Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{11}{-7}\right)+\left(\frac{-9}{-13}\right)\\= \frac{11}{7}+\frac{9}{13}\\=\frac{143}{91}+\frac{63}{91}\\=\frac{143+63}{91}\\=\frac{206}{91}\)
2. \(+\left(\frac{-4}{-3}\right)-\left(\frac{-8}{9}\right)\\= \frac{4}{3}+\frac{8}{9}\\=\frac{12}{9}+\frac{8}{9}\\=\frac{12+8}{9}\\=\frac{20}{9}\)
3. \(+\left(\frac{-13}{-3}\right)+\left(\frac{-12}{-7}\right)\\= \frac{13}{3}+\frac{12}{7}\\=\frac{91}{21}+\frac{36}{21}\\=\frac{91+36}{21}\\=\frac{127}{21}\)
4. \(+\left(\frac{14}{9}\right)+\left(\frac{-3}{2}\right)\\= \frac{14}{9}-\frac{3}{2}\\=\frac{28}{18}-\frac{27}{18}\\=\frac{28-27}{18}\\=\frac{1}{18}\)
5. \(-\left(\frac{9}{-10}\right)+\left(\frac{3}{-10}\right)\\= \frac{9}{10}-\frac{3}{10}\\=\frac{9-3}{10}\\=\frac{6}{10}\\=\frac{3}{5}\)
6. \(-\left(\frac{-2}{11}\right)-\left(\frac{-15}{-11}\right)\\= \frac{2}{11}-\frac{15}{11}\\=\frac{2-15}{11}\\=\frac{-13}{11}\)
7. \(-\left(\frac{13}{8}\right)-\left(\frac{9}{-2}\right)\\= \frac{-13}{8}+\frac{9}{2}\\=\frac{-13+9}{8}\\=\frac{-4}{8}\\=\frac{-1}{2}\)
8. \(-\left(\frac{13}{11}\right)-\left(\frac{-10}{-9}\right)\\= \frac{-13}{11}-\frac{10}{9}\\=\frac{-117}{99}-\frac{110}{99}\\=\frac{-117-110}{99}\\=\frac{-227}{99}\)
9. \(+\left(\frac{8}{-13}\right)-\left(\frac{7}{2}\right)\\= \frac{-8}{13}-\frac{7}{2}\\=\frac{-16}{26}-\frac{91}{26}\\=\frac{-16-91}{26}\\=\frac{-107}{26}\)
10. \(-\left(\frac{-15}{2}\right)-\left(\frac{13}{-7}\right)\\= \frac{15}{2}+\frac{13}{7}\\=\frac{105}{14}+\frac{26}{14}\\=\frac{105+26}{14}\\=\frac{131}{14}\)
11. \(-\left(\frac{-9}{13}\right)+\left(\frac{-8}{-11}\right)\\= \frac{9}{13}+\frac{8}{11}\\=\frac{99}{143}+\frac{104}{143}\\=\frac{99+104}{143}\\=\frac{203}{143}\)
12. \(+\left(\frac{11}{-13}\right)-\left(\frac{7}{13}\right)\\= \frac{-11}{13}-\frac{7}{13}\\=\frac{-11-7}{13}\\=\frac{-18}{13}\)