Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{13}\right)-\left(\frac{8}{-13}\right)\\= \frac{2}{13}+\frac{8}{13}\\=\frac{2+8}{13}\\=\frac{10}{13}\)
2. \(+\left(\frac{8}{-3}\right)-\left(\frac{-5}{-11}\right)\\= \frac{-8}{3}-\frac{5}{11}\\=\frac{-88}{33}-\frac{15}{33}\\=\frac{-88-15}{33}\\=\frac{-103}{33}\)
3. \(+\left(\frac{-7}{-2}\right)-\left(\frac{-5}{13}\right)\\= \frac{7}{2}+\frac{5}{13}\\=\frac{91}{26}+\frac{10}{26}\\=\frac{91+10}{26}\\=\frac{101}{26}\)
4. \(-\left(\frac{-2}{7}\right)-\left(\frac{-8}{3}\right)\\= \frac{2}{7}+\frac{8}{3}\\=\frac{6}{21}+\frac{56}{21}\\=\frac{6+56}{21}\\=\frac{62}{21}\)
5. \(+\left(\frac{-13}{-14}\right)-\left(\frac{-3}{-13}\right)\\= \frac{13}{14}-\frac{3}{13}\\=\frac{169}{182}-\frac{42}{182}\\=\frac{169-42}{182}\\=\frac{127}{182}\)
6. \(-\left(\frac{-14}{-9}\right)-\left(\frac{-9}{-10}\right)\\= \frac{-14}{9}-\frac{9}{10}\\=\frac{-140}{90}-\frac{81}{90}\\=\frac{-140-81}{90}\\=\frac{-221}{90}\)
7. \(-\left(\frac{-3}{13}\right)-\left(\frac{-4}{-3}\right)\\= \frac{3}{13}-\frac{4}{3}\\=\frac{9}{39}-\frac{52}{39}\\=\frac{9-52}{39}\\=\frac{-43}{39}\)
8. \(+\left(\frac{12}{-11}\right)+\left(\frac{7}{10}\right)\\= \frac{-12}{11}+\frac{7}{10}\\=\frac{-120}{110}+\frac{77}{110}\\=\frac{-120+77}{110}\\=\frac{-43}{110}\)
9. \(+\left(\frac{10}{11}\right)-\left(\frac{15}{-11}\right)\\= \frac{10}{11}+\frac{15}{11}\\=\frac{10+15}{11}\\=\frac{25}{11}\)
10. \(-\left(\frac{-13}{9}\right)+\left(\frac{2}{-3}\right)\\= \frac{13}{9}-\frac{2}{3}\\=\frac{13-2}{9}\\=\frac{11}{9}\)
11. \(-\left(\frac{-10}{7}\right)+\left(\frac{13}{11}\right)\\= \frac{10}{7}+\frac{13}{11}\\=\frac{110}{77}+\frac{91}{77}\\=\frac{110+91}{77}\\=\frac{201}{77}\)
12. \(-\left(\frac{-3}{-13}\right)+\left(\frac{-5}{9}\right)\\= \frac{-3}{13}-\frac{5}{9}\\=\frac{-27}{117}-\frac{65}{117}\\=\frac{-27-65}{117}\\=\frac{-92}{117}\)