Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-4}{-9}\right) -\left(\frac{-6}{-2}\right) -\left(\frac{-8}{10}\right)\\= \frac{4}{9}- \frac{6}{2}+\frac{8}{10}\\=\frac{4}{9}-\frac{3}{1}+\frac{4}{5}\\=\frac{20}{45}-\frac{135}{45}+\frac{36}{45}\\=\frac{20-135+36}{45}\\=\frac{-79}{45}\)
2. \(+\left(\frac{10}{3}\right) +\left(\frac{-9}{-3}\right) +\left(\frac{10}{3}\right)\\= \frac{10}{3}+ \frac{9}{3}+\frac{10}{3}\\=\frac{10}{3}+\frac{3}{1}+\frac{10}{3}\\=\frac{10+3+10}{3}\\=\frac{23}{3}\)
3. \(+\left(\frac{-3}{-4}\right) +\left(\frac{-6}{9}\right) +\left(\frac{12}{12}\right)\\= \frac{3}{4}- \frac{6}{9}+\frac{12}{12}\\=\frac{3}{4}-\frac{2}{3}+\frac{1}{1}\\=\frac{9}{12}-\frac{8}{12}+\frac{12}{12}\\=\frac{9-8+12}{12}\\=\frac{13}{12}\)
4. \(-\left(\frac{10}{7}\right) -\left(\frac{-2}{3}\right) +\left(\frac{3}{-2}\right)\\= \frac{-10}{7}+ \frac{2}{3}-\frac{3}{2}\\=\frac{-60}{42}+\frac{28}{42}-\frac{63}{42}\\=\frac{-60+28-63}{42}\\=\frac{-95}{42}\)
5. \(+\left(\frac{-3}{5}\right) +\left(\frac{3}{6}\right) -\left(\frac{-5}{-9}\right)\\= \frac{-3}{5}+ \frac{3}{6}-\frac{5}{9}\\=\frac{-3}{5}+\frac{1}{2}-\frac{5}{9}\\=\frac{-54}{90}+\frac{45}{90}-\frac{50}{90}\\=\frac{-54+45-50}{90}\\=\frac{-59}{90}\)
6. \(-\left(\frac{3}{-2}\right) +\left(\frac{9}{4}\right) +\left(\frac{-11}{-12}\right)\\= \frac{3}{2}+ \frac{9}{4}+\frac{11}{12}\\=\frac{18}{12}+\frac{27}{12}+\frac{11}{12}\\=\frac{18+27+11}{12}\\=\frac{56}{12}\\=\frac{14}{3}\)
7. \(-\left(\frac{2}{-7}\right) +\left(\frac{6}{-3}\right) -\left(\frac{-7}{12}\right)\\= \frac{2}{7}- \frac{6}{3}+\frac{7}{12}\\=\frac{2}{7}-\frac{2}{1}+\frac{7}{12}\\=\frac{24}{84}-\frac{168}{84}+\frac{49}{84}\\=\frac{24-168+49}{84}\\=\frac{-95}{84}\)
8. \(+\left(\frac{-3}{2}\right) -\left(\frac{-6}{-3}\right) +\left(\frac{10}{-8}\right)\\= \frac{-3}{2}- \frac{6}{3}-\frac{10}{8}\\=\frac{-3}{2}-\frac{2}{1}-\frac{5}{4}\\=\frac{-6}{4}-\frac{8}{4}-\frac{5}{4}\\=\frac{-6-8-5}{4}\\=\frac{-19}{4}\)
9. \(-\left(\frac{7}{2}\right) +\left(\frac{-2}{7}\right) +\left(\frac{-10}{6}\right)\\= \frac{-7}{2}- \frac{2}{7}-\frac{10}{6}\\=\frac{-7}{2}-\frac{2}{7}-\frac{5}{3}\\=\frac{-147}{42}-\frac{12}{42}-\frac{70}{42}\\=\frac{-147-12-70}{42}\\=\frac{-229}{42}\)
10. \(+\left(\frac{-9}{2}\right) -\left(\frac{-8}{-3}\right) -\left(\frac{-12}{-8}\right)\\= \frac{-9}{2}- \frac{8}{3}-\frac{12}{8}\\=\frac{-9}{2}-\frac{8}{3}-\frac{3}{2}\\=\frac{-27}{6}-\frac{16}{6}-\frac{9}{6}\\=\frac{-27-16-9}{6}\\=\frac{-52}{6}\\=\frac{-26}{3}\)
11. \(-\left(\frac{-8}{5}\right) -\left(\frac{-8}{6}\right) -\left(\frac{2}{-4}\right)\\= \frac{8}{5}+ \frac{8}{6}+\frac{2}{4}\\=\frac{8}{5}+\frac{4}{3}+\frac{1}{2}\\=\frac{48}{30}+\frac{40}{30}+\frac{15}{30}\\=\frac{48+40+15}{30}\\=\frac{103}{30}\)
12. \(+\left(\frac{-8}{-3}\right) -\left(\frac{-6}{8}\right) -\left(\frac{-3}{9}\right)\\= \frac{8}{3}+ \frac{6}{8}+\frac{3}{9}\\=\frac{8}{3}+\frac{3}{4}+\frac{1}{3}\\=\frac{32}{12}+\frac{9}{12}+\frac{4}{12}\\=\frac{32+9+4}{12}\\=\frac{45}{12}\\=\frac{15}{4}\)