Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{-7}\right) -\left(\frac{4}{-10}\right) +\left(\frac{-2}{5}\right)\\= \frac{-2}{7}+ \frac{4}{10}-\frac{2}{5}\\=\frac{-2}{7}+\frac{2}{5}-\frac{2}{5}\\=\frac{-10}{35}+\frac{14}{35}-\frac{14}{35}\\=\frac{-10+14-14}{35}\\=\frac{-10}{35}\\=\frac{-2}{7}\)
2. \(-\left(\frac{-3}{2}\right) +\left(\frac{7}{-10}\right) +\left(\frac{10}{2}\right)\\= \frac{3}{2}- \frac{7}{10}+\frac{10}{2}\\=\frac{3}{2}-\frac{7}{10}+\frac{5}{1}\\=\frac{15}{10}-\frac{7}{10}+\frac{50}{10}\\=\frac{15-7+50}{10}\\=\frac{58}{10}\\=\frac{29}{5}\)
3. \(+\left(\frac{5}{-2}\right) -\left(\frac{7}{2}\right) +\left(\frac{-12}{4}\right)\\= \frac{-5}{2}- \frac{7}{2}-\frac{12}{4}\\=\frac{-5}{2}-\frac{7}{2}-\frac{3}{1}\\=\frac{-5-7-3}{2}\\=\frac{-15}{2}\)
4. \(-\left(\frac{-3}{-2}\right) -\left(\frac{9}{7}\right) +\left(\frac{5}{-2}\right)\\= \frac{-3}{2}- \frac{9}{7}-\frac{5}{2}\\=\frac{-21}{14}-\frac{18}{14}-\frac{35}{14}\\=\frac{-21-18-35}{14}\\=\frac{-74}{14}\\=\frac{-37}{7}\)
5. \(+\left(\frac{10}{7}\right) +\left(\frac{-4}{9}\right) -\left(\frac{11}{-2}\right)\\= \frac{10}{7}- \frac{4}{9}+\frac{11}{2}\\=\frac{180}{126}-\frac{56}{126}+\frac{693}{126}\\=\frac{180-56+693}{126}\\=\frac{817}{126}\)
6. \(+\left(\frac{-3}{-8}\right) -\left(\frac{-6}{7}\right) +\left(\frac{-6}{4}\right)\\= \frac{3}{8}+ \frac{6}{7}-\frac{6}{4}\\=\frac{3}{8}+\frac{6}{7}-\frac{3}{2}\\=\frac{21}{56}+\frac{48}{56}-\frac{84}{56}\\=\frac{21+48-84}{56}\\=\frac{-15}{56}\)
7. \(-\left(\frac{-9}{2}\right) +\left(\frac{2}{-4}\right) +\left(\frac{3}{9}\right)\\= \frac{9}{2}- \frac{2}{4}+\frac{3}{9}\\=\frac{9}{2}-\frac{1}{2}+\frac{1}{3}\\=\frac{27}{6}-\frac{3}{6}+\frac{2}{6}\\=\frac{27-3+2}{6}\\=\frac{26}{6}\\=\frac{13}{3}\)
8. \(-\left(\frac{8}{9}\right) -\left(\frac{-2}{10}\right) +\left(\frac{-9}{-3}\right)\\= \frac{-8}{9}+ \frac{2}{10}+\frac{9}{3}\\=\frac{-8}{9}+\frac{1}{5}+\frac{3}{1}\\=\frac{-40}{45}+\frac{9}{45}+\frac{135}{45}\\=\frac{-40+9+135}{45}\\=\frac{104}{45}\)
9. \(+\left(\frac{-8}{-3}\right) +\left(\frac{-9}{4}\right) -\left(\frac{-7}{-8}\right)\\= \frac{8}{3}- \frac{9}{4}-\frac{7}{8}\\=\frac{64}{24}-\frac{54}{24}-\frac{21}{24}\\=\frac{64-54-21}{24}\\=\frac{-11}{24}\)
10. \(+\left(\frac{7}{2}\right) -\left(\frac{7}{-9}\right) +\left(\frac{-4}{-11}\right)\\= \frac{7}{2}+ \frac{7}{9}+\frac{4}{11}\\=\frac{693}{198}+\frac{154}{198}+\frac{72}{198}\\=\frac{693+154+72}{198}\\=\frac{919}{198}\)
11. \(+\left(\frac{9}{-7}\right) +\left(\frac{5}{7}\right) +\left(\frac{-9}{3}\right)\\= \frac{-9}{7}+ \frac{5}{7}-\frac{9}{3}\\=\frac{-9}{7}+\frac{5}{7}-\frac{3}{1}\\=\frac{-9+5-3}{7}\\=\frac{-7}{7}\\=\frac{-1}{1}\)
12. \(-\left(\frac{-6}{7}\right) -\left(\frac{-9}{-2}\right) -\left(\frac{5}{-3}\right)\\= \frac{6}{7}- \frac{9}{2}+\frac{5}{3}\\=\frac{36}{42}-\frac{189}{42}+\frac{70}{42}\\=\frac{36-189+70}{42}\\=\frac{-83}{42}\)