Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{-7}\right)+\left(\frac{10}{7}\right)\\= \frac{5}{7}+\frac{10}{7}\\=\frac{5+10}{7}\\=\frac{15}{7}\)
2. \(-\left(\frac{12}{-11}\right)-\left(\frac{-7}{-13}\right)\\= \frac{12}{11}-\frac{7}{13}\\=\frac{156}{143}-\frac{77}{143}\\=\frac{156-77}{143}\\=\frac{79}{143}\)
3. \(-\left(\frac{8}{-3}\right)+\left(\frac{-5}{-6}\right)\\= \frac{8}{3}+\frac{5}{6}\\=\frac{16}{6}+\frac{5}{6}\\=\frac{16+5}{6}\\=\frac{21}{6}\\=\frac{7}{2}\)
4. \(-\left(\frac{-9}{-13}\right)+\left(\frac{9}{11}\right)\\= \frac{-9}{13}+\frac{9}{11}\\=\frac{-99}{143}+\frac{117}{143}\\=\frac{-99+117}{143}\\=\frac{18}{143}\)
5. \(-\left(\frac{13}{14}\right)-\left(\frac{-2}{-9}\right)\\= \frac{-13}{14}-\frac{2}{9}\\=\frac{-117}{126}-\frac{28}{126}\\=\frac{-117-28}{126}\\=\frac{-145}{126}\)
6. \(+\left(\frac{5}{7}\right)-\left(\frac{9}{2}\right)\\= \frac{5}{7}-\frac{9}{2}\\=\frac{10}{14}-\frac{63}{14}\\=\frac{10-63}{14}\\=\frac{-53}{14}\)
7. \(-\left(\frac{4}{-7}\right)+\left(\frac{-7}{3}\right)\\= \frac{4}{7}-\frac{7}{3}\\=\frac{12}{21}-\frac{49}{21}\\=\frac{12-49}{21}\\=\frac{-37}{21}\)
8. \(-\left(\frac{14}{9}\right)-\left(\frac{4}{-13}\right)\\= \frac{-14}{9}+\frac{4}{13}\\=\frac{-182}{117}+\frac{36}{117}\\=\frac{-182+36}{117}\\=\frac{-146}{117}\)
9. \(-\left(\frac{2}{7}\right)+\left(\frac{-12}{-13}\right)\\= \frac{-2}{7}+\frac{12}{13}\\=\frac{-26}{91}+\frac{84}{91}\\=\frac{-26+84}{91}\\=\frac{58}{91}\)
10. \(+\left(\frac{7}{-6}\right)-\left(\frac{-4}{-5}\right)\\= \frac{-7}{6}-\frac{4}{5}\\=\frac{-35}{30}-\frac{24}{30}\\=\frac{-35-24}{30}\\=\frac{-59}{30}\)
11. \(-\left(\frac{-4}{-5}\right)+\left(\frac{-14}{-5}\right)\\= \frac{-4}{5}+\frac{14}{5}\\=\frac{-4+14}{5}\\=\frac{10}{5}\\=\frac{2}{1}\)
12. \(-\left(\frac{6}{7}\right)-\left(\frac{-10}{9}\right)\\= \frac{-6}{7}+\frac{10}{9}\\=\frac{-54}{63}+\frac{70}{63}\\=\frac{-54+70}{63}\\=\frac{16}{63}\)