Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{-7}\right) +\left(\frac{9}{-4}\right) -\left(\frac{-12}{4}\right)\\= \frac{-9}{7}- \frac{9}{4}+\frac{12}{4}\\=\frac{-9}{7}-\frac{9}{4}+\frac{3}{1}\\=\frac{-36}{28}-\frac{63}{28}+\frac{84}{28}\\=\frac{-36-63+84}{28}\\=\frac{-15}{28}\)
2. \(-\left(\frac{9}{-2}\right) +\left(\frac{3}{-7}\right) -\left(\frac{-7}{-12}\right)\\= \frac{9}{2}- \frac{3}{7}-\frac{7}{12}\\=\frac{378}{84}-\frac{36}{84}-\frac{49}{84}\\=\frac{378-36-49}{84}\\=\frac{293}{84}\)
3. \(-\left(\frac{4}{5}\right) +\left(\frac{-5}{-9}\right) +\left(\frac{6}{-6}\right)\\= \frac{-4}{5}+ \frac{5}{9}-\frac{6}{6}\\=\frac{-4}{5}+\frac{5}{9}-\frac{1}{1}\\=\frac{-36}{45}+\frac{25}{45}-\frac{45}{45}\\=\frac{-36+25-45}{45}\\=\frac{-56}{45}\)
4. \(+\left(\frac{-5}{-8}\right) +\left(\frac{-4}{7}\right) -\left(\frac{-10}{-11}\right)\\= \frac{5}{8}- \frac{4}{7}-\frac{10}{11}\\=\frac{385}{616}-\frac{352}{616}-\frac{560}{616}\\=\frac{385-352-560}{616}\\=\frac{-527}{616}\)
5. \(-\left(\frac{3}{-8}\right) +\left(\frac{7}{4}\right) +\left(\frac{9}{9}\right)\\= \frac{3}{8}+ \frac{7}{4}+\frac{9}{9}\\=\frac{3}{8}+\frac{7}{4}+\frac{1}{1}\\=\frac{3+7+1}{8}\\=\frac{11}{8}\)
6. \(-\left(\frac{3}{-4}\right) -\left(\frac{-3}{2}\right) -\left(\frac{-10}{3}\right)\\= \frac{3}{4}+ \frac{3}{2}+\frac{10}{3}\\=\frac{9}{12}+\frac{18}{12}+\frac{40}{12}\\=\frac{9+18+40}{12}\\=\frac{67}{12}\)
7. \(+\left(\frac{-6}{5}\right) -\left(\frac{4}{9}\right) +\left(\frac{-9}{-6}\right)\\= \frac{-6}{5}- \frac{4}{9}+\frac{9}{6}\\=\frac{-6}{5}-\frac{4}{9}+\frac{3}{2}\\=\frac{-108}{90}-\frac{40}{90}+\frac{135}{90}\\=\frac{-108-40+135}{90}\\=\frac{-13}{90}\)
8. \(+\left(\frac{10}{3}\right) -\left(\frac{10}{-5}\right) -\left(\frac{2}{-9}\right)\\= \frac{10}{3}+ \frac{10}{5}+\frac{2}{9}\\=\frac{10}{3}+\frac{2}{1}+\frac{2}{9}\\=\frac{30}{9}+\frac{18}{9}+\frac{2}{9}\\=\frac{30+18+2}{9}\\=\frac{50}{9}\)
9. \(+\left(\frac{-4}{-9}\right) -\left(\frac{-7}{10}\right) +\left(\frac{-2}{-10}\right)\\= \frac{4}{9}+ \frac{7}{10}+\frac{2}{10}\\=\frac{4}{9}+\frac{7}{10}+\frac{1}{5}\\=\frac{40}{90}+\frac{63}{90}+\frac{18}{90}\\=\frac{40+63+18}{90}\\=\frac{121}{90}\)
10. \(+\left(\frac{-8}{-9}\right) -\left(\frac{-5}{7}\right) -\left(\frac{-11}{10}\right)\\= \frac{8}{9}+ \frac{5}{7}+\frac{11}{10}\\=\frac{560}{630}+\frac{450}{630}+\frac{693}{630}\\=\frac{560+450+693}{630}\\=\frac{1703}{630}\)
11. \(+\left(\frac{-4}{-9}\right) -\left(\frac{5}{10}\right) -\left(\frac{-4}{10}\right)\\= \frac{4}{9}- \frac{5}{10}+\frac{4}{10}\\=\frac{4}{9}-\frac{1}{2}+\frac{2}{5}\\=\frac{40}{90}-\frac{45}{90}+\frac{36}{90}\\=\frac{40-45+36}{90}\\=\frac{31}{90}\)
12. \(-\left(\frac{10}{-7}\right) +\left(\frac{3}{-4}\right) +\left(\frac{-6}{-5}\right)\\= \frac{10}{7}- \frac{3}{4}+\frac{6}{5}\\=\frac{200}{140}-\frac{105}{140}+\frac{168}{140}\\=\frac{200-105+168}{140}\\=\frac{263}{140}\)