\left(\frac{6}{-4}\right) -\left(\frac{-6}{4}\right)\\= \frac{2}{5}+ \frac{6}{4}+\frac{6}{4}\\=\frac{2}{5}+\frac{3}{2}+\frac{3}{2}\\=\frac{4}{10}+\frac{15}{10}+\frac{15}{10}\\=\frac{4+15+15}{10}\\=\frac{34}{10}\\=\frac{17}{5}\)
12. \(-\left(\frac{-8}{9}\right) +\left(\frac{-10}{-10}\right) -\left(\frac{-2}{8}\right)\\= \frac{8}{9}+ \frac{10}{10}+\frac{2}{8}\\=\frac{8}{9}+\frac{1}{1}+\frac{1}{4}\\=\frac{32}{36}+\frac{36}{36}+\frac{9}{36}\\=\frac{32+36+9}{36}\\=\frac{77}{36}\)