Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{14}\right)-\left(\frac{9}{-13}\right)\\= \frac{5}{14}+\frac{9}{13}\\=\frac{65}{182}+\frac{126}{182}\\=\frac{65+126}{182}\\=\frac{191}{182}\)
2. \(+\left(\frac{12}{11}\right)-\left(\frac{2}{7}\right)\\= \frac{12}{11}-\frac{2}{7}\\=\frac{84}{77}-\frac{22}{77}\\=\frac{84-22}{77}\\=\frac{62}{77}\)
3. \(+\left(\frac{7}{-4}\right)-\left(\frac{12}{-11}\right)\\= \frac{-7}{4}+\frac{12}{11}\\=\frac{-77}{44}+\frac{48}{44}\\=\frac{-77+48}{44}\\=\frac{-29}{44}\)
4. \(-\left(\frac{13}{10}\right)+\left(\frac{3}{2}\right)\\= \frac{-13}{10}+\frac{3}{2}\\=\frac{-13+3}{10}\\=\frac{-10}{10}\\=\frac{-1}{1}\)
5. \(+\left(\frac{2}{7}\right)+\left(\frac{-11}{-2}\right)\\= \frac{2}{7}+\frac{11}{2}\\=\frac{4}{14}+\frac{77}{14}\\=\frac{4+77}{14}\\=\frac{81}{14}\)
6. \(-\left(\frac{-4}{5}\right)-\left(\frac{9}{13}\right)\\= \frac{4}{5}-\frac{9}{13}\\=\frac{52}{65}-\frac{45}{65}\\=\frac{52-45}{65}\\=\frac{7}{65}\)
7. \(-\left(\frac{-11}{-12}\right)-\left(\frac{-9}{7}\right)\\= \frac{-11}{12}+\frac{9}{7}\\=\frac{-77}{84}+\frac{108}{84}\\=\frac{-77+108}{84}\\=\frac{31}{84}\)
8. \(+\left(\frac{10}{3}\right)+\left(\frac{-14}{13}\right)\\= \frac{10}{3}-\frac{14}{13}\\=\frac{130}{39}-\frac{42}{39}\\=\frac{130-42}{39}\\=\frac{88}{39}\)
9. \(+\left(\frac{4}{-13}\right)-\left(\frac{12}{-5}\right)\\= \frac{-4}{13}+\frac{12}{5}\\=\frac{-20}{65}+\frac{156}{65}\\=\frac{-20+156}{65}\\=\frac{136}{65}\)
10. \(+\left(\frac{-11}{2}\right)+\left(\frac{13}{-10}\right)\\= \frac{-11}{2}-\frac{13}{10}\\=\frac{-55}{10}-\frac{13}{10}\\=\frac{-55-13}{10}\\=\frac{-68}{10}\\=\frac{-34}{5}\)
11. \(+\left(\frac{-14}{13}\right)+\left(\frac{4}{7}\right)\\= \frac{-14}{13}+\frac{4}{7}\\=\frac{-98}{91}+\frac{52}{91}\\=\frac{-98+52}{91}\\=\frac{-46}{91}\)
12. \(-\left(\frac{-12}{-11}\right)-\left(\frac{6}{-11}\right)\\= \frac{-12}{11}+\frac{6}{11}\\=\frac{-12+6}{11}\\=\frac{-6}{11}\)