Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{13}\right)+\left(\frac{14}{9}\right)\\= \frac{10}{13}+\frac{14}{9}\\=\frac{90}{117}+\frac{182}{117}\\=\frac{90+182}{117}\\=\frac{272}{117}\)
2. \(+\left(\frac{9}{-10}\right)+\left(\frac{-13}{-2}\right)\\= \frac{-9}{10}+\frac{13}{2}\\=\frac{-9+13}{10}\\=\frac{4}{10}\\=\frac{2}{5}\)
3. \(-\left(\frac{3}{-8}\right)-\left(\frac{-10}{-3}\right)\\= \frac{3}{8}-\frac{10}{3}\\=\frac{9}{24}-\frac{80}{24}\\=\frac{9-80}{24}\\=\frac{-71}{24}\)
4. \(+\left(\frac{10}{3}\right)-\left(\frac{8}{3}\right)\\= \frac{10}{3}-\frac{8}{3}\\=\frac{10-8}{3}\\=\frac{2}{3}\)
5. \(-\left(\frac{-3}{-10}\right)+\left(\frac{-2}{-13}\right)\\= \frac{-3}{10}+\frac{2}{13}\\=\frac{-39}{130}+\frac{20}{130}\\=\frac{-39+20}{130}\\=\frac{-19}{130}\)
6. \(+\left(\frac{-5}{2}\right)-\left(\frac{-6}{-5}\right)\\= \frac{-5}{2}-\frac{6}{5}\\=\frac{-25}{10}-\frac{12}{10}\\=\frac{-25-12}{10}\\=\frac{-37}{10}\)
7. \(-\left(\frac{-15}{-2}\right)+\left(\frac{-9}{4}\right)\\= \frac{-15}{2}-\frac{9}{4}\\=\frac{-30}{4}-\frac{9}{4}\\=\frac{-30-9}{4}\\=\frac{-39}{4}\)
8. \(+\left(\frac{-14}{-5}\right)-\left(\frac{-11}{-7}\right)\\= \frac{14}{5}-\frac{11}{7}\\=\frac{98}{35}-\frac{55}{35}\\=\frac{98-55}{35}\\=\frac{43}{35}\)
9. \(-\left(\frac{-4}{-3}\right)+\left(\frac{5}{9}\right)\\= \frac{-4}{3}+\frac{5}{9}\\=\frac{-12}{9}+\frac{5}{9}\\=\frac{-12+5}{9}\\=\frac{-7}{9}\)
10. \(+\left(\frac{-5}{-3}\right)+\left(\frac{-14}{9}\right)\\= \frac{5}{3}-\frac{14}{9}\\=\frac{15}{9}-\frac{14}{9}\\=\frac{15-14}{9}\\=\frac{1}{9}\)
11. \(+\left(\frac{-11}{10}\right)-\left(\frac{-13}{10}\right)\\= \frac{-11}{10}+\frac{13}{10}\\=\frac{-11+13}{10}\\=\frac{2}{10}\\=\frac{1}{5}\)
12. \(+\left(\frac{-14}{-3}\right)-\left(\frac{-6}{5}\right)\\= \frac{14}{3}+\frac{6}{5}\\=\frac{70}{15}+\frac{18}{15}\\=\frac{70+18}{15}\\=\frac{88}{15}\)