Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{3}\right) +\left(\frac{-5}{-8}\right) -\left(\frac{-10}{9}\right)\\= \frac{5}{3}+ \frac{5}{8}+\frac{10}{9}\\=\frac{120}{72}+\frac{45}{72}+\frac{80}{72}\\=\frac{120+45+80}{72}\\=\frac{245}{72}\)
2. \(+\left(\frac{9}{-4}\right) -\left(\frac{-8}{-8}\right) +\left(\frac{-11}{-6}\right)\\= \frac{-9}{4}- \frac{8}{8}+\frac{11}{6}\\=\frac{-9}{4}-\frac{1}{1}+\frac{11}{6}\\=\frac{-27}{12}-\frac{12}{12}+\frac{22}{12}\\=\frac{-27-12+22}{12}\\=\frac{-17}{12}\)
3. \(+\left(\frac{-5}{4}\right) -\left(\frac{10}{7}\right) -\left(\frac{2}{4}\right)\\= \frac{-5}{4}- \frac{10}{7}-\frac{2}{4}\\=\frac{-5}{4}-\frac{10}{7}-\frac{1}{2}\\=\frac{-35}{28}-\frac{40}{28}-\frac{14}{28}\\=\frac{-35-40-14}{28}\\=\frac{-89}{28}\)
4. \(+\left(\frac{-2}{-3}\right) +\left(\frac{-2}{-9}\right) -\left(\frac{-10}{9}\right)\\= \frac{2}{3}+ \frac{2}{9}+\frac{10}{9}\\=\frac{6}{9}+\frac{2}{9}+\frac{10}{9}\\=\frac{6+2+10}{9}\\=\frac{18}{9}\\=\frac{2}{1}\)
5. \(-\left(\frac{-7}{9}\right) +\left(\frac{7}{5}\right) -\left(\frac{5}{9}\right)\\= \frac{7}{9}+ \frac{7}{5}-\frac{5}{9}\\=\frac{35}{45}+\frac{63}{45}-\frac{25}{45}\\=\frac{35+63-25}{45}\\=\frac{73}{45}\)
6. \(-\left(\frac{-3}{5}\right) +\left(\frac{-9}{4}\right) +\left(\frac{-9}{-10}\right)\\= \frac{3}{5}- \frac{9}{4}+\frac{9}{10}\\=\frac{12}{20}-\frac{45}{20}+\frac{18}{20}\\=\frac{12-45+18}{20}\\=\frac{-15}{20}\\=\frac{-3}{4}\)
7. \(-\left(\frac{2}{3}\right) +\left(\frac{-5}{-5}\right) +\left(\frac{2}{-6}\right)\\= \frac{-2}{3}+ \frac{5}{5}-\frac{2}{6}\\=\frac{-2}{3}+\frac{1}{1}-\frac{1}{3}\\=\frac{-2+1-1}{3}\\=\frac{-2}{3}\)
8. \(-\left(\frac{6}{5}\right) +\left(\frac{-9}{-4}\right) +\left(\frac{-7}{6}\right)\\= \frac{-6}{5}+ \frac{9}{4}-\frac{7}{6}\\=\frac{-72}{60}+\frac{135}{60}-\frac{70}{60}\\=\frac{-72+135-70}{60}\\=\frac{-7}{60}\)
9. \(-\left(\frac{-10}{7}\right) +\left(\frac{-5}{4}\right) -\left(\frac{-7}{11}\right)\\= \frac{10}{7}- \frac{5}{4}+\frac{7}{11}\\=\frac{440}{308}-\frac{385}{308}+\frac{196}{308}\\=\frac{440-385+196}{308}\\=\frac{251}{308}\)
10. \(-\left(\frac{-9}{-2}\right) +\left(\frac{-3}{2}\right) +\left(\frac{7}{3}\right)\\= \frac{-9}{2}- \frac{3}{2}+\frac{7}{3}\\=\frac{-27}{6}-\frac{9}{6}+\frac{14}{6}\\=\frac{-27-9+14}{6}\\=\frac{-22}{6}\\=\frac{-11}{3}\)
11. \(+\left(\frac{-2}{-5}\right) +\left(\frac{-9}{6}\right) -\left(\frac{2}{4}\right)\\= \frac{2}{5}- \frac{9}{6}-\frac{2}{4}\\=\frac{2}{5}-\frac{3}{2}-\frac{1}{2}\\=\frac{4}{10}-\frac{15}{10}-\frac{5}{10}\\=\frac{4-15-5}{10}\\=\frac{-16}{10}\\=\frac{-8}{5}\)
12. \(+\left(\frac{-4}{-3}\right) +\left(\frac{-7}{-9}\right) +\left(\frac{-9}{10}\right)\\= \frac{4}{3}+ \frac{7}{9}-\frac{9}{10}\\=\frac{120}{90}+\frac{70}{90}-\frac{81}{90}\\=\frac{120+70-81}{90}\\=\frac{109}{90}\)