Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{7}{3}\right) -\left(\frac{-5}{-8}\right) -\left(\frac{-12}{-5}\right)\\= \frac{7}{3}- \frac{5}{8}-\frac{12}{5}\\=\frac{280}{120}-\frac{75}{120}-\frac{288}{120}\\=\frac{280-75-288}{120}\\=\frac{-83}{120}\)
2. \(+\left(\frac{10}{3}\right) +\left(\frac{-4}{-8}\right) -\left(\frac{8}{-8}\right)\\= \frac{10}{3}+ \frac{4}{8}+\frac{8}{8}\\=\frac{10}{3}+\frac{1}{2}+\frac{1}{1}\\=\frac{20}{6}+\frac{3}{6}+\frac{6}{6}\\=\frac{20+3+6}{6}\\=\frac{29}{6}\)
3. \(-\left(\frac{2}{-3}\right) -\left(\frac{8}{3}\right) +\left(\frac{7}{-9}\right)\\= \frac{2}{3}- \frac{8}{3}-\frac{7}{9}\\=\frac{6}{9}-\frac{24}{9}-\frac{7}{9}\\=\frac{6-24-7}{9}\\=\frac{-25}{9}\)
4. \(-\left(\frac{-6}{-5}\right) -\left(\frac{9}{6}\right) -\left(\frac{7}{3}\right)\\= \frac{-6}{5}- \frac{9}{6}-\frac{7}{3}\\=\frac{-6}{5}-\frac{3}{2}-\frac{7}{3}\\=\frac{-36}{30}-\frac{45}{30}-\frac{70}{30}\\=\frac{-36-45-70}{30}\\=\frac{-151}{30}\)
5. \(+\left(\frac{-2}{5}\right) -\left(\frac{-3}{-5}\right) +\left(\frac{-9}{-7}\right)\\= \frac{-2}{5}- \frac{3}{5}+\frac{9}{7}\\=\frac{-14}{35}-\frac{21}{35}+\frac{45}{35}\\=\frac{-14-21+45}{35}\\=\frac{10}{35}\\=\frac{2}{7}\)
6. \(+\left(\frac{4}{-9}\right) -\left(\frac{-3}{10}\right) -\left(\frac{4}{4}\right)\\= \frac{-4}{9}+ \frac{3}{10}-\frac{4}{4}\\=\frac{-4}{9}+\frac{3}{10}-\frac{1}{1}\\=\frac{-40}{90}+\frac{27}{90}-\frac{90}{90}\\=\frac{-40+27-90}{90}\\=\frac{-103}{90}\)
7. \(+\left(\frac{10}{7}\right) +\left(\frac{5}{-2}\right) +\left(\frac{-9}{-9}\right)\\= \frac{10}{7}- \frac{5}{2}+\frac{9}{9}\\=\frac{10}{7}-\frac{5}{2}+\frac{1}{1}\\=\frac{20}{14}-\frac{35}{14}+\frac{14}{14}\\=\frac{20-35+14}{14}\\=\frac{-1}{14}\)
8. \(-\left(\frac{-4}{9}\right) -\left(\frac{5}{9}\right) -\left(\frac{-8}{-6}\right)\\= \frac{4}{9}- \frac{5}{9}-\frac{8}{6}\\=\frac{4}{9}-\frac{5}{9}-\frac{4}{3}\\=\frac{4-5-4}{9}\\=\frac{-5}{9}\)
9. \(+\left(\frac{-3}{-7}\right) +\left(\frac{4}{-4}\right) -\left(\frac{3}{-12}\right)\\= \frac{3}{7}- \frac{4}{4}+\frac{3}{12}\\=\frac{3}{7}-\frac{1}{1}+\frac{1}{4}\\=\frac{12}{28}-\frac{28}{28}+\frac{7}{28}\\=\frac{12-28+7}{28}\\=\frac{-9}{28}\)
10. \(-\left(\frac{6}{-5}\right) -\left(\frac{-5}{5}\right) -\left(\frac{-9}{-5}\right)\\= \frac{6}{5}+ \frac{5}{5}-\frac{9}{5}\\=\frac{6}{5}+\frac{1}{1}-\frac{9}{5}\\=\frac{6+1-9}{5}\\=\frac{-2}{5}\)
11. \(+\left(\frac{4}{3}\right) +\left(\frac{-10}{3}\right) -\left(\frac{-4}{-2}\right)\\= \frac{4}{3}- \frac{10}{3}-\frac{4}{2}\\=\frac{4}{3}-\frac{10}{3}-\frac{2}{1}\\=\frac{4-10-2}{3}\\=\frac{-8}{3}\)
12. \(+\left(\frac{-5}{-2}\right) -\left(\frac{-2}{8}\right) -\left(\frac{-4}{3}\right)\\= \frac{5}{2}+ \frac{2}{8}+\frac{4}{3}\\=\frac{5}{2}+\frac{1}{4}+\frac{4}{3}\\=\frac{30}{12}+\frac{3}{12}+\frac{16}{12}\\=\frac{30+3+16}{12}\\=\frac{49}{12}\)