Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-8}{-3}\right) -\left(\frac{7}{8}\right) -\left(\frac{-10}{-7}\right)\\= \frac{-8}{3}- \frac{7}{8}-\frac{10}{7}\\=\frac{-448}{168}-\frac{147}{168}-\frac{240}{168}\\=\frac{-448-147-240}{168}\\=\frac{-835}{168}\)
2. \(-\left(\frac{-10}{-3}\right) -\left(\frac{-9}{-6}\right) -\left(\frac{-5}{6}\right)\\= \frac{-10}{3}- \frac{9}{6}+\frac{5}{6}\\=\frac{-10}{3}-\frac{3}{2}+\frac{5}{6}\\=\frac{-20}{6}-\frac{9}{6}+\frac{5}{6}\\=\frac{-20-9+5}{6}\\=\frac{-24}{6}\\=\frac{-4}{1}\)
3. \(+\left(\frac{-10}{-7}\right) -\left(\frac{7}{10}\right) +\left(\frac{12}{-10}\right)\\= \frac{10}{7}- \frac{7}{10}-\frac{12}{10}\\=\frac{10}{7}-\frac{7}{10}-\frac{6}{5}\\=\frac{100}{70}-\frac{49}{70}-\frac{84}{70}\\=\frac{100-49-84}{70}\\=\frac{-33}{70}\)
4. \(+\left(\frac{-10}{9}\right) -\left(\frac{-8}{-4}\right) +\left(\frac{-5}{-4}\right)\\= \frac{-10}{9}- \frac{8}{4}+\frac{5}{4}\\=\frac{-10}{9}-\frac{2}{1}+\frac{5}{4}\\=\frac{-40}{36}-\frac{72}{36}+\frac{45}{36}\\=\frac{-40-72+45}{36}\\=\frac{-67}{36}\)
5. \(+\left(\frac{10}{3}\right) +\left(\frac{-10}{3}\right) -\left(\frac{7}{-12}\right)\\= \frac{10}{3}- \frac{10}{3}+\frac{7}{12}\\=\frac{40}{12}-\frac{40}{12}+\frac{7}{12}\\=\frac{40-40+7}{12}\\=\frac{7}{12}\)
6. \(+\left(\frac{-5}{-6}\right) +\left(\frac{6}{-10}\right) +\left(\frac{-5}{-3}\right)\\= \frac{5}{6}- \frac{6}{10}+\frac{5}{3}\\=\frac{5}{6}-\frac{3}{5}+\frac{5}{3}\\=\frac{25}{30}-\frac{18}{30}+\frac{50}{30}\\=\frac{25-18+50}{30}\\=\frac{57}{30}\\=\frac{19}{10}\)
7. \(+\left(\frac{10}{-3}\right) -\left(\frac{10}{8}\right) +\left(\frac{8}{12}\right)\\= \frac{-10}{3}- \frac{10}{8}+\frac{8}{12}\\=\frac{-10}{3}-\frac{5}{4}+\frac{2}{3}\\=\frac{-40}{12}-\frac{15}{12}+\frac{8}{12}\\=\frac{-40-15+8}{12}\\=\frac{-47}{12}\)
8. \(+\left(\frac{-2}{-9}\right) +\left(\frac{-4}{-3}\right) +\left(\frac{-3}{4}\right)\\= \frac{2}{9}+ \frac{4}{3}-\frac{3}{4}\\=\frac{8}{36}+\frac{48}{36}-\frac{27}{36}\\=\frac{8+48-27}{36}\\=\frac{29}{36}\)
9. \(-\left(\frac{9}{7}\right) +\left(\frac{-9}{2}\right) -\left(\frac{-4}{2}\right)\\= \frac{-9}{7}- \frac{9}{2}+\frac{4}{2}\\=\frac{-9}{7}-\frac{9}{2}+\frac{2}{1}\\=\frac{-18}{14}-\frac{63}{14}+\frac{28}{14}\\=\frac{-18-63+28}{14}\\=\frac{-53}{14}\)
10. \(+\left(\frac{10}{-3}\right) +\left(\frac{-10}{4}\right) -\left(\frac{2}{9}\right)\\= \frac{-10}{3}- \frac{10}{4}-\frac{2}{9}\\=\frac{-10}{3}-\frac{5}{2}-\frac{2}{9}\\=\frac{-60}{18}-\frac{45}{18}-\frac{4}{18}\\=\frac{-60-45-4}{18}\\=\frac{-109}{18}\)
11. \(+\left(\frac{-3}{2}\right) -\left(\frac{4}{10}\right) +\left(\frac{-3}{10}\right)\\= \frac{-3}{2}- \frac{4}{10}-\frac{3}{10}\\=\frac{-3}{2}-\frac{2}{5}-\frac{3}{10}\\=\frac{-15}{10}-\frac{4}{10}-\frac{3}{10}\\=\frac{-15-4-3}{10}\\=\frac{-22}{10}\\=\frac{-11}{5}\)
12. \(-\left(\frac{-3}{7}\right) +\left(\frac{8}{8}\right) +\left(\frac{12}{7}\right)\\= \frac{3}{7}+ \frac{8}{8}+\frac{12}{7}\\=\frac{3}{7}+\frac{1}{1}+\frac{12}{7}\\=\frac{3+1+12}{7}\\=\frac{16}{7}\)