Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{-2}\right) -\left(\frac{-2}{7}\right) +\left(\frac{3}{-9}\right)\\= \frac{-9}{2}+ \frac{2}{7}-\frac{3}{9}\\=\frac{-9}{2}+\frac{2}{7}-\frac{1}{3}\\=\frac{-189}{42}+\frac{12}{42}-\frac{14}{42}\\=\frac{-189+12-14}{42}\\=\frac{-191}{42}\)
2. \(-\left(\frac{-3}{2}\right) -\left(\frac{-2}{-6}\right) -\left(\frac{12}{-7}\right)\\= \frac{3}{2}- \frac{2}{6}+\frac{12}{7}\\=\frac{3}{2}-\frac{1}{3}+\frac{12}{7}\\=\frac{63}{42}-\frac{14}{42}+\frac{72}{42}\\=\frac{63-14+72}{42}\\=\frac{121}{42}\)
3. \(-\left(\frac{4}{3}\right) -\left(\frac{-2}{-6}\right) +\left(\frac{8}{-10}\right)\\= \frac{-4}{3}- \frac{2}{6}-\frac{8}{10}\\=\frac{-4}{3}-\frac{1}{3}-\frac{4}{5}\\=\frac{-20}{15}-\frac{5}{15}-\frac{12}{15}\\=\frac{-20-5-12}{15}\\=\frac{-37}{15}\)
4. \(+\left(\frac{-3}{-4}\right) +\left(\frac{2}{-6}\right) +\left(\frac{3}{-8}\right)\\= \frac{3}{4}- \frac{2}{6}-\frac{3}{8}\\=\frac{3}{4}-\frac{1}{3}-\frac{3}{8}\\=\frac{18}{24}-\frac{8}{24}-\frac{9}{24}\\=\frac{18-8-9}{24}\\=\frac{1}{24}\)
5. \(+\left(\frac{-9}{-8}\right) -\left(\frac{4}{2}\right) -\left(\frac{-3}{4}\right)\\= \frac{9}{8}- \frac{4}{2}+\frac{3}{4}\\=\frac{9}{8}-\frac{2}{1}+\frac{3}{4}\\=\frac{9-2+3}{8}\\=\frac{10}{8}\\=\frac{5}{4}\)
6. \(+\left(\frac{-8}{-5}\right) +\left(\frac{5}{-9}\right) +\left(\frac{10}{2}\right)\\= \frac{8}{5}- \frac{5}{9}+\frac{10}{2}\\=\frac{8}{5}-\frac{5}{9}+\frac{5}{1}\\=\frac{72}{45}-\frac{25}{45}+\frac{225}{45}\\=\frac{72-25+225}{45}\\=\frac{272}{45}\)
7. \(-\left(\frac{-3}{7}\right) -\left(\frac{5}{-9}\right) +\left(\frac{12}{-7}\right)\\= \frac{3}{7}+ \frac{5}{9}-\frac{12}{7}\\=\frac{27}{63}+\frac{35}{63}-\frac{108}{63}\\=\frac{27+35-108}{63}\\=\frac{-46}{63}\)
8. \(+\left(\frac{-2}{-9}\right) +\left(\frac{-6}{-10}\right) -\left(\frac{2}{-9}\right)\\= \frac{2}{9}+ \frac{6}{10}+\frac{2}{9}\\=\frac{2}{9}+\frac{3}{5}+\frac{2}{9}\\=\frac{10}{45}+\frac{27}{45}+\frac{10}{45}\\=\frac{10+27+10}{45}\\=\frac{47}{45}\)
9. \(+\left(\frac{3}{4}\right) +\left(\frac{4}{-6}\right) -\left(\frac{12}{3}\right)\\= \frac{3}{4}- \frac{4}{6}-\frac{12}{3}\\=\frac{3}{4}-\frac{2}{3}-\frac{4}{1}\\=\frac{9}{12}-\frac{8}{12}-\frac{48}{12}\\=\frac{9-8-48}{12}\\=\frac{-47}{12}\)
10. \(-\left(\frac{4}{3}\right) -\left(\frac{-4}{-9}\right) -\left(\frac{-5}{-8}\right)\\= \frac{-4}{3}- \frac{4}{9}-\frac{5}{8}\\=\frac{-96}{72}-\frac{32}{72}-\frac{45}{72}\\=\frac{-96-32-45}{72}\\=\frac{-173}{72}\)
11. \(-\left(\frac{7}{2}\right) +\left(\frac{-4}{10}\right) -\left(\frac{-4}{10}\right)\\= \frac{-7}{2}- \frac{4}{10}+\frac{4}{10}\\=\frac{-7}{2}-\frac{2}{5}+\frac{2}{5}\\=\frac{-35}{10}-\frac{4}{10}+\frac{4}{10}\\=\frac{-35-4+4}{10}\\=\frac{-35}{10}\\=\frac{-7}{2}\)
12. \(+\left(\frac{4}{-9}\right) +\left(\frac{-8}{-8}\right) +\left(\frac{-3}{9}\right)\\= \frac{-4}{9}+ \frac{8}{8}-\frac{3}{9}\\=\frac{-4}{9}+\frac{1}{1}-\frac{1}{3}\\=\frac{-4+1-1}{9}\\=\frac{-4}{9}\)