Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{10}{-7}\right) +\left(\frac{-6}{-9}\right) +\left(\frac{-8}{9}\right)\\= \frac{-10}{7}+ \frac{6}{9}-\frac{8}{9}\\=\frac{-10}{7}+\frac{2}{3}-\frac{8}{9}\\=\frac{-90}{63}+\frac{42}{63}-\frac{56}{63}\\=\frac{-90+42-56}{63}\\=\frac{-104}{63}\)
2. \(+\left(\frac{-8}{-9}\right) +\left(\frac{6}{-3}\right) +\left(\frac{12}{-11}\right)\\= \frac{8}{9}- \frac{6}{3}-\frac{12}{11}\\=\frac{8}{9}-\frac{2}{1}-\frac{12}{11}\\=\frac{88}{99}-\frac{198}{99}-\frac{108}{99}\\=\frac{88-198-108}{99}\\=\frac{-218}{99}\)
3. \(+\left(\frac{-10}{-3}\right) +\left(\frac{5}{10}\right) -\left(\frac{6}{12}\right)\\= \frac{10}{3}+ \frac{5}{10}-\frac{6}{12}\\=\frac{10}{3}+\frac{1}{2}-\frac{1}{2}\\=\frac{20}{6}+\frac{3}{6}-\frac{3}{6}\\=\frac{20+3-3}{6}\\=\frac{20}{6}\\=\frac{10}{3}\)
4. \(-\left(\frac{2}{-3}\right) -\left(\frac{-2}{10}\right) -\left(\frac{11}{9}\right)\\= \frac{2}{3}+ \frac{2}{10}-\frac{11}{9}\\=\frac{2}{3}+\frac{1}{5}-\frac{11}{9}\\=\frac{30}{45}+\frac{9}{45}-\frac{55}{45}\\=\frac{30+9-55}{45}\\=\frac{-16}{45}\)
5. \(+\left(\frac{7}{-2}\right) +\left(\frac{-4}{5}\right) -\left(\frac{5}{-10}\right)\\= \frac{-7}{2}- \frac{4}{5}+\frac{5}{10}\\=\frac{-7}{2}-\frac{4}{5}+\frac{1}{2}\\=\frac{-35}{10}-\frac{8}{10}+\frac{5}{10}\\=\frac{-35-8+5}{10}\\=\frac{-38}{10}\\=\frac{-19}{5}\)
6. \(+\left(\frac{9}{-2}\right) -\left(\frac{2}{2}\right) -\left(\frac{11}{-3}\right)\\= \frac{-9}{2}- \frac{2}{2}+\frac{11}{3}\\=\frac{-9}{2}-\frac{1}{1}+\frac{11}{3}\\=\frac{-27}{6}-\frac{6}{6}+\frac{22}{6}\\=\frac{-27-6+22}{6}\\=\frac{-11}{6}\)
7. \(-\left(\frac{-7}{9}\right) -\left(\frac{9}{9}\right) -\left(\frac{-6}{-11}\right)\\= \frac{7}{9}- \frac{9}{9}-\frac{6}{11}\\=\frac{7}{9}-\frac{1}{1}-\frac{6}{11}\\=\frac{77}{99}-\frac{99}{99}-\frac{54}{99}\\=\frac{77-99-54}{99}\\=\frac{-76}{99}\)
8. \(-\left(\frac{6}{-7}\right) -\left(\frac{-7}{-4}\right) +\left(\frac{5}{-10}\right)\\= \frac{6}{7}- \frac{7}{4}-\frac{5}{10}\\=\frac{6}{7}-\frac{7}{4}-\frac{1}{2}\\=\frac{24}{28}-\frac{49}{28}-\frac{14}{28}\\=\frac{24-49-14}{28}\\=\frac{-39}{28}\)
9. \(-\left(\frac{8}{9}\right) +\left(\frac{3}{6}\right) +\left(\frac{-5}{-9}\right)\\= \frac{-8}{9}+ \frac{3}{6}+\frac{5}{9}\\=\frac{-8}{9}+\frac{1}{2}+\frac{5}{9}\\=\frac{-16}{18}+\frac{9}{18}+\frac{10}{18}\\=\frac{-16+9+10}{18}\\=\frac{3}{18}\\=\frac{1}{6}\)
10. \(+\left(\frac{5}{4}\right) -\left(\frac{-4}{7}\right) -\left(\frac{-4}{-11}\right)\\= \frac{5}{4}+ \frac{4}{7}-\frac{4}{11}\\=\frac{385}{308}+\frac{176}{308}-\frac{112}{308}\\=\frac{385+176-112}{308}\\=\frac{449}{308}\)
11. \(-\left(\frac{-7}{9}\right) -\left(\frac{-5}{-10}\right) -\left(\frac{7}{-9}\right)\\= \frac{7}{9}- \frac{5}{10}+\frac{7}{9}\\=\frac{7}{9}-\frac{1}{2}+\frac{7}{9}\\=\frac{14}{18}-\frac{9}{18}+\frac{14}{18}\\=\frac{14-9+14}{18}\\=\frac{19}{18}\)
12. \(+\left(\frac{-4}{-9}\right) +\left(\frac{2}{-7}\right) -\left(\frac{2}{-3}\right)\\= \frac{4}{9}- \frac{2}{7}+\frac{2}{3}\\=\frac{28}{63}-\frac{18}{63}+\frac{42}{63}\\=\frac{28-18+42}{63}\\=\frac{52}{63}\)