Breuken haakjesregel (reeks 1)

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Bereken

1. \(-\left(\frac{-2}{-9}\right)-\left(\frac{-5}{9}\right)\)
2. \(-\left(\frac{-7}{5}\right)+\left(\frac{-15}{-11}\right)\)
3. \(-\left(\frac{-13}{-11}\right)-\left(\frac{-2}{3}\right)\)
4. \(-\left(\frac{4}{7}\right)+\left(\frac{-11}{-4}\right)\)
5. \(-\left(\frac{-3}{4}\right)+\left(\frac{12}{-5}\right)\)
6. \(-\left(\frac{4}{-5}\right)+\left(\frac{3}{-2}\right)\)
7. \(+\left(\frac{-11}{-9}\right)-\left(\frac{9}{-7}\right)\)
8. \(+\left(\frac{13}{10}\right)-\left(\frac{14}{5}\right)\)
9. \(+\left(\frac{-4}{-13}\right)-\left(\frac{-10}{7}\right)\)
10. \(+\left(\frac{-2}{5}\right)+\left(\frac{-8}{-5}\right)\)
11. \(+\left(\frac{-9}{4}\right)-\left(\frac{-11}{12}\right)\)
12. \(-\left(\frac{10}{3}\right)-\left(\frac{-5}{-6}\right)\)

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{-9}\right)-\left(\frac{-5}{9}\right)\\= \frac{-2}{9}+\frac{5}{9}\\=\frac{-2+5}{9}\\=\frac{3}{9}\\=\frac{1}{3}\)
2. \(-\left(\frac{-7}{5}\right)+\left(\frac{-15}{-11}\right)\\= \frac{7}{5}+\frac{15}{11}\\=\frac{77}{55}+\frac{75}{55}\\=\frac{77+75}{55}\\=\frac{152}{55}\)
3. \(-\left(\frac{-13}{-11}\right)-\left(\frac{-2}{3}\right)\\= \frac{-13}{11}+\frac{2}{3}\\=\frac{-39}{33}+\frac{22}{33}\\=\frac{-39+22}{33}\\=\frac{-17}{33}\)
4. \(-\left(\frac{4}{7}\right)+\left(\frac{-11}{-4}\right)\\= \frac{-4}{7}+\frac{11}{4}\\=\frac{-16}{28}+\frac{77}{28}\\=\frac{-16+77}{28}\\=\frac{61}{28}\)
5. \(-\left(\frac{-3}{4}\right)+\left(\frac{12}{-5}\right)\\= \frac{3}{4}-\frac{12}{5}\\=\frac{15}{20}-\frac{48}{20}\\=\frac{15-48}{20}\\=\frac{-33}{20}\)
6. \(-\left(\frac{4}{-5}\right)+\left(\frac{3}{-2}\right)\\= \frac{4}{5}-\frac{3}{2}\\=\frac{8}{10}-\frac{15}{10}\\=\frac{8-15}{10}\\=\frac{-7}{10}\)
7. \(+\left(\frac{-11}{-9}\right)-\left(\frac{9}{-7}\right)\\= \frac{11}{9}+\frac{9}{7}\\=\frac{77}{63}+\frac{81}{63}\\=\frac{77+81}{63}\\=\frac{158}{63}\)
8. \(+\left(\frac{13}{10}\right)-\left(\frac{14}{5}\right)\\= \frac{13}{10}-\frac{14}{5}\\=\frac{13-14}{10}\\=\frac{-1}{10}\)
9. \(+\left(\frac{-4}{-13}\right)-\left(\frac{-10}{7}\right)\\= \frac{4}{13}+\frac{10}{7}\\=\frac{28}{91}+\frac{130}{91}\\=\frac{28+130}{91}\\=\frac{158}{91}\)
10. \(+\left(\frac{-2}{5}\right)+\left(\frac{-8}{-5}\right)\\= \frac{-2}{5}+\frac{8}{5}\\=\frac{-2+8}{5}\\=\frac{6}{5}\)
11. \(+\left(\frac{-9}{4}\right)-\left(\frac{-11}{12}\right)\\= \frac{-9}{4}+\frac{11}{12}\\=\frac{-27}{12}+\frac{11}{12}\\=\frac{-27+11}{12}\\=\frac{-16}{12}\\=\frac{-4}{3}\)
12. \(-\left(\frac{10}{3}\right)-\left(\frac{-5}{-6}\right)\\= \frac{-10}{3}-\frac{5}{6}\\=\frac{-20}{6}-\frac{5}{6}\\=\frac{-20-5}{6}\\=\frac{-25}{6}\)