Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{-13}\right)+\left(\frac{-2}{-13}\right)\\= \frac{3}{13}+\frac{2}{13}\\=\frac{3+2}{13}\\=\frac{5}{13}\)
2. \(-\left(\frac{9}{2}\right)+\left(\frac{4}{-11}\right)\\= \frac{-9}{2}-\frac{4}{11}\\=\frac{-99}{22}-\frac{8}{22}\\=\frac{-99-8}{22}\\=\frac{-107}{22}\)
3. \(+\left(\frac{7}{5}\right)-\left(\frac{-5}{-9}\right)\\= \frac{7}{5}-\frac{5}{9}\\=\frac{63}{45}-\frac{25}{45}\\=\frac{63-25}{45}\\=\frac{38}{45}\)
4. \(-\left(\frac{-10}{-7}\right)-\left(\frac{15}{-4}\right)\\= \frac{-10}{7}+\frac{15}{4}\\=\frac{-40}{28}+\frac{105}{28}\\=\frac{-40+105}{28}\\=\frac{65}{28}\)
5. \(-\left(\frac{2}{-11}\right)+\left(\frac{-4}{7}\right)\\= \frac{2}{11}-\frac{4}{7}\\=\frac{14}{77}-\frac{44}{77}\\=\frac{14-44}{77}\\=\frac{-30}{77}\)
6. \(+\left(\frac{-5}{4}\right)-\left(\frac{4}{-5}\right)\\= \frac{-5}{4}+\frac{4}{5}\\=\frac{-25}{20}+\frac{16}{20}\\=\frac{-25+16}{20}\\=\frac{-9}{20}\)
7. \(-\left(\frac{15}{-11}\right)-\left(\frac{11}{-13}\right)\\= \frac{15}{11}+\frac{11}{13}\\=\frac{195}{143}+\frac{121}{143}\\=\frac{195+121}{143}\\=\frac{316}{143}\)
8. \(-\left(\frac{-14}{-9}\right)+\left(\frac{2}{-9}\right)\\= \frac{-14}{9}-\frac{2}{9}\\=\frac{-14-2}{9}\\=\frac{-16}{9}\)
9. \(-\left(\frac{6}{-11}\right)-\left(\frac{-8}{11}\right)\\= \frac{6}{11}+\frac{8}{11}\\=\frac{6+8}{11}\\=\frac{14}{11}\)
10. \(+\left(\frac{-3}{13}\right)+\left(\frac{7}{4}\right)\\= \frac{-3}{13}+\frac{7}{4}\\=\frac{-12}{52}+\frac{91}{52}\\=\frac{-12+91}{52}\\=\frac{79}{52}\)
11. \(-\left(\frac{-3}{5}\right)+\left(\frac{-15}{11}\right)\\= \frac{3}{5}-\frac{15}{11}\\=\frac{33}{55}-\frac{75}{55}\\=\frac{33-75}{55}\\=\frac{-42}{55}\)
12. \(+\left(\frac{-12}{-11}\right)-\left(\frac{3}{-7}\right)\\= \frac{12}{11}+\frac{3}{7}\\=\frac{84}{77}+\frac{33}{77}\\=\frac{84+33}{77}\\=\frac{117}{77}\)