Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{14}{-9}\right)+\left(\frac{12}{-5}\right)\\= \frac{14}{9}-\frac{12}{5}\\=\frac{70}{45}-\frac{108}{45}\\=\frac{70-108}{45}\\=\frac{-38}{45}\)
2. \(-\left(\frac{14}{11}\right)-\left(\frac{11}{14}\right)\\= \frac{-14}{11}-\frac{11}{14}\\=\frac{-196}{154}-\frac{121}{154}\\=\frac{-196-121}{154}\\=\frac{-317}{154}\)
3. \(+\left(\frac{5}{4}\right)+\left(\frac{-14}{9}\right)\\= \frac{5}{4}-\frac{14}{9}\\=\frac{45}{36}-\frac{56}{36}\\=\frac{45-56}{36}\\=\frac{-11}{36}\)
4. \(+\left(\frac{-6}{-13}\right)-\left(\frac{6}{13}\right)\\= \frac{6}{13}-\frac{6}{13}\\=\frac{6-6}{13}\\=\frac{0}{13}\\=\frac{0}{1}\)
5. \(+\left(\frac{6}{11}\right)+\left(\frac{15}{-2}\right)\\= \frac{6}{11}-\frac{15}{2}\\=\frac{12}{22}-\frac{165}{22}\\=\frac{12-165}{22}\\=\frac{-153}{22}\)
6. \(+\left(\frac{9}{11}\right)+\left(\frac{-7}{8}\right)\\= \frac{9}{11}-\frac{7}{8}\\=\frac{72}{88}-\frac{77}{88}\\=\frac{72-77}{88}\\=\frac{-5}{88}\)
7. \(+\left(\frac{5}{-2}\right)+\left(\frac{-12}{7}\right)\\= \frac{-5}{2}-\frac{12}{7}\\=\frac{-35}{14}-\frac{24}{14}\\=\frac{-35-24}{14}\\=\frac{-59}{14}\)
8. \(-\left(\frac{12}{11}\right)+\left(\frac{-2}{-3}\right)\\= \frac{-12}{11}+\frac{2}{3}\\=\frac{-36}{33}+\frac{22}{33}\\=\frac{-36+22}{33}\\=\frac{-14}{33}\)
9. \(+\left(\frac{14}{11}\right)+\left(\frac{-7}{-10}\right)\\= \frac{14}{11}+\frac{7}{10}\\=\frac{140}{110}+\frac{77}{110}\\=\frac{140+77}{110}\\=\frac{217}{110}\)
10. \(+\left(\frac{-13}{10}\right)+\left(\frac{5}{9}\right)\\= \frac{-13}{10}+\frac{5}{9}\\=\frac{-117}{90}+\frac{50}{90}\\=\frac{-117+50}{90}\\=\frac{-67}{90}\)
11. \(+\left(\frac{-10}{7}\right)+\left(\frac{-3}{-10}\right)\\= \frac{-10}{7}+\frac{3}{10}\\=\frac{-100}{70}+\frac{21}{70}\\=\frac{-100+21}{70}\\=\frac{-79}{70}\)
12. \(-\left(\frac{-15}{-11}\right)+\left(\frac{-5}{8}\right)\\= \frac{-15}{11}-\frac{5}{8}\\=\frac{-120}{88}-\frac{55}{88}\\=\frac{-120-55}{88}\\=\frac{-175}{88}\)