Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{-6}\right) +\left(\frac{-3}{8}\right) -\left(\frac{-9}{6}\right)\\= \frac{7}{6}- \frac{3}{8}+\frac{9}{6}\\=\frac{7}{6}-\frac{3}{8}+\frac{3}{2}\\=\frac{28}{24}-\frac{9}{24}+\frac{36}{24}\\=\frac{28-9+36}{24}\\=\frac{55}{24}\)
2. \(-\left(\frac{-4}{-9}\right) -\left(\frac{7}{4}\right) +\left(\frac{2}{4}\right)\\= \frac{-4}{9}- \frac{7}{4}+\frac{2}{4}\\=\frac{-4}{9}-\frac{7}{4}+\frac{1}{2}\\=\frac{-16}{36}-\frac{63}{36}+\frac{18}{36}\\=\frac{-16-63+18}{36}\\=\frac{-61}{36}\)
3. \(-\left(\frac{-10}{3}\right) +\left(\frac{5}{-3}\right) +\left(\frac{6}{8}\right)\\= \frac{10}{3}- \frac{5}{3}+\frac{6}{8}\\=\frac{10}{3}-\frac{5}{3}+\frac{3}{4}\\=\frac{40}{12}-\frac{20}{12}+\frac{9}{12}\\=\frac{40-20+9}{12}\\=\frac{29}{12}\)
4. \(+\left(\frac{-4}{9}\right) +\left(\frac{10}{-10}\right) +\left(\frac{4}{-4}\right)\\= \frac{-4}{9}- \frac{10}{10}-\frac{4}{4}\\=\frac{-4}{9}-\frac{1}{1}-\frac{1}{1}\\=\frac{-4-1-1}{9}\\=\frac{-6}{9}\\=\frac{-2}{3}\)
5. \(+\left(\frac{-8}{-7}\right) +\left(\frac{2}{-9}\right) -\left(\frac{-7}{-8}\right)\\= \frac{8}{7}- \frac{2}{9}-\frac{7}{8}\\=\frac{576}{504}-\frac{112}{504}-\frac{441}{504}\\=\frac{576-112-441}{504}\\=\frac{23}{504}\)
6. \(-\left(\frac{-6}{-7}\right) -\left(\frac{9}{5}\right) +\left(\frac{-4}{3}\right)\\= \frac{-6}{7}- \frac{9}{5}-\frac{4}{3}\\=\frac{-90}{105}-\frac{189}{105}-\frac{140}{105}\\=\frac{-90-189-140}{105}\\=\frac{-419}{105}\)
7. \(+\left(\frac{-5}{6}\right) +\left(\frac{5}{-10}\right) -\left(\frac{6}{-9}\right)\\= \frac{-5}{6}- \frac{5}{10}+\frac{6}{9}\\=\frac{-5}{6}-\frac{1}{2}+\frac{2}{3}\\=\frac{-5-1+2}{6}\\=\frac{-4}{6}\\=\frac{-2}{3}\)
8. \(+\left(\frac{4}{-3}\right) -\left(\frac{5}{-2}\right) -\left(\frac{-2}{-4}\right)\\= \frac{-4}{3}+ \frac{5}{2}-\frac{2}{4}\\=\frac{-4}{3}+\frac{5}{2}-\frac{1}{2}\\=\frac{-8}{6}+\frac{15}{6}-\frac{3}{6}\\=\frac{-8+15-3}{6}\\=\frac{4}{6}\\=\frac{2}{3}\)
9. \(-\left(\frac{2}{3}\right) -\left(\frac{8}{3}\right) -\left(\frac{-3}{-6}\right)\\= \frac{-2}{3}- \frac{8}{3}-\frac{3}{6}\\=\frac{-2}{3}-\frac{8}{3}-\frac{1}{2}\\=\frac{-4}{6}-\frac{16}{6}-\frac{3}{6}\\=\frac{-4-16-3}{6}\\=\frac{-23}{6}\)
10. \(-\left(\frac{-10}{-3}\right) +\left(\frac{6}{10}\right) -\left(\frac{3}{4}\right)\\= \frac{-10}{3}+ \frac{6}{10}-\frac{3}{4}\\=\frac{-10}{3}+\frac{3}{5}-\frac{3}{4}\\=\frac{-200}{60}+\frac{36}{60}-\frac{45}{60}\\=\frac{-200+36-45}{60}\\=\frac{-209}{60}\)
11. \(+\left(\frac{-3}{8}\right) -\left(\frac{4}{5}\right) -\left(\frac{3}{-8}\right)\\= \frac{-3}{8}- \frac{4}{5}+\frac{3}{8}\\=\frac{-15}{40}-\frac{32}{40}+\frac{15}{40}\\=\frac{-15-32+15}{40}\\=\frac{-32}{40}\\=\frac{-4}{5}\)
12. \(+\left(\frac{-2}{-7}\right) -\left(\frac{-10}{-7}\right) +\left(\frac{-12}{-8}\right)\\= \frac{2}{7}- \frac{10}{7}+\frac{12}{8}\\=\frac{2}{7}-\frac{10}{7}+\frac{3}{2}\\=\frac{4}{14}-\frac{20}{14}+\frac{21}{14}\\=\frac{4-20+21}{14}\\=\frac{5}{14}\)