Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-11}\right)-\left(\frac{15}{-7}\right)\\= \frac{10}{11}+\frac{15}{7}\\=\frac{70}{77}+\frac{165}{77}\\=\frac{70+165}{77}\\=\frac{235}{77}\)
2. \(+\left(\frac{13}{8}\right)-\left(\frac{13}{2}\right)\\= \frac{13}{8}-\frac{13}{2}\\=\frac{13-13}{8}\\=\frac{0}{8}\\=\frac{0}{1}\)
3. \(+\left(\frac{13}{-2}\right)+\left(\frac{-2}{-3}\right)\\= \frac{-13}{2}+\frac{2}{3}\\=\frac{-39}{6}+\frac{4}{6}\\=\frac{-39+4}{6}\\=\frac{-35}{6}\)
4. \(+\left(\frac{-2}{-13}\right)-\left(\frac{14}{9}\right)\\= \frac{2}{13}-\frac{14}{9}\\=\frac{18}{117}-\frac{182}{117}\\=\frac{18-182}{117}\\=\frac{-164}{117}\)
5. \(+\left(\frac{6}{-13}\right)+\left(\frac{-5}{2}\right)\\= \frac{-6}{13}-\frac{5}{2}\\=\frac{-12}{26}-\frac{65}{26}\\=\frac{-12-65}{26}\\=\frac{-77}{26}\)
6. \(-\left(\frac{-9}{-13}\right)+\left(\frac{14}{5}\right)\\= \frac{-9}{13}+\frac{14}{5}\\=\frac{-45}{65}+\frac{182}{65}\\=\frac{-45+182}{65}\\=\frac{137}{65}\)
7. \(+\left(\frac{6}{5}\right)+\left(\frac{2}{-3}\right)\\= \frac{6}{5}-\frac{2}{3}\\=\frac{18}{15}-\frac{10}{15}\\=\frac{18-10}{15}\\=\frac{8}{15}\)
8. \(-\left(\frac{7}{8}\right)+\left(\frac{12}{-5}\right)\\= \frac{-7}{8}-\frac{12}{5}\\=\frac{-35}{40}-\frac{96}{40}\\=\frac{-35-96}{40}\\=\frac{-131}{40}\)
9. \(+\left(\frac{9}{7}\right)-\left(\frac{-13}{-2}\right)\\= \frac{9}{7}-\frac{13}{2}\\=\frac{18}{14}-\frac{91}{14}\\=\frac{18-91}{14}\\=\frac{-73}{14}\)
10. \(+\left(\frac{6}{-11}\right)+\left(\frac{-9}{14}\right)\\= \frac{-6}{11}-\frac{9}{14}\\=\frac{-84}{154}-\frac{99}{154}\\=\frac{-84-99}{154}\\=\frac{-183}{154}\)
11. \(-\left(\frac{-2}{3}\right)+\left(\frac{14}{-5}\right)\\= \frac{2}{3}-\frac{14}{5}\\=\frac{10}{15}-\frac{42}{15}\\=\frac{10-42}{15}\\=\frac{-32}{15}\)
12. \(-\left(\frac{12}{-13}\right)-\left(\frac{9}{7}\right)\\= \frac{12}{13}-\frac{9}{7}\\=\frac{84}{91}-\frac{117}{91}\\=\frac{84-117}{91}\\=\frac{-33}{91}\)