Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{-5}\right)-\left(\frac{5}{4}\right)\\= \frac{7}{5}-\frac{5}{4}\\=\frac{28}{20}-\frac{25}{20}\\=\frac{28-25}{20}\\=\frac{3}{20}\)
2. \(+\left(\frac{15}{13}\right)+\left(\frac{-15}{7}\right)\\= \frac{15}{13}-\frac{15}{7}\\=\frac{105}{91}-\frac{195}{91}\\=\frac{105-195}{91}\\=\frac{-90}{91}\)
3. \(-\left(\frac{-2}{7}\right)+\left(\frac{-8}{-9}\right)\\= \frac{2}{7}+\frac{8}{9}\\=\frac{18}{63}+\frac{56}{63}\\=\frac{18+56}{63}\\=\frac{74}{63}\)
4. \(+\left(\frac{12}{5}\right)+\left(\frac{-9}{10}\right)\\= \frac{12}{5}-\frac{9}{10}\\=\frac{24}{10}-\frac{9}{10}\\=\frac{24-9}{10}\\=\frac{15}{10}\\=\frac{3}{2}\)
5. \(-\left(\frac{-15}{4}\right)+\left(\frac{-12}{13}\right)\\= \frac{15}{4}-\frac{12}{13}\\=\frac{195}{52}-\frac{48}{52}\\=\frac{195-48}{52}\\=\frac{147}{52}\)
6. \(+\left(\frac{-14}{-9}\right)-\left(\frac{-7}{6}\right)\\= \frac{14}{9}+\frac{7}{6}\\=\frac{28}{18}+\frac{21}{18}\\=\frac{28+21}{18}\\=\frac{49}{18}\)
7. \(-\left(\frac{5}{4}\right)+\left(\frac{10}{-13}\right)\\= \frac{-5}{4}-\frac{10}{13}\\=\frac{-65}{52}-\frac{40}{52}\\=\frac{-65-40}{52}\\=\frac{-105}{52}\)
8. \(+\left(\frac{6}{13}\right)-\left(\frac{-8}{7}\right)\\= \frac{6}{13}+\frac{8}{7}\\=\frac{42}{91}+\frac{104}{91}\\=\frac{42+104}{91}\\=\frac{146}{91}\)
9. \(-\left(\frac{2}{11}\right)-\left(\frac{-3}{-13}\right)\\= \frac{-2}{11}-\frac{3}{13}\\=\frac{-26}{143}-\frac{33}{143}\\=\frac{-26-33}{143}\\=\frac{-59}{143}\)
10. \(-\left(\frac{14}{-9}\right)+\left(\frac{-10}{3}\right)\\= \frac{14}{9}-\frac{10}{3}\\=\frac{14-10}{9}\\=\frac{4}{9}\)
11. \(+\left(\frac{15}{11}\right)-\left(\frac{4}{-9}\right)\\= \frac{15}{11}+\frac{4}{9}\\=\frac{135}{99}+\frac{44}{99}\\=\frac{135+44}{99}\\=\frac{179}{99}\)
12. \(-\left(\frac{7}{12}\right)-\left(\frac{3}{5}\right)\\= \frac{-7}{12}-\frac{3}{5}\\=\frac{-35}{60}-\frac{36}{60}\\=\frac{-35-36}{60}\\=\frac{-71}{60}\)