Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{4}{-3}\right)+\left(\frac{-2}{-3}\right)\\= \frac{-4}{3}+\frac{2}{3}\\=\frac{-4+2}{3}\\=\frac{-2}{3}\)
2. \(+\left(\frac{11}{14}\right)+\left(\frac{-10}{7}\right)\\= \frac{11}{14}-\frac{10}{7}\\=\frac{11-10}{14}\\=\frac{1}{14}\)
3. \(-\left(\frac{6}{-11}\right)-\left(\frac{-6}{11}\right)\\= \frac{6}{11}+\frac{6}{11}\\=\frac{6+6}{11}\\=\frac{12}{11}\)
4. \(+\left(\frac{3}{13}\right)+\left(\frac{-12}{-11}\right)\\= \frac{3}{13}+\frac{12}{11}\\=\frac{33}{143}+\frac{156}{143}\\=\frac{33+156}{143}\\=\frac{189}{143}\)
5. \(-\left(\frac{-14}{-11}\right)+\left(\frac{-7}{-12}\right)\\= \frac{-14}{11}+\frac{7}{12}\\=\frac{-168}{132}+\frac{77}{132}\\=\frac{-168+77}{132}\\=\frac{-91}{132}\)
6. \(-\left(\frac{3}{-10}\right)+\left(\frac{-4}{9}\right)\\= \frac{3}{10}-\frac{4}{9}\\=\frac{27}{90}-\frac{40}{90}\\=\frac{27-40}{90}\\=\frac{-13}{90}\)
7. \(+\left(\frac{2}{11}\right)-\left(\frac{-10}{-3}\right)\\= \frac{2}{11}-\frac{10}{3}\\=\frac{6}{33}-\frac{110}{33}\\=\frac{6-110}{33}\\=\frac{-104}{33}\)
8. \(-\left(\frac{-6}{5}\right)-\left(\frac{10}{9}\right)\\= \frac{6}{5}-\frac{10}{9}\\=\frac{54}{45}-\frac{50}{45}\\=\frac{54-50}{45}\\=\frac{4}{45}\)
9. \(-\left(\frac{3}{-4}\right)-\left(\frac{-9}{-13}\right)\\= \frac{3}{4}-\frac{9}{13}\\=\frac{39}{52}-\frac{36}{52}\\=\frac{39-36}{52}\\=\frac{3}{52}\)
10. \(+\left(\frac{-4}{3}\right)+\left(\frac{-3}{-2}\right)\\= \frac{-4}{3}+\frac{3}{2}\\=\frac{-8}{6}+\frac{9}{6}\\=\frac{-8+9}{6}\\=\frac{1}{6}\)
11. \(-\left(\frac{5}{-2}\right)+\left(\frac{-12}{5}\right)\\= \frac{5}{2}-\frac{12}{5}\\=\frac{25}{10}-\frac{24}{10}\\=\frac{25-24}{10}\\=\frac{1}{10}\)
12. \(+\left(\frac{10}{13}\right)+\left(\frac{9}{-10}\right)\\= \frac{10}{13}-\frac{9}{10}\\=\frac{100}{130}-\frac{117}{130}\\=\frac{100-117}{130}\\=\frac{-17}{130}\)