Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{-7}\right) -\left(\frac{3}{8}\right) -\left(\frac{-6}{4}\right)\\= \frac{5}{7}- \frac{3}{8}+\frac{6}{4}\\=\frac{5}{7}-\frac{3}{8}+\frac{3}{2}\\=\frac{40}{56}-\frac{21}{56}+\frac{84}{56}\\=\frac{40-21+84}{56}\\=\frac{103}{56}\)
2. \(+\left(\frac{-4}{9}\right) -\left(\frac{-4}{9}\right) -\left(\frac{11}{5}\right)\\= \frac{-4}{9}+ \frac{4}{9}-\frac{11}{5}\\=\frac{-20}{45}+\frac{20}{45}-\frac{99}{45}\\=\frac{-20+20-99}{45}\\=\frac{-99}{45}\\=\frac{-11}{5}\)
3. \(-\left(\frac{-3}{-2}\right) -\left(\frac{-6}{6}\right) +\left(\frac{3}{-3}\right)\\= \frac{-3}{2}+ \frac{6}{6}-\frac{3}{3}\\=\frac{-3}{2}+\frac{1}{1}-\frac{1}{1}\\=\frac{-3+1-1}{2}\\=\frac{-3}{2}\)
4. \(-\left(\frac{-4}{-9}\right) +\left(\frac{-8}{-8}\right) +\left(\frac{-11}{5}\right)\\= \frac{-4}{9}+ \frac{8}{8}-\frac{11}{5}\\=\frac{-4}{9}+\frac{1}{1}-\frac{11}{5}\\=\frac{-20}{45}+\frac{45}{45}-\frac{99}{45}\\=\frac{-20+45-99}{45}\\=\frac{-74}{45}\)
5. \(-\left(\frac{8}{-3}\right) -\left(\frac{10}{3}\right) -\left(\frac{-3}{-12}\right)\\= \frac{8}{3}- \frac{10}{3}-\frac{3}{12}\\=\frac{8}{3}-\frac{10}{3}-\frac{1}{4}\\=\frac{32}{12}-\frac{40}{12}-\frac{3}{12}\\=\frac{32-40-3}{12}\\=\frac{-11}{12}\)
6. \(+\left(\frac{2}{-3}\right) +\left(\frac{5}{7}\right) -\left(\frac{-6}{-8}\right)\\= \frac{-2}{3}+ \frac{5}{7}-\frac{6}{8}\\=\frac{-2}{3}+\frac{5}{7}-\frac{3}{4}\\=\frac{-56}{84}+\frac{60}{84}-\frac{63}{84}\\=\frac{-56+60-63}{84}\\=\frac{-59}{84}\)
7. \(-\left(\frac{-10}{-3}\right) -\left(\frac{-2}{7}\right) +\left(\frac{-2}{8}\right)\\= \frac{-10}{3}+ \frac{2}{7}-\frac{2}{8}\\=\frac{-10}{3}+\frac{2}{7}-\frac{1}{4}\\=\frac{-280}{84}+\frac{24}{84}-\frac{21}{84}\\=\frac{-280+24-21}{84}\\=\frac{-277}{84}\)
8. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-5}{8}\right) +\left(\frac{6}{-9}\right)\\= \frac{-10}{7}- \frac{5}{8}-\frac{6}{9}\\=\frac{-10}{7}-\frac{5}{8}-\frac{2}{3}\\=\frac{-240}{168}-\frac{105}{168}-\frac{112}{168}\\=\frac{-240-105-112}{168}\\=\frac{-457}{168}\)
9. \(+\left(\frac{-5}{-6}\right) +\left(\frac{8}{2}\right) +\left(\frac{-7}{-4}\right)\\= \frac{5}{6}+ \frac{8}{2}+\frac{7}{4}\\=\frac{5}{6}+\frac{4}{1}+\frac{7}{4}\\=\frac{10}{12}+\frac{48}{12}+\frac{21}{12}\\=\frac{10+48+21}{12}\\=\frac{79}{12}\)
10. \(-\left(\frac{-4}{7}\right) +\left(\frac{-9}{-9}\right) +\left(\frac{7}{-2}\right)\\= \frac{4}{7}+ \frac{9}{9}-\frac{7}{2}\\=\frac{4}{7}+\frac{1}{1}-\frac{7}{2}\\=\frac{8}{14}+\frac{14}{14}-\frac{49}{14}\\=\frac{8+14-49}{14}\\=\frac{-27}{14}\)
11. \(-\left(\frac{2}{-3}\right) -\left(\frac{-2}{-10}\right) +\left(\frac{-10}{-3}\right)\\= \frac{2}{3}- \frac{2}{10}+\frac{10}{3}\\=\frac{2}{3}-\frac{1}{5}+\frac{10}{3}\\=\frac{10}{15}-\frac{3}{15}+\frac{50}{15}\\=\frac{10-3+50}{15}\\=\frac{57}{15}\\=\frac{19}{5}\)
12. \(+\left(\frac{-7}{6}\right) -\left(\frac{5}{-6}\right) +\left(\frac{10}{4}\right)\\= \frac{-7}{6}+ \frac{5}{6}+\frac{10}{4}\\=\frac{-7}{6}+\frac{5}{6}+\frac{5}{2}\\=\frac{-7+5+5}{6}\\=\frac{3}{6}\\=\frac{1}{2}\)