Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{8}{9}\right) -\left(\frac{2}{6}\right) -\left(\frac{11}{8}\right)\\= \frac{8}{9}- \frac{2}{6}-\frac{11}{8}\\=\frac{8}{9}-\frac{1}{3}-\frac{11}{8}\\=\frac{64}{72}-\frac{24}{72}-\frac{99}{72}\\=\frac{64-24-99}{72}\\=\frac{-59}{72}\)
2. \(+\left(\frac{7}{8}\right) -\left(\frac{-6}{-7}\right) +\left(\frac{-5}{-10}\right)\\= \frac{7}{8}- \frac{6}{7}+\frac{5}{10}\\=\frac{7}{8}-\frac{6}{7}+\frac{1}{2}\\=\frac{49}{56}-\frac{48}{56}+\frac{28}{56}\\=\frac{49-48+28}{56}\\=\frac{29}{56}\)
3. \(-\left(\frac{-9}{7}\right) +\left(\frac{4}{-7}\right) +\left(\frac{-12}{8}\right)\\= \frac{9}{7}- \frac{4}{7}-\frac{12}{8}\\=\frac{9}{7}-\frac{4}{7}-\frac{3}{2}\\=\frac{18}{14}-\frac{8}{14}-\frac{21}{14}\\=\frac{18-8-21}{14}\\=\frac{-11}{14}\)
4. \(+\left(\frac{-8}{-3}\right) +\left(\frac{3}{8}\right) +\left(\frac{2}{8}\right)\\= \frac{8}{3}+ \frac{3}{8}+\frac{2}{8}\\=\frac{8}{3}+\frac{3}{8}+\frac{1}{4}\\=\frac{64}{24}+\frac{9}{24}+\frac{6}{24}\\=\frac{64+9+6}{24}\\=\frac{79}{24}\)
5. \(+\left(\frac{6}{-7}\right) -\left(\frac{2}{9}\right) +\left(\frac{5}{-9}\right)\\= \frac{-6}{7}- \frac{2}{9}-\frac{5}{9}\\=\frac{-54}{63}-\frac{14}{63}-\frac{35}{63}\\=\frac{-54-14-35}{63}\\=\frac{-103}{63}\)
6. \(+\left(\frac{3}{7}\right) -\left(\frac{7}{-7}\right) -\left(\frac{4}{-7}\right)\\= \frac{3}{7}+ \frac{7}{7}+\frac{4}{7}\\=\frac{3}{7}+\frac{1}{1}+\frac{4}{7}\\=\frac{3+1+4}{7}\\=\frac{8}{7}\)
7. \(-\left(\frac{-9}{2}\right) +\left(\frac{-6}{-7}\right) +\left(\frac{-8}{-12}\right)\\= \frac{9}{2}+ \frac{6}{7}+\frac{8}{12}\\=\frac{9}{2}+\frac{6}{7}+\frac{2}{3}\\=\frac{189}{42}+\frac{36}{42}+\frac{28}{42}\\=\frac{189+36+28}{42}\\=\frac{253}{42}\)
8. \(-\left(\frac{7}{-8}\right) -\left(\frac{-3}{-3}\right) -\left(\frac{3}{12}\right)\\= \frac{7}{8}- \frac{3}{3}-\frac{3}{12}\\=\frac{7}{8}-\frac{1}{1}-\frac{1}{4}\\=\frac{7-1-1}{8}\\=\frac{5}{8}\)
9. \(+\left(\frac{-8}{3}\right) +\left(\frac{-5}{-9}\right) +\left(\frac{-5}{-10}\right)\\= \frac{-8}{3}+ \frac{5}{9}+\frac{5}{10}\\=\frac{-8}{3}+\frac{5}{9}+\frac{1}{2}\\=\frac{-48}{18}+\frac{10}{18}+\frac{9}{18}\\=\frac{-48+10+9}{18}\\=\frac{-29}{18}\)
10. \(-\left(\frac{-9}{4}\right) -\left(\frac{2}{-8}\right) -\left(\frac{-9}{8}\right)\\= \frac{9}{4}+ \frac{2}{8}+\frac{9}{8}\\=\frac{9}{4}+\frac{1}{4}+\frac{9}{8}\\=\frac{18}{8}+\frac{2}{8}+\frac{9}{8}\\=\frac{18+2+9}{8}\\=\frac{29}{8}\)
11. \(-\left(\frac{10}{7}\right) +\left(\frac{3}{-8}\right) -\left(\frac{-2}{4}\right)\\= \frac{-10}{7}- \frac{3}{8}+\frac{2}{4}\\=\frac{-10}{7}-\frac{3}{8}+\frac{1}{2}\\=\frac{-80}{56}-\frac{21}{56}+\frac{28}{56}\\=\frac{-80-21+28}{56}\\=\frac{-73}{56}\)
12. \(-\left(\frac{-3}{5}\right) +\left(\frac{8}{6}\right) +\left(\frac{-2}{-12}\right)\\= \frac{3}{5}+ \frac{8}{6}+\frac{2}{12}\\=\frac{3}{5}+\frac{4}{3}+\frac{1}{6}\\=\frac{18}{30}+\frac{40}{30}+\frac{5}{30}\\=\frac{18+40+5}{30}\\=\frac{63}{30}\\=\frac{21}{10}\)