Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{7}\right) -\left(\frac{-8}{-2}\right) +\left(\frac{-9}{7}\right)\\= \frac{-10}{7}- \frac{8}{2}-\frac{9}{7}\\=\frac{-10}{7}-\frac{4}{1}-\frac{9}{7}\\=\frac{-10-4-9}{7}\\=\frac{-23}{7}\)
2. \(-\left(\frac{4}{-9}\right) -\left(\frac{-2}{7}\right) -\left(\frac{12}{-6}\right)\\= \frac{4}{9}+ \frac{2}{7}+\frac{12}{6}\\=\frac{4}{9}+\frac{2}{7}+\frac{2}{1}\\=\frac{28}{63}+\frac{18}{63}+\frac{126}{63}\\=\frac{28+18+126}{63}\\=\frac{172}{63}\)
3. \(+\left(\frac{-5}{-4}\right) +\left(\frac{-7}{-2}\right) -\left(\frac{-4}{7}\right)\\= \frac{5}{4}+ \frac{7}{2}+\frac{4}{7}\\=\frac{35}{28}+\frac{98}{28}+\frac{16}{28}\\=\frac{35+98+16}{28}\\=\frac{149}{28}\)
4. \(+\left(\frac{-4}{-3}\right) -\left(\frac{3}{2}\right) +\left(\frac{-6}{-6}\right)\\= \frac{4}{3}- \frac{3}{2}+\frac{6}{6}\\=\frac{4}{3}-\frac{3}{2}+\frac{1}{1}\\=\frac{8}{6}-\frac{9}{6}+\frac{6}{6}\\=\frac{8-9+6}{6}\\=\frac{5}{6}\)
5. \(+\left(\frac{-6}{-5}\right) -\left(\frac{10}{8}\right) -\left(\frac{7}{2}\right)\\= \frac{6}{5}- \frac{10}{8}-\frac{7}{2}\\=\frac{6}{5}-\frac{5}{4}-\frac{7}{2}\\=\frac{24}{20}-\frac{25}{20}-\frac{70}{20}\\=\frac{24-25-70}{20}\\=\frac{-71}{20}\)
6. \(+\left(\frac{-10}{7}\right) +\left(\frac{-7}{-10}\right) -\left(\frac{8}{4}\right)\\= \frac{-10}{7}+ \frac{7}{10}-\frac{8}{4}\\=\frac{-10}{7}+\frac{7}{10}-\frac{2}{1}\\=\frac{-100}{70}+\frac{49}{70}-\frac{140}{70}\\=\frac{-100+49-140}{70}\\=\frac{-191}{70}\)
7. \(-\left(\frac{10}{7}\right) -\left(\frac{2}{5}\right) -\left(\frac{-9}{7}\right)\\= \frac{-10}{7}- \frac{2}{5}+\frac{9}{7}\\=\frac{-50}{35}-\frac{14}{35}+\frac{45}{35}\\=\frac{-50-14+45}{35}\\=\frac{-19}{35}\)
8. \(-\left(\frac{-10}{-7}\right) -\left(\frac{-8}{4}\right) +\left(\frac{10}{12}\right)\\= \frac{-10}{7}+ \frac{8}{4}+\frac{10}{12}\\=\frac{-10}{7}+\frac{2}{1}+\frac{5}{6}\\=\frac{-60}{42}+\frac{84}{42}+\frac{35}{42}\\=\frac{-60+84+35}{42}\\=\frac{59}{42}\)
9. \(+\left(\frac{8}{3}\right) -\left(\frac{-2}{-5}\right) +\left(\frac{-6}{-2}\right)\\= \frac{8}{3}- \frac{2}{5}+\frac{6}{2}\\=\frac{8}{3}-\frac{2}{5}+\frac{3}{1}\\=\frac{40}{15}-\frac{6}{15}+\frac{45}{15}\\=\frac{40-6+45}{15}\\=\frac{79}{15}\)
10. \(+\left(\frac{8}{9}\right) +\left(\frac{10}{-4}\right) +\left(\frac{-12}{-8}\right)\\= \frac{8}{9}- \frac{10}{4}+\frac{12}{8}\\=\frac{8}{9}-\frac{5}{2}+\frac{3}{2}\\=\frac{16}{18}-\frac{45}{18}+\frac{27}{18}\\=\frac{16-45+27}{18}\\=\frac{-2}{18}\\=\frac{-1}{9}\)
11. \(-\left(\frac{-10}{7}\right) -\left(\frac{-6}{2}\right) -\left(\frac{2}{-9}\right)\\= \frac{10}{7}+ \frac{6}{2}+\frac{2}{9}\\=\frac{10}{7}+\frac{3}{1}+\frac{2}{9}\\=\frac{90}{63}+\frac{189}{63}+\frac{14}{63}\\=\frac{90+189+14}{63}\\=\frac{293}{63}\)
12. \(-\left(\frac{-7}{-5}\right) +\left(\frac{6}{-4}\right) -\left(\frac{-10}{5}\right)\\= \frac{-7}{5}- \frac{6}{4}+\frac{10}{5}\\=\frac{-7}{5}-\frac{3}{2}+\frac{2}{1}\\=\frac{-14}{10}-\frac{15}{10}+\frac{20}{10}\\=\frac{-14-15+20}{10}\\=\frac{-9}{10}\)