Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{-4}\right) +\left(\frac{7}{-9}\right) +\left(\frac{-12}{5}\right)\\= \frac{9}{4}- \frac{7}{9}-\frac{12}{5}\\=\frac{405}{180}-\frac{140}{180}-\frac{432}{180}\\=\frac{405-140-432}{180}\\=\frac{-167}{180}\)
2. \(+\left(\frac{-2}{7}\right) +\left(\frac{5}{-9}\right) +\left(\frac{12}{4}\right)\\= \frac{-2}{7}- \frac{5}{9}+\frac{12}{4}\\=\frac{-2}{7}-\frac{5}{9}+\frac{3}{1}\\=\frac{-18}{63}-\frac{35}{63}+\frac{189}{63}\\=\frac{-18-35+189}{63}\\=\frac{136}{63}\)
3. \(+\left(\frac{-5}{9}\right) -\left(\frac{10}{-10}\right) -\left(\frac{-8}{9}\right)\\= \frac{-5}{9}+ \frac{10}{10}+\frac{8}{9}\\=\frac{-5}{9}+\frac{1}{1}+\frac{8}{9}\\=\frac{-5+1+8}{9}\\=\frac{4}{9}\)
4. \(+\left(\frac{5}{6}\right) +\left(\frac{2}{2}\right) +\left(\frac{-9}{-8}\right)\\= \frac{5}{6}+ \frac{2}{2}+\frac{9}{8}\\=\frac{5}{6}+\frac{1}{1}+\frac{9}{8}\\=\frac{20}{24}+\frac{24}{24}+\frac{27}{24}\\=\frac{20+24+27}{24}\\=\frac{71}{24}\)
5. \(+\left(\frac{-2}{-9}\right) -\left(\frac{-5}{10}\right) -\left(\frac{9}{2}\right)\\= \frac{2}{9}+ \frac{5}{10}-\frac{9}{2}\\=\frac{2}{9}+\frac{1}{2}-\frac{9}{2}\\=\frac{4}{18}+\frac{9}{18}-\frac{81}{18}\\=\frac{4+9-81}{18}\\=\frac{-68}{18}\\=\frac{-34}{9}\)
6. \(+\left(\frac{6}{-5}\right) +\left(\frac{-5}{10}\right) +\left(\frac{-6}{2}\right)\\= \frac{-6}{5}- \frac{5}{10}-\frac{6}{2}\\=\frac{-6}{5}-\frac{1}{2}-\frac{3}{1}\\=\frac{-12}{10}-\frac{5}{10}-\frac{30}{10}\\=\frac{-12-5-30}{10}\\=\frac{-47}{10}\)
7. \(+\left(\frac{-9}{4}\right) -\left(\frac{-2}{5}\right) -\left(\frac{-7}{-12}\right)\\= \frac{-9}{4}+ \frac{2}{5}-\frac{7}{12}\\=\frac{-135}{60}+\frac{24}{60}-\frac{35}{60}\\=\frac{-135+24-35}{60}\\=\frac{-146}{60}\\=\frac{-73}{30}\)
8. \(-\left(\frac{6}{7}\right) +\left(\frac{-8}{9}\right) +\left(\frac{-10}{-5}\right)\\= \frac{-6}{7}- \frac{8}{9}+\frac{10}{5}\\=\frac{-6}{7}-\frac{8}{9}+\frac{2}{1}\\=\frac{-54}{63}-\frac{56}{63}+\frac{126}{63}\\=\frac{-54-56+126}{63}\\=\frac{16}{63}\)
9. \(-\left(\frac{-4}{7}\right) +\left(\frac{-9}{10}\right) -\left(\frac{-5}{-3}\right)\\= \frac{4}{7}- \frac{9}{10}-\frac{5}{3}\\=\frac{120}{210}-\frac{189}{210}-\frac{350}{210}\\=\frac{120-189-350}{210}\\=\frac{-419}{210}\)
10. \(+\left(\frac{-9}{5}\right) -\left(\frac{-10}{-3}\right) -\left(\frac{-8}{5}\right)\\= \frac{-9}{5}- \frac{10}{3}+\frac{8}{5}\\=\frac{-27}{15}-\frac{50}{15}+\frac{24}{15}\\=\frac{-27-50+24}{15}\\=\frac{-53}{15}\)
11. \(+\left(\frac{-7}{8}\right) +\left(\frac{-2}{6}\right) +\left(\frac{-11}{4}\right)\\= \frac{-7}{8}- \frac{2}{6}-\frac{11}{4}\\=\frac{-7}{8}-\frac{1}{3}-\frac{11}{4}\\=\frac{-21}{24}-\frac{8}{24}-\frac{66}{24}\\=\frac{-21-8-66}{24}\\=\frac{-95}{24}\)
12. \(-\left(\frac{5}{6}\right) -\left(\frac{2}{5}\right) -\left(\frac{-3}{6}\right)\\= \frac{-5}{6}- \frac{2}{5}+\frac{3}{6}\\=\frac{-5}{6}-\frac{2}{5}+\frac{1}{2}\\=\frac{-25}{30}-\frac{12}{30}+\frac{15}{30}\\=\frac{-25-12+15}{30}\\=\frac{-22}{30}\\=\frac{-11}{15}\)