Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{-2}\right)-\left(\frac{-12}{-7}\right)\\= \frac{7}{2}-\frac{12}{7}\\=\frac{49}{14}-\frac{24}{14}\\=\frac{49-24}{14}\\=\frac{25}{14}\)
2. \(+\left(\frac{-4}{13}\right)+\left(\frac{6}{-11}\right)\\= \frac{-4}{13}-\frac{6}{11}\\=\frac{-44}{143}-\frac{78}{143}\\=\frac{-44-78}{143}\\=\frac{-122}{143}\)
3. \(+\left(\frac{2}{9}\right)+\left(\frac{4}{7}\right)\\= \frac{2}{9}+\frac{4}{7}\\=\frac{14}{63}+\frac{36}{63}\\=\frac{14+36}{63}\\=\frac{50}{63}\)
4. \(+\left(\frac{2}{5}\right)-\left(\frac{-15}{-2}\right)\\= \frac{2}{5}-\frac{15}{2}\\=\frac{4}{10}-\frac{75}{10}\\=\frac{4-75}{10}\\=\frac{-71}{10}\)
5. \(-\left(\frac{5}{-9}\right)+\left(\frac{-5}{-12}\right)\\= \frac{5}{9}+\frac{5}{12}\\=\frac{20}{36}+\frac{15}{36}\\=\frac{20+15}{36}\\=\frac{35}{36}\)
6. \(+\left(\frac{-8}{5}\right)-\left(\frac{-13}{-4}\right)\\= \frac{-8}{5}-\frac{13}{4}\\=\frac{-32}{20}-\frac{65}{20}\\=\frac{-32-65}{20}\\=\frac{-97}{20}\)
7. \(+\left(\frac{-6}{5}\right)+\left(\frac{-9}{8}\right)\\= \frac{-6}{5}-\frac{9}{8}\\=\frac{-48}{40}-\frac{45}{40}\\=\frac{-48-45}{40}\\=\frac{-93}{40}\)
8. \(-\left(\frac{-6}{-5}\right)+\left(\frac{-4}{11}\right)\\= \frac{-6}{5}-\frac{4}{11}\\=\frac{-66}{55}-\frac{20}{55}\\=\frac{-66-20}{55}\\=\frac{-86}{55}\)
9. \(+\left(\frac{-4}{7}\right)+\left(\frac{8}{-3}\right)\\= \frac{-4}{7}-\frac{8}{3}\\=\frac{-12}{21}-\frac{56}{21}\\=\frac{-12-56}{21}\\=\frac{-68}{21}\)
10. \(-\left(\frac{11}{10}\right)+\left(\frac{-4}{-13}\right)\\= \frac{-11}{10}+\frac{4}{13}\\=\frac{-143}{130}+\frac{40}{130}\\=\frac{-143+40}{130}\\=\frac{-103}{130}\)
11. \(-\left(\frac{2}{-7}\right)-\left(\frac{12}{13}\right)\\= \frac{2}{7}-\frac{12}{13}\\=\frac{26}{91}-\frac{84}{91}\\=\frac{26-84}{91}\\=\frac{-58}{91}\)
12. \(-\left(\frac{-15}{7}\right)-\left(\frac{5}{-11}\right)\\= \frac{15}{7}+\frac{5}{11}\\=\frac{165}{77}+\frac{35}{77}\\=\frac{165+35}{77}\\=\frac{200}{77}\)