Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-14}{9}\right)+\left(\frac{-10}{-3}\right)\\= \frac{14}{9}+\frac{10}{3}\\=\frac{14+10}{9}\\=\frac{24}{9}\\=\frac{8}{3}\)
2. \(-\left(\frac{-7}{-2}\right)+\left(\frac{-15}{-2}\right)\\= \frac{-7}{2}+\frac{15}{2}\\=\frac{-7+15}{2}\\=\frac{8}{2}\\=\frac{4}{1}\)
3. \(+\left(\frac{-15}{-13}\right)+\left(\frac{-13}{2}\right)\\= \frac{15}{13}-\frac{13}{2}\\=\frac{30}{26}-\frac{169}{26}\\=\frac{30-169}{26}\\=\frac{-139}{26}\)
4. \(-\left(\frac{10}{-3}\right)+\left(\frac{12}{-5}\right)\\= \frac{10}{3}-\frac{12}{5}\\=\frac{50}{15}-\frac{36}{15}\\=\frac{50-36}{15}\\=\frac{14}{15}\)
5. \(+\left(\frac{-13}{8}\right)-\left(\frac{-6}{-5}\right)\\= \frac{-13}{8}-\frac{6}{5}\\=\frac{-65}{40}-\frac{48}{40}\\=\frac{-65-48}{40}\\=\frac{-113}{40}\)
6. \(+\left(\frac{-7}{-5}\right)+\left(\frac{15}{13}\right)\\= \frac{7}{5}+\frac{15}{13}\\=\frac{91}{65}+\frac{75}{65}\\=\frac{91+75}{65}\\=\frac{166}{65}\)
7. \(-\left(\frac{15}{-2}\right)+\left(\frac{15}{2}\right)\\= \frac{15}{2}+\frac{15}{2}\\=\frac{15+15}{2}\\=\frac{30}{2}\\=\frac{15}{1}\)
8. \(+\left(\frac{-5}{14}\right)-\left(\frac{3}{-10}\right)\\= \frac{-5}{14}+\frac{3}{10}\\=\frac{-25}{70}+\frac{21}{70}\\=\frac{-25+21}{70}\\=\frac{-4}{70}\\=\frac{-2}{35}\)
9. \(-\left(\frac{-3}{-7}\right)-\left(\frac{9}{-13}\right)\\= \frac{-3}{7}+\frac{9}{13}\\=\frac{-39}{91}+\frac{63}{91}\\=\frac{-39+63}{91}\\=\frac{24}{91}\)
10. \(+\left(\frac{7}{-2}\right)+\left(\frac{-15}{7}\right)\\= \frac{-7}{2}-\frac{15}{7}\\=\frac{-49}{14}-\frac{30}{14}\\=\frac{-49-30}{14}\\=\frac{-79}{14}\)
11. \(-\left(\frac{-5}{6}\right)+\left(\frac{3}{-10}\right)\\= \frac{5}{6}-\frac{3}{10}\\=\frac{25}{30}-\frac{9}{30}\\=\frac{25-9}{30}\\=\frac{16}{30}\\=\frac{8}{15}\)
12. \(-\left(\frac{-10}{-9}\right)-\left(\frac{2}{-9}\right)\\= \frac{-10}{9}+\frac{2}{9}\\=\frac{-10+2}{9}\\=\frac{-8}{9}\)