Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{7}{13}\right)+\left(\frac{13}{11}\right)\\= \frac{7}{13}+\frac{13}{11}\\=\frac{77}{143}+\frac{169}{143}\\=\frac{77+169}{143}\\=\frac{246}{143}\)
2. \(-\left(\frac{14}{5}\right)+\left(\frac{13}{2}\right)\\= \frac{-14}{5}+\frac{13}{2}\\=\frac{-28}{10}+\frac{65}{10}\\=\frac{-28+65}{10}\\=\frac{37}{10}\)
3. \(+\left(\frac{-9}{-2}\right)+\left(\frac{-2}{-7}\right)\\= \frac{9}{2}+\frac{2}{7}\\=\frac{63}{14}+\frac{4}{14}\\=\frac{63+4}{14}\\=\frac{67}{14}\)
4. \(+\left(\frac{12}{-5}\right)-\left(\frac{-5}{2}\right)\\= \frac{-12}{5}+\frac{5}{2}\\=\frac{-24}{10}+\frac{25}{10}\\=\frac{-24+25}{10}\\=\frac{1}{10}\)
5. \(+\left(\frac{-3}{-7}\right)+\left(\frac{-9}{-10}\right)\\= \frac{3}{7}+\frac{9}{10}\\=\frac{30}{70}+\frac{63}{70}\\=\frac{30+63}{70}\\=\frac{93}{70}\)
6. \(+\left(\frac{14}{9}\right)+\left(\frac{5}{8}\right)\\= \frac{14}{9}+\frac{5}{8}\\=\frac{112}{72}+\frac{45}{72}\\=\frac{112+45}{72}\\=\frac{157}{72}\)
7. \(-\left(\frac{15}{2}\right)-\left(\frac{6}{13}\right)\\= \frac{-15}{2}-\frac{6}{13}\\=\frac{-195}{26}-\frac{12}{26}\\=\frac{-195-12}{26}\\=\frac{-207}{26}\)
8. \(-\left(\frac{-12}{-5}\right)-\left(\frac{-15}{2}\right)\\= \frac{-12}{5}+\frac{15}{2}\\=\frac{-24}{10}+\frac{75}{10}\\=\frac{-24+75}{10}\\=\frac{51}{10}\)
9. \(+\left(\frac{4}{-11}\right)-\left(\frac{-14}{5}\right)\\= \frac{-4}{11}+\frac{14}{5}\\=\frac{-20}{55}+\frac{154}{55}\\=\frac{-20+154}{55}\\=\frac{134}{55}\)
10. \(-\left(\frac{11}{5}\right)-\left(\frac{14}{-9}\right)\\= \frac{-11}{5}+\frac{14}{9}\\=\frac{-99}{45}+\frac{70}{45}\\=\frac{-99+70}{45}\\=\frac{-29}{45}\)
11. \(-\left(\frac{12}{-11}\right)+\left(\frac{-11}{-8}\right)\\= \frac{12}{11}+\frac{11}{8}\\=\frac{96}{88}+\frac{121}{88}\\=\frac{96+121}{88}\\=\frac{217}{88}\)
12. \(-\left(\frac{-11}{13}\right)-\left(\frac{-6}{-5}\right)\\= \frac{11}{13}-\frac{6}{5}\\=\frac{55}{65}-\frac{78}{65}\\=\frac{55-78}{65}\\=\frac{-23}{65}\)