Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{-2}\right) +\left(\frac{2}{-7}\right) -\left(\frac{5}{5}\right)\\= \frac{7}{2}- \frac{2}{7}-\frac{5}{5}\\=\frac{7}{2}-\frac{2}{7}-\frac{1}{1}\\=\frac{49}{14}-\frac{4}{14}-\frac{14}{14}\\=\frac{49-4-14}{14}\\=\frac{31}{14}\)
2. \(-\left(\frac{-10}{7}\right) -\left(\frac{4}{-8}\right) -\left(\frac{2}{-3}\right)\\= \frac{10}{7}+ \frac{4}{8}+\frac{2}{3}\\=\frac{10}{7}+\frac{1}{2}+\frac{2}{3}\\=\frac{60}{42}+\frac{21}{42}+\frac{28}{42}\\=\frac{60+21+28}{42}\\=\frac{109}{42}\)
3. \(-\left(\frac{-5}{-4}\right) +\left(\frac{3}{9}\right) -\left(\frac{-10}{5}\right)\\= \frac{-5}{4}+ \frac{3}{9}+\frac{10}{5}\\=\frac{-5}{4}+\frac{1}{3}+\frac{2}{1}\\=\frac{-15}{12}+\frac{4}{12}+\frac{24}{12}\\=\frac{-15+4+24}{12}\\=\frac{13}{12}\)
4. \(+\left(\frac{-9}{8}\right) -\left(\frac{6}{9}\right) +\left(\frac{4}{7}\right)\\= \frac{-9}{8}- \frac{6}{9}+\frac{4}{7}\\=\frac{-9}{8}-\frac{2}{3}+\frac{4}{7}\\=\frac{-189}{168}-\frac{112}{168}+\frac{96}{168}\\=\frac{-189-112+96}{168}\\=\frac{-205}{168}\)
5. \(+\left(\frac{-8}{-5}\right) -\left(\frac{-9}{-2}\right) +\left(\frac{7}{-9}\right)\\= \frac{8}{5}- \frac{9}{2}-\frac{7}{9}\\=\frac{144}{90}-\frac{405}{90}-\frac{70}{90}\\=\frac{144-405-70}{90}\\=\frac{-331}{90}\)
6. \(+\left(\frac{10}{-7}\right) +\left(\frac{-9}{-7}\right) -\left(\frac{-8}{9}\right)\\= \frac{-10}{7}+ \frac{9}{7}+\frac{8}{9}\\=\frac{-90}{63}+\frac{81}{63}+\frac{56}{63}\\=\frac{-90+81+56}{63}\\=\frac{47}{63}\)
7. \(-\left(\frac{9}{-7}\right) -\left(\frac{-9}{7}\right) -\left(\frac{5}{10}\right)\\= \frac{9}{7}+ \frac{9}{7}-\frac{5}{10}\\=\frac{9}{7}+\frac{9}{7}-\frac{1}{2}\\=\frac{18}{14}+\frac{18}{14}-\frac{7}{14}\\=\frac{18+18-7}{14}\\=\frac{29}{14}\)
8. \(+\left(\frac{-7}{3}\right) -\left(\frac{3}{-6}\right) -\left(\frac{-4}{-4}\right)\\= \frac{-7}{3}+ \frac{3}{6}-\frac{4}{4}\\=\frac{-7}{3}+\frac{1}{2}-\frac{1}{1}\\=\frac{-14}{6}+\frac{3}{6}-\frac{6}{6}\\=\frac{-14+3-6}{6}\\=\frac{-17}{6}\)
9. \(+\left(\frac{7}{3}\right) -\left(\frac{5}{9}\right) +\left(\frac{-2}{4}\right)\\= \frac{7}{3}- \frac{5}{9}-\frac{2}{4}\\=\frac{7}{3}-\frac{5}{9}-\frac{1}{2}\\=\frac{42}{18}-\frac{10}{18}-\frac{9}{18}\\=\frac{42-10-9}{18}\\=\frac{23}{18}\)
10. \(+\left(\frac{3}{-2}\right) +\left(\frac{-7}{9}\right) +\left(\frac{8}{10}\right)\\= \frac{-3}{2}- \frac{7}{9}+\frac{8}{10}\\=\frac{-3}{2}-\frac{7}{9}+\frac{4}{5}\\=\frac{-135}{90}-\frac{70}{90}+\frac{72}{90}\\=\frac{-135-70+72}{90}\\=\frac{-133}{90}\)
11. \(-\left(\frac{-8}{-3}\right) -\left(\frac{-2}{-2}\right) -\left(\frac{3}{12}\right)\\= \frac{-8}{3}- \frac{2}{2}-\frac{3}{12}\\=\frac{-8}{3}-\frac{1}{1}-\frac{1}{4}\\=\frac{-32}{12}-\frac{12}{12}-\frac{3}{12}\\=\frac{-32-12-3}{12}\\=\frac{-47}{12}\)
12. \(+\left(\frac{5}{-2}\right) -\left(\frac{-9}{-9}\right) +\left(\frac{6}{4}\right)\\= \frac{-5}{2}- \frac{9}{9}+\frac{6}{4}\\=\frac{-5}{2}-\frac{1}{1}+\frac{3}{2}\\=\frac{-5-1+3}{2}\\=\frac{-3}{2}\)