Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{-5}\right)+\left(\frac{5}{-4}\right)\\= \frac{9}{5}-\frac{5}{4}\\=\frac{36}{20}-\frac{25}{20}\\=\frac{36-25}{20}\\=\frac{11}{20}\)
2. \(+\left(\frac{-15}{11}\right)-\left(\frac{-15}{-11}\right)\\= \frac{-15}{11}-\frac{15}{11}\\=\frac{-15-15}{11}\\=\frac{-30}{11}\)
3. \(+\left(\frac{-15}{-4}\right)+\left(\frac{12}{-5}\right)\\= \frac{15}{4}-\frac{12}{5}\\=\frac{75}{20}-\frac{48}{20}\\=\frac{75-48}{20}\\=\frac{27}{20}\)
4. \(+\left(\frac{8}{9}\right)-\left(\frac{8}{-3}\right)\\= \frac{8}{9}+\frac{8}{3}\\=\frac{8+8}{9}\\=\frac{16}{9}\)
5. \(-\left(\frac{11}{13}\right)+\left(\frac{7}{8}\right)\\= \frac{-11}{13}+\frac{7}{8}\\=\frac{-88}{104}+\frac{91}{104}\\=\frac{-88+91}{104}\\=\frac{3}{104}\)
6. \(-\left(\frac{-12}{-7}\right)+\left(\frac{6}{-5}\right)\\= \frac{-12}{7}-\frac{6}{5}\\=\frac{-60}{35}-\frac{42}{35}\\=\frac{-60-42}{35}\\=\frac{-102}{35}\)
7. \(-\left(\frac{9}{2}\right)-\left(\frac{-4}{-3}\right)\\= \frac{-9}{2}-\frac{4}{3}\\=\frac{-27}{6}-\frac{8}{6}\\=\frac{-27-8}{6}\\=\frac{-35}{6}\)
8. \(-\left(\frac{3}{-11}\right)-\left(\frac{13}{11}\right)\\= \frac{3}{11}-\frac{13}{11}\\=\frac{3-13}{11}\\=\frac{-10}{11}\)
9. \(-\left(\frac{8}{9}\right)+\left(\frac{9}{-2}\right)\\= \frac{-8}{9}-\frac{9}{2}\\=\frac{-16}{18}-\frac{81}{18}\\=\frac{-16-81}{18}\\=\frac{-97}{18}\)
10. \(+\left(\frac{-3}{-4}\right)-\left(\frac{-12}{-11}\right)\\= \frac{3}{4}-\frac{12}{11}\\=\frac{33}{44}-\frac{48}{44}\\=\frac{33-48}{44}\\=\frac{-15}{44}\)
11. \(+\left(\frac{6}{5}\right)-\left(\frac{15}{-11}\right)\\= \frac{6}{5}+\frac{15}{11}\\=\frac{66}{55}+\frac{75}{55}\\=\frac{66+75}{55}\\=\frac{141}{55}\)
12. \(-\left(\frac{-10}{13}\right)-\left(\frac{-11}{-5}\right)\\= \frac{10}{13}-\frac{11}{5}\\=\frac{50}{65}-\frac{143}{65}\\=\frac{50-143}{65}\\=\frac{-93}{65}\)