Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-7}\right) -\left(\frac{3}{-4}\right) +\left(\frac{4}{-7}\right)\\= \frac{10}{7}+ \frac{3}{4}-\frac{4}{7}\\=\frac{40}{28}+\frac{21}{28}-\frac{16}{28}\\=\frac{40+21-16}{28}\\=\frac{45}{28}\)
2. \(+\left(\frac{-2}{-7}\right) -\left(\frac{2}{-6}\right) -\left(\frac{-7}{-6}\right)\\= \frac{2}{7}+ \frac{2}{6}-\frac{7}{6}\\=\frac{2}{7}+\frac{1}{3}-\frac{7}{6}\\=\frac{12}{42}+\frac{14}{42}-\frac{49}{42}\\=\frac{12+14-49}{42}\\=\frac{-23}{42}\)
3. \(-\left(\frac{-4}{3}\right) +\left(\frac{-9}{8}\right) +\left(\frac{-9}{-4}\right)\\= \frac{4}{3}- \frac{9}{8}+\frac{9}{4}\\=\frac{32}{24}-\frac{27}{24}+\frac{54}{24}\\=\frac{32-27+54}{24}\\=\frac{59}{24}\)
4. \(+\left(\frac{-7}{6}\right) -\left(\frac{5}{-6}\right) +\left(\frac{-5}{-10}\right)\\= \frac{-7}{6}+ \frac{5}{6}+\frac{5}{10}\\=\frac{-7}{6}+\frac{5}{6}+\frac{1}{2}\\=\frac{-7+5+1}{6}\\=\frac{-1}{6}\)
5. \(+\left(\frac{-8}{-9}\right) +\left(\frac{9}{-5}\right) +\left(\frac{-11}{7}\right)\\= \frac{8}{9}- \frac{9}{5}-\frac{11}{7}\\=\frac{280}{315}-\frac{567}{315}-\frac{495}{315}\\=\frac{280-567-495}{315}\\=\frac{-782}{315}\)
6. \(+\left(\frac{2}{-5}\right) +\left(\frac{5}{-8}\right) +\left(\frac{-5}{-6}\right)\\= \frac{-2}{5}- \frac{5}{8}+\frac{5}{6}\\=\frac{-48}{120}-\frac{75}{120}+\frac{100}{120}\\=\frac{-48-75+100}{120}\\=\frac{-23}{120}\)
7. \(+\left(\frac{-9}{-4}\right) -\left(\frac{-6}{-5}\right) +\left(\frac{7}{12}\right)\\= \frac{9}{4}- \frac{6}{5}+\frac{7}{12}\\=\frac{135}{60}-\frac{72}{60}+\frac{35}{60}\\=\frac{135-72+35}{60}\\=\frac{98}{60}\\=\frac{49}{30}\)
8. \(+\left(\frac{-3}{8}\right) +\left(\frac{-10}{-6}\right) +\left(\frac{10}{-2}\right)\\= \frac{-3}{8}+ \frac{10}{6}-\frac{10}{2}\\=\frac{-3}{8}+\frac{5}{3}-\frac{5}{1}\\=\frac{-9}{24}+\frac{40}{24}-\frac{120}{24}\\=\frac{-9+40-120}{24}\\=\frac{-89}{24}\)
9. \(+\left(\frac{3}{8}\right) -\left(\frac{-3}{-6}\right) +\left(\frac{-7}{8}\right)\\= \frac{3}{8}- \frac{3}{6}-\frac{7}{8}\\=\frac{3}{8}-\frac{1}{2}-\frac{7}{8}\\=\frac{3-1-7}{8}\\=\frac{-5}{8}\)
10. \(+\left(\frac{7}{8}\right) +\left(\frac{-8}{-4}\right) -\left(\frac{-12}{9}\right)\\= \frac{7}{8}+ \frac{8}{4}+\frac{12}{9}\\=\frac{7}{8}+\frac{2}{1}+\frac{4}{3}\\=\frac{21}{24}+\frac{48}{24}+\frac{32}{24}\\=\frac{21+48+32}{24}\\=\frac{101}{24}\)
11. \(+\left(\frac{-7}{-6}\right) +\left(\frac{-6}{-7}\right) -\left(\frac{-8}{4}\right)\\= \frac{7}{6}+ \frac{6}{7}+\frac{8}{4}\\=\frac{7}{6}+\frac{6}{7}+\frac{2}{1}\\=\frac{49}{42}+\frac{36}{42}+\frac{84}{42}\\=\frac{49+36+84}{42}\\=\frac{169}{42}\)
12. \(+\left(\frac{4}{-5}\right) +\left(\frac{-8}{10}\right) +\left(\frac{-6}{-12}\right)\\= \frac{-4}{5}- \frac{8}{10}+\frac{6}{12}\\=\frac{-4}{5}-\frac{4}{5}+\frac{1}{2}\\=\frac{-8}{10}-\frac{8}{10}+\frac{5}{10}\\=\frac{-8-8+5}{10}\\=\frac{-11}{10}\)