Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{-8}\right) +\left(\frac{7}{-2}\right) +\left(\frac{-8}{-10}\right)\\= \frac{5}{8}- \frac{7}{2}+\frac{8}{10}\\=\frac{5}{8}-\frac{7}{2}+\frac{4}{5}\\=\frac{25}{40}-\frac{140}{40}+\frac{32}{40}\\=\frac{25-140+32}{40}\\=\frac{-83}{40}\)
2. \(+\left(\frac{10}{3}\right) -\left(\frac{5}{-9}\right) +\left(\frac{10}{-2}\right)\\= \frac{10}{3}+ \frac{5}{9}-\frac{10}{2}\\=\frac{10}{3}+\frac{5}{9}-\frac{5}{1}\\=\frac{30}{9}+\frac{5}{9}-\frac{45}{9}\\=\frac{30+5-45}{9}\\=\frac{-10}{9}\)
3. \(+\left(\frac{9}{2}\right) -\left(\frac{-4}{4}\right) +\left(\frac{6}{-10}\right)\\= \frac{9}{2}+ \frac{4}{4}-\frac{6}{10}\\=\frac{9}{2}+\frac{1}{1}-\frac{3}{5}\\=\frac{45}{10}+\frac{10}{10}-\frac{6}{10}\\=\frac{45+10-6}{10}\\=\frac{49}{10}\)
4. \(-\left(\frac{4}{-9}\right) -\left(\frac{3}{-5}\right) -\left(\frac{-12}{-9}\right)\\= \frac{4}{9}+ \frac{3}{5}-\frac{12}{9}\\=\frac{4}{9}+\frac{3}{5}-\frac{4}{3}\\=\frac{20}{45}+\frac{27}{45}-\frac{60}{45}\\=\frac{20+27-60}{45}\\=\frac{-13}{45}\)
5. \(-\left(\frac{3}{5}\right) -\left(\frac{-4}{-7}\right) -\left(\frac{10}{10}\right)\\= \frac{-3}{5}- \frac{4}{7}-\frac{10}{10}\\=\frac{-3}{5}-\frac{4}{7}-\frac{1}{1}\\=\frac{-21}{35}-\frac{20}{35}-\frac{35}{35}\\=\frac{-21-20-35}{35}\\=\frac{-76}{35}\)
6. \(+\left(\frac{10}{9}\right) +\left(\frac{7}{-10}\right) +\left(\frac{-9}{12}\right)\\= \frac{10}{9}- \frac{7}{10}-\frac{9}{12}\\=\frac{10}{9}-\frac{7}{10}-\frac{3}{4}\\=\frac{200}{180}-\frac{126}{180}-\frac{135}{180}\\=\frac{200-126-135}{180}\\=\frac{-61}{180}\)
7. \(-\left(\frac{-10}{3}\right) +\left(\frac{-7}{-3}\right) -\left(\frac{-8}{11}\right)\\= \frac{10}{3}+ \frac{7}{3}+\frac{8}{11}\\=\frac{110}{33}+\frac{77}{33}+\frac{24}{33}\\=\frac{110+77+24}{33}\\=\frac{211}{33}\)
8. \(+\left(\frac{9}{4}\right) +\left(\frac{2}{-4}\right) +\left(\frac{-12}{12}\right)\\= \frac{9}{4}- \frac{2}{4}-\frac{12}{12}\\=\frac{9}{4}-\frac{1}{2}-\frac{1}{1}\\=\frac{9-1-1}{4}\\=\frac{7}{4}\)
9. \(+\left(\frac{4}{-5}\right) -\left(\frac{3}{-10}\right) -\left(\frac{9}{2}\right)\\= \frac{-4}{5}+ \frac{3}{10}-\frac{9}{2}\\=\frac{-8}{10}+\frac{3}{10}-\frac{45}{10}\\=\frac{-8+3-45}{10}\\=\frac{-50}{10}\\=\frac{-5}{1}\)
10. \(-\left(\frac{9}{-2}\right) -\left(\frac{3}{-10}\right) -\left(\frac{-8}{-3}\right)\\= \frac{9}{2}+ \frac{3}{10}-\frac{8}{3}\\=\frac{135}{30}+\frac{9}{30}-\frac{80}{30}\\=\frac{135+9-80}{30}\\=\frac{64}{30}\\=\frac{32}{15}\)
11. \(-\left(\frac{2}{-9}\right) -\left(\frac{2}{-5}\right) +\left(\frac{-6}{-2}\right)\\= \frac{2}{9}+ \frac{2}{5}+\frac{6}{2}\\=\frac{2}{9}+\frac{2}{5}+\frac{3}{1}\\=\frac{10}{45}+\frac{18}{45}+\frac{135}{45}\\=\frac{10+18+135}{45}\\=\frac{163}{45}\)
12. \(+\left(\frac{-7}{-8}\right) -\left(\frac{-8}{-10}\right) +\left(\frac{-4}{-8}\right)\\= \frac{7}{8}- \frac{8}{10}+\frac{4}{8}\\=\frac{7}{8}-\frac{4}{5}+\frac{1}{2}\\=\frac{35}{40}-\frac{32}{40}+\frac{20}{40}\\=\frac{35-32+20}{40}\\=\frac{23}{40}\)