Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{-4}\right) +\left(\frac{8}{-4}\right) -\left(\frac{-8}{11}\right)\\= \frac{-3}{4}- \frac{8}{4}+\frac{8}{11}\\=\frac{-3}{4}-\frac{2}{1}+\frac{8}{11}\\=\frac{-33}{44}-\frac{88}{44}+\frac{32}{44}\\=\frac{-33-88+32}{44}\\=\frac{-89}{44}\)
2. \(+\left(\frac{2}{-3}\right) -\left(\frac{-7}{4}\right) +\left(\frac{-3}{3}\right)\\= \frac{-2}{3}+ \frac{7}{4}-\frac{3}{3}\\=\frac{-2}{3}+\frac{7}{4}-\frac{1}{1}\\=\frac{-8}{12}+\frac{21}{12}-\frac{12}{12}\\=\frac{-8+21-12}{12}\\=\frac{1}{12}\)
3. \(-\left(\frac{8}{-3}\right) -\left(\frac{-2}{8}\right) -\left(\frac{11}{4}\right)\\= \frac{8}{3}+ \frac{2}{8}-\frac{11}{4}\\=\frac{8}{3}+\frac{1}{4}-\frac{11}{4}\\=\frac{32}{12}+\frac{3}{12}-\frac{33}{12}\\=\frac{32+3-33}{12}\\=\frac{2}{12}\\=\frac{1}{6}\)
4. \(+\left(\frac{-4}{-9}\right) +\left(\frac{8}{2}\right) -\left(\frac{12}{12}\right)\\= \frac{4}{9}+ \frac{8}{2}-\frac{12}{12}\\=\frac{4}{9}+\frac{4}{1}-\frac{1}{1}\\=\frac{4+4-1}{9}\\=\frac{7}{9}\)
5. \(-\left(\frac{-8}{-3}\right) +\left(\frac{-2}{-2}\right) -\left(\frac{-12}{4}\right)\\= \frac{-8}{3}+ \frac{2}{2}+\frac{12}{4}\\=\frac{-8}{3}+\frac{1}{1}+\frac{3}{1}\\=\frac{-8+1+3}{3}\\=\frac{-4}{3}\)
6. \(-\left(\frac{-3}{-7}\right) -\left(\frac{9}{-4}\right) -\left(\frac{-12}{5}\right)\\= \frac{-3}{7}+ \frac{9}{4}+\frac{12}{5}\\=\frac{-60}{140}+\frac{315}{140}+\frac{336}{140}\\=\frac{-60+315+336}{140}\\=\frac{591}{140}\)
7. \(+\left(\frac{-3}{7}\right) +\left(\frac{-6}{9}\right) -\left(\frac{6}{-12}\right)\\= \frac{-3}{7}- \frac{6}{9}+\frac{6}{12}\\=\frac{-3}{7}-\frac{2}{3}+\frac{1}{2}\\=\frac{-18}{42}-\frac{28}{42}+\frac{21}{42}\\=\frac{-18-28+21}{42}\\=\frac{-25}{42}\)
8. \(+\left(\frac{6}{-7}\right) +\left(\frac{9}{-8}\right) -\left(\frac{-8}{3}\right)\\= \frac{-6}{7}- \frac{9}{8}+\frac{8}{3}\\=\frac{-144}{168}-\frac{189}{168}+\frac{448}{168}\\=\frac{-144-189+448}{168}\\=\frac{115}{168}\)
9. \(+\left(\frac{8}{7}\right) +\left(\frac{8}{2}\right) -\left(\frac{5}{12}\right)\\= \frac{8}{7}+ \frac{8}{2}-\frac{5}{12}\\=\frac{8}{7}+\frac{4}{1}-\frac{5}{12}\\=\frac{96}{84}+\frac{336}{84}-\frac{35}{84}\\=\frac{96+336-35}{84}\\=\frac{397}{84}\)
10. \(+\left(\frac{-4}{3}\right) +\left(\frac{7}{6}\right) +\left(\frac{-12}{12}\right)\\= \frac{-4}{3}+ \frac{7}{6}-\frac{12}{12}\\=\frac{-4}{3}+\frac{7}{6}-\frac{1}{1}\\=\frac{-8}{6}+\frac{7}{6}-\frac{6}{6}\\=\frac{-8+7-6}{6}\\=\frac{-7}{6}\)
11. \(-\left(\frac{-9}{2}\right) +\left(\frac{-5}{8}\right) +\left(\frac{-10}{10}\right)\\= \frac{9}{2}- \frac{5}{8}-\frac{10}{10}\\=\frac{9}{2}-\frac{5}{8}-\frac{1}{1}\\=\frac{36}{8}-\frac{5}{8}-\frac{8}{8}\\=\frac{36-5-8}{8}\\=\frac{23}{8}\)
12. \(+\left(\frac{7}{8}\right) +\left(\frac{2}{2}\right) +\left(\frac{-3}{-3}\right)\\= \frac{7}{8}+ \frac{2}{2}+\frac{3}{3}\\=\frac{7}{8}+\frac{1}{1}+\frac{1}{1}\\=\frac{7+1+1}{8}\\=\frac{9}{8}\)