Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{4}\right) -\left(\frac{-2}{4}\right) -\left(\frac{-10}{9}\right)\\= \frac{-5}{4}+ \frac{2}{4}+\frac{10}{9}\\=\frac{-5}{4}+\frac{1}{2}+\frac{10}{9}\\=\frac{-45}{36}+\frac{18}{36}+\frac{40}{36}\\=\frac{-45+18+40}{36}\\=\frac{13}{36}\)
2. \(-\left(\frac{-3}{5}\right) -\left(\frac{-10}{5}\right) +\left(\frac{5}{8}\right)\\= \frac{3}{5}+ \frac{10}{5}+\frac{5}{8}\\=\frac{3}{5}+\frac{2}{1}+\frac{5}{8}\\=\frac{24}{40}+\frac{80}{40}+\frac{25}{40}\\=\frac{24+80+25}{40}\\=\frac{129}{40}\)
3. \(-\left(\frac{-6}{-7}\right) -\left(\frac{6}{3}\right) +\left(\frac{3}{-2}\right)\\= \frac{-6}{7}- \frac{6}{3}-\frac{3}{2}\\=\frac{-6}{7}-\frac{2}{1}-\frac{3}{2}\\=\frac{-12}{14}-\frac{28}{14}-\frac{21}{14}\\=\frac{-12-28-21}{14}\\=\frac{-61}{14}\)
4. \(-\left(\frac{10}{-7}\right) +\left(\frac{2}{5}\right) +\left(\frac{6}{6}\right)\\= \frac{10}{7}+ \frac{2}{5}+\frac{6}{6}\\=\frac{10}{7}+\frac{2}{5}+\frac{1}{1}\\=\frac{50}{35}+\frac{14}{35}+\frac{35}{35}\\=\frac{50+14+35}{35}\\=\frac{99}{35}\)
5. \(-\left(\frac{-3}{-5}\right) -\left(\frac{-4}{-10}\right) +\left(\frac{5}{7}\right)\\= \frac{-3}{5}- \frac{4}{10}+\frac{5}{7}\\=\frac{-3}{5}-\frac{2}{5}+\frac{5}{7}\\=\frac{-21}{35}-\frac{14}{35}+\frac{25}{35}\\=\frac{-21-14+25}{35}\\=\frac{-10}{35}\\=\frac{-2}{7}\)
6. \(+\left(\frac{-5}{-2}\right) +\left(\frac{8}{-8}\right) -\left(\frac{-2}{4}\right)\\= \frac{5}{2}- \frac{8}{8}+\frac{2}{4}\\=\frac{5}{2}-\frac{1}{1}+\frac{1}{2}\\=\frac{5-1+1}{2}\\=\frac{5}{2}\)
7. \(+\left(\frac{10}{7}\right) -\left(\frac{-5}{-7}\right) -\left(\frac{7}{-4}\right)\\= \frac{10}{7}- \frac{5}{7}+\frac{7}{4}\\=\frac{40}{28}-\frac{20}{28}+\frac{49}{28}\\=\frac{40-20+49}{28}\\=\frac{69}{28}\)
8. \(+\left(\frac{8}{9}\right) +\left(\frac{-3}{2}\right) -\left(\frac{-10}{-7}\right)\\= \frac{8}{9}- \frac{3}{2}-\frac{10}{7}\\=\frac{112}{126}-\frac{189}{126}-\frac{180}{126}\\=\frac{112-189-180}{126}\\=\frac{-257}{126}\)
9. \(-\left(\frac{2}{3}\right) -\left(\frac{-5}{6}\right) -\left(\frac{12}{-2}\right)\\= \frac{-2}{3}+ \frac{5}{6}+\frac{12}{2}\\=\frac{-2}{3}+\frac{5}{6}+\frac{6}{1}\\=\frac{-4}{6}+\frac{5}{6}+\frac{36}{6}\\=\frac{-4+5+36}{6}\\=\frac{37}{6}\)
10. \(+\left(\frac{10}{9}\right) +\left(\frac{-9}{6}\right) -\left(\frac{10}{6}\right)\\= \frac{10}{9}- \frac{9}{6}-\frac{10}{6}\\=\frac{10}{9}-\frac{3}{2}-\frac{5}{3}\\=\frac{20}{18}-\frac{27}{18}-\frac{30}{18}\\=\frac{20-27-30}{18}\\=\frac{-37}{18}\)
11. \(-\left(\frac{6}{7}\right) +\left(\frac{-4}{8}\right) -\left(\frac{5}{2}\right)\\= \frac{-6}{7}- \frac{4}{8}-\frac{5}{2}\\=\frac{-6}{7}-\frac{1}{2}-\frac{5}{2}\\=\frac{-12}{14}-\frac{7}{14}-\frac{35}{14}\\=\frac{-12-7-35}{14}\\=\frac{-54}{14}\\=\frac{-27}{7}\)
12. \(-\left(\frac{8}{9}\right) -\left(\frac{-4}{-9}\right) -\left(\frac{11}{-9}\right)\\= \frac{-8}{9}- \frac{4}{9}+\frac{11}{9}\\=\frac{-8-4+11}{9}\\=\frac{-1}{9}\)