Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{-7}\right) +\left(\frac{4}{6}\right) +\left(\frac{-4}{-9}\right)\\= \frac{5}{7}+ \frac{4}{6}+\frac{4}{9}\\=\frac{5}{7}+\frac{2}{3}+\frac{4}{9}\\=\frac{45}{63}+\frac{42}{63}+\frac{28}{63}\\=\frac{45+42+28}{63}\\=\frac{115}{63}\)
2. \(-\left(\frac{-4}{3}\right) -\left(\frac{-2}{9}\right) +\left(\frac{-5}{6}\right)\\= \frac{4}{3}+ \frac{2}{9}-\frac{5}{6}\\=\frac{24}{18}+\frac{4}{18}-\frac{15}{18}\\=\frac{24+4-15}{18}\\=\frac{13}{18}\)
3. \(+\left(\frac{2}{-9}\right) -\left(\frac{-6}{-4}\right) +\left(\frac{8}{-5}\right)\\= \frac{-2}{9}- \frac{6}{4}-\frac{8}{5}\\=\frac{-2}{9}-\frac{3}{2}-\frac{8}{5}\\=\frac{-20}{90}-\frac{135}{90}-\frac{144}{90}\\=\frac{-20-135-144}{90}\\=\frac{-299}{90}\)
4. \(+\left(\frac{-5}{-8}\right) -\left(\frac{3}{-9}\right) +\left(\frac{-4}{-5}\right)\\= \frac{5}{8}+ \frac{3}{9}+\frac{4}{5}\\=\frac{5}{8}+\frac{1}{3}+\frac{4}{5}\\=\frac{75}{120}+\frac{40}{120}+\frac{96}{120}\\=\frac{75+40+96}{120}\\=\frac{211}{120}\)
5. \(-\left(\frac{4}{9}\right) +\left(\frac{-2}{-6}\right) -\left(\frac{-11}{3}\right)\\= \frac{-4}{9}+ \frac{2}{6}+\frac{11}{3}\\=\frac{-4}{9}+\frac{1}{3}+\frac{11}{3}\\=\frac{-4+1+11}{9}\\=\frac{8}{9}\)
6. \(-\left(\frac{-7}{5}\right) +\left(\frac{8}{7}\right) -\left(\frac{-4}{2}\right)\\= \frac{7}{5}+ \frac{8}{7}+\frac{4}{2}\\=\frac{7}{5}+\frac{8}{7}+\frac{2}{1}\\=\frac{49}{35}+\frac{40}{35}+\frac{70}{35}\\=\frac{49+40+70}{35}\\=\frac{159}{35}\)
7. \(-\left(\frac{-4}{5}\right) +\left(\frac{-9}{-10}\right) -\left(\frac{9}{-9}\right)\\= \frac{4}{5}+ \frac{9}{10}+\frac{9}{9}\\=\frac{4}{5}+\frac{9}{10}+\frac{1}{1}\\=\frac{8}{10}+\frac{9}{10}+\frac{10}{10}\\=\frac{8+9+10}{10}\\=\frac{27}{10}\)
8. \(-\left(\frac{6}{7}\right) -\left(\frac{3}{7}\right) -\left(\frac{-4}{5}\right)\\= \frac{-6}{7}- \frac{3}{7}+\frac{4}{5}\\=\frac{-30}{35}-\frac{15}{35}+\frac{28}{35}\\=\frac{-30-15+28}{35}\\=\frac{-17}{35}\)
9. \(-\left(\frac{-6}{5}\right) -\left(\frac{7}{5}\right) -\left(\frac{5}{-8}\right)\\= \frac{6}{5}- \frac{7}{5}+\frac{5}{8}\\=\frac{48}{40}-\frac{56}{40}+\frac{25}{40}\\=\frac{48-56+25}{40}\\=\frac{17}{40}\)
10. \(+\left(\frac{-4}{9}\right) -\left(\frac{4}{-6}\right) -\left(\frac{-5}{3}\right)\\= \frac{-4}{9}+ \frac{4}{6}+\frac{5}{3}\\=\frac{-4}{9}+\frac{2}{3}+\frac{5}{3}\\=\frac{-4+2+5}{9}\\=\frac{3}{9}\\=\frac{1}{3}\)
11. \(+\left(\frac{4}{-7}\right) -\left(\frac{-4}{4}\right) +\left(\frac{-5}{8}\right)\\= \frac{-4}{7}+ \frac{4}{4}-\frac{5}{8}\\=\frac{-4}{7}+\frac{1}{1}-\frac{5}{8}\\=\frac{-32}{56}+\frac{56}{56}-\frac{35}{56}\\=\frac{-32+56-35}{56}\\=\frac{-11}{56}\)
12. \(-\left(\frac{-2}{-3}\right) +\left(\frac{-7}{8}\right) -\left(\frac{-4}{-7}\right)\\= \frac{-2}{3}- \frac{7}{8}-\frac{4}{7}\\=\frac{-112}{168}-\frac{147}{168}-\frac{96}{168}\\=\frac{-112-147-96}{168}\\=\frac{-355}{168}\)