Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{3}\right) -\left(\frac{5}{2}\right) +\left(\frac{3}{5}\right)\\= \frac{-5}{3}- \frac{5}{2}+\frac{3}{5}\\=\frac{-50}{30}-\frac{75}{30}+\frac{18}{30}\\=\frac{-50-75+18}{30}\\=\frac{-107}{30}\)
2. \(-\left(\frac{5}{4}\right) +\left(\frac{7}{-6}\right) +\left(\frac{-5}{-9}\right)\\= \frac{-5}{4}- \frac{7}{6}+\frac{5}{9}\\=\frac{-45}{36}-\frac{42}{36}+\frac{20}{36}\\=\frac{-45-42+20}{36}\\=\frac{-67}{36}\)
3. \(-\left(\frac{9}{-5}\right) -\left(\frac{4}{-10}\right) +\left(\frac{5}{-11}\right)\\= \frac{9}{5}+ \frac{4}{10}-\frac{5}{11}\\=\frac{9}{5}+\frac{2}{5}-\frac{5}{11}\\=\frac{99}{55}+\frac{22}{55}-\frac{25}{55}\\=\frac{99+22-25}{55}\\=\frac{96}{55}\)
4. \(-\left(\frac{9}{2}\right) -\left(\frac{3}{2}\right) -\left(\frac{-11}{7}\right)\\= \frac{-9}{2}- \frac{3}{2}+\frac{11}{7}\\=\frac{-63}{14}-\frac{21}{14}+\frac{22}{14}\\=\frac{-63-21+22}{14}\\=\frac{-62}{14}\\=\frac{-31}{7}\)
5. \(-\left(\frac{-2}{9}\right) +\left(\frac{2}{-6}\right) -\left(\frac{10}{-7}\right)\\= \frac{2}{9}- \frac{2}{6}+\frac{10}{7}\\=\frac{2}{9}-\frac{1}{3}+\frac{10}{7}\\=\frac{14}{63}-\frac{21}{63}+\frac{90}{63}\\=\frac{14-21+90}{63}\\=\frac{83}{63}\)
6. \(-\left(\frac{7}{-8}\right) -\left(\frac{9}{-3}\right) -\left(\frac{-11}{-6}\right)\\= \frac{7}{8}+ \frac{9}{3}-\frac{11}{6}\\=\frac{7}{8}+\frac{3}{1}-\frac{11}{6}\\=\frac{21}{24}+\frac{72}{24}-\frac{44}{24}\\=\frac{21+72-44}{24}\\=\frac{49}{24}\)
7. \(-\left(\frac{7}{-4}\right) -\left(\frac{3}{5}\right) +\left(\frac{5}{-9}\right)\\= \frac{7}{4}- \frac{3}{5}-\frac{5}{9}\\=\frac{315}{180}-\frac{108}{180}-\frac{100}{180}\\=\frac{315-108-100}{180}\\=\frac{107}{180}\)
8. \(-\left(\frac{-4}{-9}\right) -\left(\frac{5}{-3}\right) -\left(\frac{-10}{5}\right)\\= \frac{-4}{9}+ \frac{5}{3}+\frac{10}{5}\\=\frac{-4}{9}+\frac{5}{3}+\frac{2}{1}\\=\frac{-4+5+2}{9}\\=\frac{3}{9}\\=\frac{1}{3}\)
9. \(-\left(\frac{-9}{2}\right) +\left(\frac{4}{-9}\right) -\left(\frac{-7}{2}\right)\\= \frac{9}{2}- \frac{4}{9}+\frac{7}{2}\\=\frac{81}{18}-\frac{8}{18}+\frac{63}{18}\\=\frac{81-8+63}{18}\\=\frac{136}{18}\\=\frac{68}{9}\)
10. \(-\left(\frac{-3}{8}\right) +\left(\frac{7}{5}\right) +\left(\frac{5}{-6}\right)\\= \frac{3}{8}+ \frac{7}{5}-\frac{5}{6}\\=\frac{45}{120}+\frac{168}{120}-\frac{100}{120}\\=\frac{45+168-100}{120}\\=\frac{113}{120}\)
11. \(+\left(\frac{-10}{-7}\right) +\left(\frac{-4}{6}\right) -\left(\frac{-9}{-4}\right)\\= \frac{10}{7}- \frac{4}{6}-\frac{9}{4}\\=\frac{10}{7}-\frac{2}{3}-\frac{9}{4}\\=\frac{120}{84}-\frac{56}{84}-\frac{189}{84}\\=\frac{120-56-189}{84}\\=\frac{-125}{84}\)
12. \(+\left(\frac{5}{3}\right) +\left(\frac{5}{4}\right) -\left(\frac{10}{2}\right)\\= \frac{5}{3}+ \frac{5}{4}-\frac{10}{2}\\=\frac{5}{3}+\frac{5}{4}-\frac{5}{1}\\=\frac{20}{12}+\frac{15}{12}-\frac{60}{12}\\=\frac{20+15-60}{12}\\=\frac{-25}{12}\)