Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-8}{-7}\right) +\left(\frac{-2}{2}\right) -\left(\frac{-11}{11}\right)\\= \frac{-8}{7}- \frac{2}{2}+\frac{11}{11}\\=\frac{-8}{7}-\frac{1}{1}+\frac{1}{1}\\=\frac{-8-1+1}{7}\\=\frac{-8}{7}\)
2. \(-\left(\frac{-7}{8}\right) -\left(\frac{2}{4}\right) +\left(\frac{10}{10}\right)\\= \frac{7}{8}- \frac{2}{4}+\frac{10}{10}\\=\frac{7}{8}-\frac{1}{2}+\frac{1}{1}\\=\frac{7-1+1}{8}\\=\frac{7}{8}\)
3. \(+\left(\frac{5}{8}\right) +\left(\frac{-6}{6}\right) +\left(\frac{10}{-3}\right)\\= \frac{5}{8}- \frac{6}{6}-\frac{10}{3}\\=\frac{5}{8}-\frac{1}{1}-\frac{10}{3}\\=\frac{15}{24}-\frac{24}{24}-\frac{80}{24}\\=\frac{15-24-80}{24}\\=\frac{-89}{24}\)
4. \(+\left(\frac{-8}{-7}\right) +\left(\frac{5}{2}\right) +\left(\frac{12}{-6}\right)\\= \frac{8}{7}+ \frac{5}{2}-\frac{12}{6}\\=\frac{8}{7}+\frac{5}{2}-\frac{2}{1}\\=\frac{16}{14}+\frac{35}{14}-\frac{28}{14}\\=\frac{16+35-28}{14}\\=\frac{23}{14}\)
5. \(+\left(\frac{4}{5}\right) -\left(\frac{-5}{5}\right) +\left(\frac{-5}{2}\right)\\= \frac{4}{5}+ \frac{5}{5}-\frac{5}{2}\\=\frac{4}{5}+\frac{1}{1}-\frac{5}{2}\\=\frac{8}{10}+\frac{10}{10}-\frac{25}{10}\\=\frac{8+10-25}{10}\\=\frac{-7}{10}\)
6. \(+\left(\frac{3}{2}\right) +\left(\frac{-3}{-4}\right) -\left(\frac{-12}{8}\right)\\= \frac{3}{2}+ \frac{3}{4}+\frac{12}{8}\\=\frac{3}{2}+\frac{3}{4}+\frac{3}{2}\\=\frac{6}{4}+\frac{3}{4}+\frac{6}{4}\\=\frac{6+3+6}{4}\\=\frac{15}{4}\)
7. \(+\left(\frac{7}{4}\right) -\left(\frac{-7}{9}\right) -\left(\frac{-8}{-2}\right)\\= \frac{7}{4}+ \frac{7}{9}-\frac{8}{2}\\=\frac{7}{4}+\frac{7}{9}-\frac{4}{1}\\=\frac{63}{36}+\frac{28}{36}-\frac{144}{36}\\=\frac{63+28-144}{36}\\=\frac{-53}{36}\)
8. \(-\left(\frac{-10}{3}\right) -\left(\frac{-5}{10}\right) +\left(\frac{-2}{-12}\right)\\= \frac{10}{3}+ \frac{5}{10}+\frac{2}{12}\\=\frac{10}{3}+\frac{1}{2}+\frac{1}{6}\\=\frac{20}{6}+\frac{3}{6}+\frac{1}{6}\\=\frac{20+3+1}{6}\\=\frac{24}{6}\\=\frac{4}{1}\)
9. \(+\left(\frac{3}{-4}\right) -\left(\frac{10}{5}\right) -\left(\frac{-2}{2}\right)\\= \frac{-3}{4}- \frac{10}{5}+\frac{2}{2}\\=\frac{-3}{4}-\frac{2}{1}+\frac{1}{1}\\=\frac{-3-2+1}{4}\\=\frac{-4}{4}\\=\frac{-1}{1}\)
10. \(+\left(\frac{10}{-7}\right) -\left(\frac{7}{-2}\right) -\left(\frac{6}{-7}\right)\\= \frac{-10}{7}+ \frac{7}{2}+\frac{6}{7}\\=\frac{-20}{14}+\frac{49}{14}+\frac{12}{14}\\=\frac{-20+49+12}{14}\\=\frac{41}{14}\)
11. \(-\left(\frac{9}{2}\right) +\left(\frac{-7}{-6}\right) -\left(\frac{8}{-7}\right)\\= \frac{-9}{2}+ \frac{7}{6}+\frac{8}{7}\\=\frac{-189}{42}+\frac{49}{42}+\frac{48}{42}\\=\frac{-189+49+48}{42}\\=\frac{-92}{42}\\=\frac{-46}{21}\)
12. \(-\left(\frac{2}{-7}\right) -\left(\frac{-8}{-9}\right) -\left(\frac{4}{-2}\right)\\= \frac{2}{7}- \frac{8}{9}+\frac{4}{2}\\=\frac{2}{7}-\frac{8}{9}+\frac{2}{1}\\=\frac{18}{63}-\frac{56}{63}+\frac{126}{63}\\=\frac{18-56+126}{63}\\=\frac{88}{63}\)