Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{2}\right) +\left(\frac{-9}{-6}\right) -\left(\frac{-2}{6}\right)\\= \frac{5}{2}+ \frac{9}{6}+\frac{2}{6}\\=\frac{5}{2}+\frac{3}{2}+\frac{1}{3}\\=\frac{15}{6}+\frac{9}{6}+\frac{2}{6}\\=\frac{15+9+2}{6}\\=\frac{26}{6}\\=\frac{13}{3}\)
2. \(+\left(\frac{6}{-5}\right) -\left(\frac{-9}{8}\right) +\left(\frac{11}{2}\right)\\= \frac{-6}{5}+ \frac{9}{8}+\frac{11}{2}\\=\frac{-48}{40}+\frac{45}{40}+\frac{220}{40}\\=\frac{-48+45+220}{40}\\=\frac{217}{40}\)
3. \(-\left(\frac{-8}{5}\right) +\left(\frac{-10}{3}\right) -\left(\frac{-2}{-5}\right)\\= \frac{8}{5}- \frac{10}{3}-\frac{2}{5}\\=\frac{24}{15}-\frac{50}{15}-\frac{6}{15}\\=\frac{24-50-6}{15}\\=\frac{-32}{15}\)
4. \(-\left(\frac{4}{5}\right) +\left(\frac{7}{-2}\right) +\left(\frac{10}{10}\right)\\= \frac{-4}{5}- \frac{7}{2}+\frac{10}{10}\\=\frac{-4}{5}-\frac{7}{2}+\frac{1}{1}\\=\frac{-8}{10}-\frac{35}{10}+\frac{10}{10}\\=\frac{-8-35+10}{10}\\=\frac{-33}{10}\)
5. \(+\left(\frac{7}{6}\right) -\left(\frac{4}{-8}\right) +\left(\frac{-3}{9}\right)\\= \frac{7}{6}+ \frac{4}{8}-\frac{3}{9}\\=\frac{7}{6}+\frac{1}{2}-\frac{1}{3}\\=\frac{7+1-1}{6}\\=\frac{7}{6}\)
6. \(+\left(\frac{-2}{9}\right) -\left(\frac{-7}{2}\right) +\left(\frac{12}{12}\right)\\= \frac{-2}{9}+ \frac{7}{2}+\frac{12}{12}\\=\frac{-2}{9}+\frac{7}{2}+\frac{1}{1}\\=\frac{-4}{18}+\frac{63}{18}+\frac{18}{18}\\=\frac{-4+63+18}{18}\\=\frac{77}{18}\)
7. \(+\left(\frac{3}{-2}\right) -\left(\frac{-3}{7}\right) +\left(\frac{-5}{8}\right)\\= \frac{-3}{2}+ \frac{3}{7}-\frac{5}{8}\\=\frac{-84}{56}+\frac{24}{56}-\frac{35}{56}\\=\frac{-84+24-35}{56}\\=\frac{-95}{56}\)
8. \(+\left(\frac{2}{5}\right) -\left(\frac{6}{10}\right) -\left(\frac{-9}{-11}\right)\\= \frac{2}{5}- \frac{6}{10}-\frac{9}{11}\\=\frac{2}{5}-\frac{3}{5}-\frac{9}{11}\\=\frac{22}{55}-\frac{33}{55}-\frac{45}{55}\\=\frac{22-33-45}{55}\\=\frac{-56}{55}\)
9. \(-\left(\frac{10}{-7}\right) -\left(\frac{-3}{7}\right) -\left(\frac{4}{-8}\right)\\= \frac{10}{7}+ \frac{3}{7}+\frac{4}{8}\\=\frac{10}{7}+\frac{3}{7}+\frac{1}{2}\\=\frac{20}{14}+\frac{6}{14}+\frac{7}{14}\\=\frac{20+6+7}{14}\\=\frac{33}{14}\)
10. \(-\left(\frac{-2}{-9}\right) -\left(\frac{8}{-5}\right) -\left(\frac{-12}{-4}\right)\\= \frac{-2}{9}+ \frac{8}{5}-\frac{12}{4}\\=\frac{-2}{9}+\frac{8}{5}-\frac{3}{1}\\=\frac{-10}{45}+\frac{72}{45}-\frac{135}{45}\\=\frac{-10+72-135}{45}\\=\frac{-73}{45}\)
11. \(-\left(\frac{4}{-7}\right) +\left(\frac{-5}{9}\right) +\left(\frac{-6}{-7}\right)\\= \frac{4}{7}- \frac{5}{9}+\frac{6}{7}\\=\frac{36}{63}-\frac{35}{63}+\frac{54}{63}\\=\frac{36-35+54}{63}\\=\frac{55}{63}\)
12. \(-\left(\frac{-10}{7}\right) +\left(\frac{7}{-6}\right) +\left(\frac{2}{10}\right)\\= \frac{10}{7}- \frac{7}{6}+\frac{2}{10}\\=\frac{10}{7}-\frac{7}{6}+\frac{1}{5}\\=\frac{300}{210}-\frac{245}{210}+\frac{42}{210}\\=\frac{300-245+42}{210}\\=\frac{97}{210}\)