Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{9}\right) +\left(\frac{3}{6}\right) -\left(\frac{-2}{2}\right)\\= \frac{-10}{9}+ \frac{3}{6}+\frac{2}{2}\\=\frac{-10}{9}+\frac{1}{2}+\frac{1}{1}\\=\frac{-20}{18}+\frac{9}{18}+\frac{18}{18}\\=\frac{-20+9+18}{18}\\=\frac{7}{18}\)
2. \(+\left(\frac{-10}{-9}\right) -\left(\frac{8}{-2}\right) -\left(\frac{10}{-11}\right)\\= \frac{10}{9}+ \frac{8}{2}+\frac{10}{11}\\=\frac{10}{9}+\frac{4}{1}+\frac{10}{11}\\=\frac{110}{99}+\frac{396}{99}+\frac{90}{99}\\=\frac{110+396+90}{99}\\=\frac{596}{99}\)
3. \(-\left(\frac{-5}{6}\right) +\left(\frac{-3}{-5}\right) +\left(\frac{-2}{-3}\right)\\= \frac{5}{6}+ \frac{3}{5}+\frac{2}{3}\\=\frac{25}{30}+\frac{18}{30}+\frac{20}{30}\\=\frac{25+18+20}{30}\\=\frac{63}{30}\\=\frac{21}{10}\)
4. \(-\left(\frac{4}{-7}\right) +\left(\frac{-8}{-2}\right) -\left(\frac{-9}{9}\right)\\= \frac{4}{7}+ \frac{8}{2}+\frac{9}{9}\\=\frac{4}{7}+\frac{4}{1}+\frac{1}{1}\\=\frac{4+4+1}{7}\\=\frac{9}{7}\)
5. \(+\left(\frac{-9}{8}\right) -\left(\frac{9}{-7}\right) +\left(\frac{-12}{7}\right)\\= \frac{-9}{8}+ \frac{9}{7}-\frac{12}{7}\\=\frac{-63}{56}+\frac{72}{56}-\frac{96}{56}\\=\frac{-63+72-96}{56}\\=\frac{-87}{56}\)
6. \(+\left(\frac{4}{9}\right) -\left(\frac{-2}{9}\right) +\left(\frac{3}{-3}\right)\\= \frac{4}{9}+ \frac{2}{9}-\frac{3}{3}\\=\frac{4}{9}+\frac{2}{9}-\frac{1}{1}\\=\frac{4+2-1}{9}\\=\frac{5}{9}\)
7. \(+\left(\frac{-2}{-9}\right) +\left(\frac{-6}{-7}\right) -\left(\frac{12}{8}\right)\\= \frac{2}{9}+ \frac{6}{7}-\frac{12}{8}\\=\frac{2}{9}+\frac{6}{7}-\frac{3}{2}\\=\frac{28}{126}+\frac{108}{126}-\frac{189}{126}\\=\frac{28+108-189}{126}\\=\frac{-53}{126}\)
8. \(-\left(\frac{-8}{-3}\right) -\left(\frac{9}{-10}\right) +\left(\frac{-12}{-6}\right)\\= \frac{-8}{3}+ \frac{9}{10}+\frac{12}{6}\\=\frac{-8}{3}+\frac{9}{10}+\frac{2}{1}\\=\frac{-80}{30}+\frac{27}{30}+\frac{60}{30}\\=\frac{-80+27+60}{30}\\=\frac{7}{30}\)
9. \(-\left(\frac{-10}{-7}\right) -\left(\frac{6}{-8}\right) -\left(\frac{-12}{5}\right)\\= \frac{-10}{7}+ \frac{6}{8}+\frac{12}{5}\\=\frac{-10}{7}+\frac{3}{4}+\frac{12}{5}\\=\frac{-200}{140}+\frac{105}{140}+\frac{336}{140}\\=\frac{-200+105+336}{140}\\=\frac{241}{140}\)
10. \(+\left(\frac{3}{5}\right) +\left(\frac{-8}{-8}\right) +\left(\frac{6}{12}\right)\\= \frac{3}{5}+ \frac{8}{8}+\frac{6}{12}\\=\frac{3}{5}+\frac{1}{1}+\frac{1}{2}\\=\frac{6}{10}+\frac{10}{10}+\frac{5}{10}\\=\frac{6+10+5}{10}\\=\frac{21}{10}\)
11. \(-\left(\frac{6}{-5}\right) -\left(\frac{-6}{-9}\right) +\left(\frac{-9}{-8}\right)\\= \frac{6}{5}- \frac{6}{9}+\frac{9}{8}\\=\frac{6}{5}-\frac{2}{3}+\frac{9}{8}\\=\frac{144}{120}-\frac{80}{120}+\frac{135}{120}\\=\frac{144-80+135}{120}\\=\frac{199}{120}\)
12. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-3}{-7}\right) +\left(\frac{-5}{-8}\right)\\= \frac{6}{5}- \frac{3}{7}+\frac{5}{8}\\=\frac{336}{280}-\frac{120}{280}+\frac{175}{280}\\=\frac{336-120+175}{280}\\=\frac{391}{280}\)