Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{11}{-14}\right)-\left(\frac{12}{-11}\right)\\= \frac{-11}{14}+\frac{12}{11}\\=\frac{-121}{154}+\frac{168}{154}\\=\frac{-121+168}{154}\\=\frac{47}{154}\)
2. \(+\left(\frac{13}{11}\right)-\left(\frac{-13}{10}\right)\\= \frac{13}{11}+\frac{13}{10}\\=\frac{130}{110}+\frac{143}{110}\\=\frac{130+143}{110}\\=\frac{273}{110}\)
3. \(+\left(\frac{-13}{-3}\right)-\left(\frac{-9}{-13}\right)\\= \frac{13}{3}-\frac{9}{13}\\=\frac{169}{39}-\frac{27}{39}\\=\frac{169-27}{39}\\=\frac{142}{39}\)
4. \(-\left(\frac{-13}{9}\right)-\left(\frac{10}{-3}\right)\\= \frac{13}{9}+\frac{10}{3}\\=\frac{13+10}{9}\\=\frac{23}{9}\)
5. \(-\left(\frac{10}{-11}\right)-\left(\frac{2}{-3}\right)\\= \frac{10}{11}+\frac{2}{3}\\=\frac{30}{33}+\frac{22}{33}\\=\frac{30+22}{33}\\=\frac{52}{33}\)
6. \(+\left(\frac{10}{-3}\right)-\left(\frac{11}{12}\right)\\= \frac{-10}{3}-\frac{11}{12}\\=\frac{-40}{12}-\frac{11}{12}\\=\frac{-40-11}{12}\\=\frac{-51}{12}\\=\frac{-17}{4}\)
7. \(-\left(\frac{14}{3}\right)+\left(\frac{15}{-13}\right)\\= \frac{-14}{3}-\frac{15}{13}\\=\frac{-182}{39}-\frac{45}{39}\\=\frac{-182-45}{39}\\=\frac{-227}{39}\)
8. \(+\left(\frac{3}{14}\right)+\left(\frac{7}{10}\right)\\= \frac{3}{14}+\frac{7}{10}\\=\frac{15}{70}+\frac{49}{70}\\=\frac{15+49}{70}\\=\frac{64}{70}\\=\frac{32}{35}\)
9. \(+\left(\frac{11}{7}\right)-\left(\frac{-5}{3}\right)\\= \frac{11}{7}+\frac{5}{3}\\=\frac{33}{21}+\frac{35}{21}\\=\frac{33+35}{21}\\=\frac{68}{21}\)
10. \(+\left(\frac{4}{-7}\right)-\left(\frac{-6}{11}\right)\\= \frac{-4}{7}+\frac{6}{11}\\=\frac{-44}{77}+\frac{42}{77}\\=\frac{-44+42}{77}\\=\frac{-2}{77}\)
11. \(-\left(\frac{8}{5}\right)+\left(\frac{6}{-7}\right)\\= \frac{-8}{5}-\frac{6}{7}\\=\frac{-56}{35}-\frac{30}{35}\\=\frac{-56-30}{35}\\=\frac{-86}{35}\)
12. \(-\left(\frac{-2}{13}\right)+\left(\frac{-3}{5}\right)\\= \frac{2}{13}-\frac{3}{5}\\=\frac{10}{65}-\frac{39}{65}\\=\frac{10-39}{65}\\=\frac{-29}{65}\)