Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{-2}\right)+\left(\frac{-8}{9}\right)\\= \frac{9}{2}-\frac{8}{9}\\=\frac{81}{18}-\frac{16}{18}\\=\frac{81-16}{18}\\=\frac{65}{18}\)
2. \(+\left(\frac{4}{-5}\right)+\left(\frac{-5}{-9}\right)\\= \frac{-4}{5}+\frac{5}{9}\\=\frac{-36}{45}+\frac{25}{45}\\=\frac{-36+25}{45}\\=\frac{-11}{45}\)
3. \(+\left(\frac{-12}{11}\right)+\left(\frac{-8}{13}\right)\\= \frac{-12}{11}-\frac{8}{13}\\=\frac{-156}{143}-\frac{88}{143}\\=\frac{-156-88}{143}\\=\frac{-244}{143}\)
4. \(-\left(\frac{12}{-5}\right)-\left(\frac{15}{-4}\right)\\= \frac{12}{5}+\frac{15}{4}\\=\frac{48}{20}+\frac{75}{20}\\=\frac{48+75}{20}\\=\frac{123}{20}\)
5. \(-\left(\frac{4}{9}\right)+\left(\frac{3}{5}\right)\\= \frac{-4}{9}+\frac{3}{5}\\=\frac{-20}{45}+\frac{27}{45}\\=\frac{-20+27}{45}\\=\frac{7}{45}\)
6. \(+\left(\frac{-6}{-5}\right)-\left(\frac{-15}{-11}\right)\\= \frac{6}{5}-\frac{15}{11}\\=\frac{66}{55}-\frac{75}{55}\\=\frac{66-75}{55}\\=\frac{-9}{55}\)
7. \(-\left(\frac{13}{6}\right)-\left(\frac{10}{13}\right)\\= \frac{-13}{6}-\frac{10}{13}\\=\frac{-169}{78}-\frac{60}{78}\\=\frac{-169-60}{78}\\=\frac{-229}{78}\)
8. \(-\left(\frac{5}{-6}\right)+\left(\frac{-9}{-13}\right)\\= \frac{5}{6}+\frac{9}{13}\\=\frac{65}{78}+\frac{54}{78}\\=\frac{65+54}{78}\\=\frac{119}{78}\)
9. \(+\left(\frac{-15}{-7}\right)-\left(\frac{-6}{-5}\right)\\= \frac{15}{7}-\frac{6}{5}\\=\frac{75}{35}-\frac{42}{35}\\=\frac{75-42}{35}\\=\frac{33}{35}\)
10. \(-\left(\frac{9}{5}\right)+\left(\frac{12}{11}\right)\\= \frac{-9}{5}+\frac{12}{11}\\=\frac{-99}{55}+\frac{60}{55}\\=\frac{-99+60}{55}\\=\frac{-39}{55}\)
11. \(-\left(\frac{-13}{-14}\right)-\left(\frac{-10}{-11}\right)\\= \frac{-13}{14}-\frac{10}{11}\\=\frac{-143}{154}-\frac{140}{154}\\=\frac{-143-140}{154}\\=\frac{-283}{154}\)
12. \(+\left(\frac{10}{-7}\right)-\left(\frac{-2}{-7}\right)\\= \frac{-10}{7}-\frac{2}{7}\\=\frac{-10-2}{7}\\=\frac{-12}{7}\)