Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{-2}\right) -\left(\frac{4}{-7}\right) -\left(\frac{-4}{8}\right)\\= \frac{-3}{2}+ \frac{4}{7}+\frac{4}{8}\\=\frac{-3}{2}+\frac{4}{7}+\frac{1}{2}\\=\frac{-21}{14}+\frac{8}{14}+\frac{7}{14}\\=\frac{-21+8+7}{14}\\=\frac{-6}{14}\\=\frac{-3}{7}\)
2. \(-\left(\frac{-6}{7}\right) -\left(\frac{-5}{-10}\right) +\left(\frac{-7}{-8}\right)\\= \frac{6}{7}- \frac{5}{10}+\frac{7}{8}\\=\frac{6}{7}-\frac{1}{2}+\frac{7}{8}\\=\frac{48}{56}-\frac{28}{56}+\frac{49}{56}\\=\frac{48-28+49}{56}\\=\frac{69}{56}\)
3. \(-\left(\frac{4}{9}\right) +\left(\frac{-6}{-6}\right) -\left(\frac{-9}{-10}\right)\\= \frac{-4}{9}+ \frac{6}{6}-\frac{9}{10}\\=\frac{-4}{9}+\frac{1}{1}-\frac{9}{10}\\=\frac{-40}{90}+\frac{90}{90}-\frac{81}{90}\\=\frac{-40+90-81}{90}\\=\frac{-31}{90}\)
4. \(+\left(\frac{-2}{3}\right) +\left(\frac{-3}{-8}\right) +\left(\frac{2}{-4}\right)\\= \frac{-2}{3}+ \frac{3}{8}-\frac{2}{4}\\=\frac{-2}{3}+\frac{3}{8}-\frac{1}{2}\\=\frac{-16}{24}+\frac{9}{24}-\frac{12}{24}\\=\frac{-16+9-12}{24}\\=\frac{-19}{24}\)
5. \(+\left(\frac{2}{-5}\right) -\left(\frac{9}{2}\right) +\left(\frac{-3}{-9}\right)\\= \frac{-2}{5}- \frac{9}{2}+\frac{3}{9}\\=\frac{-2}{5}-\frac{9}{2}+\frac{1}{3}\\=\frac{-12}{30}-\frac{135}{30}+\frac{10}{30}\\=\frac{-12-135+10}{30}\\=\frac{-137}{30}\)
6. \(-\left(\frac{2}{-3}\right) +\left(\frac{9}{-2}\right) +\left(\frac{10}{11}\right)\\= \frac{2}{3}- \frac{9}{2}+\frac{10}{11}\\=\frac{44}{66}-\frac{297}{66}+\frac{60}{66}\\=\frac{44-297+60}{66}\\=\frac{-193}{66}\)
7. \(+\left(\frac{-10}{7}\right) -\left(\frac{-2}{-10}\right) -\left(\frac{10}{-8}\right)\\= \frac{-10}{7}- \frac{2}{10}+\frac{10}{8}\\=\frac{-10}{7}-\frac{1}{5}+\frac{5}{4}\\=\frac{-200}{140}-\frac{28}{140}+\frac{175}{140}\\=\frac{-200-28+175}{140}\\=\frac{-53}{140}\)
8. \(-\left(\frac{6}{5}\right) -\left(\frac{-3}{-3}\right) -\left(\frac{5}{11}\right)\\= \frac{-6}{5}- \frac{3}{3}-\frac{5}{11}\\=\frac{-6}{5}-\frac{1}{1}-\frac{5}{11}\\=\frac{-66}{55}-\frac{55}{55}-\frac{25}{55}\\=\frac{-66-55-25}{55}\\=\frac{-146}{55}\)
9. \(-\left(\frac{-2}{-9}\right) -\left(\frac{8}{-9}\right) -\left(\frac{9}{9}\right)\\= \frac{-2}{9}+ \frac{8}{9}-\frac{9}{9}\\=\frac{-2}{9}+\frac{8}{9}-\frac{1}{1}\\=\frac{-2+8-1}{9}\\=\frac{5}{9}\)
10. \(+\left(\frac{-6}{5}\right) -\left(\frac{-2}{9}\right) -\left(\frac{12}{3}\right)\\= \frac{-6}{5}+ \frac{2}{9}-\frac{12}{3}\\=\frac{-6}{5}+\frac{2}{9}-\frac{4}{1}\\=\frac{-54}{45}+\frac{10}{45}-\frac{180}{45}\\=\frac{-54+10-180}{45}\\=\frac{-224}{45}\)
11. \(+\left(\frac{-7}{-5}\right) +\left(\frac{3}{-2}\right) +\left(\frac{-9}{-6}\right)\\= \frac{7}{5}- \frac{3}{2}+\frac{9}{6}\\=\frac{7}{5}-\frac{3}{2}+\frac{3}{2}\\=\frac{14}{10}-\frac{15}{10}+\frac{15}{10}\\=\frac{14-15+15}{10}\\=\frac{14}{10}\\=\frac{7}{5}\)
12. \(+\left(\frac{-4}{-3}\right) -\left(\frac{8}{9}\right) +\left(\frac{5}{6}\right)\\= \frac{4}{3}- \frac{8}{9}+\frac{5}{6}\\=\frac{24}{18}-\frac{16}{18}+\frac{15}{18}\\=\frac{24-16+15}{18}\\=\frac{23}{18}\)