Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-14}{3}\right)+\left(\frac{7}{5}\right)\\= \frac{-14}{3}+\frac{7}{5}\\=\frac{-70}{15}+\frac{21}{15}\\=\frac{-70+21}{15}\\=\frac{-49}{15}\)
2. \(+\left(\frac{-4}{5}\right)+\left(\frac{-10}{7}\right)\\= \frac{-4}{5}-\frac{10}{7}\\=\frac{-28}{35}-\frac{50}{35}\\=\frac{-28-50}{35}\\=\frac{-78}{35}\)
3. \(-\left(\frac{11}{-2}\right)-\left(\frac{9}{10}\right)\\= \frac{11}{2}-\frac{9}{10}\\=\frac{55}{10}-\frac{9}{10}\\=\frac{55-9}{10}\\=\frac{46}{10}\\=\frac{23}{5}\)
4. \(-\left(\frac{3}{-13}\right)+\left(\frac{-11}{-6}\right)\\= \frac{3}{13}+\frac{11}{6}\\=\frac{18}{78}+\frac{143}{78}\\=\frac{18+143}{78}\\=\frac{161}{78}\)
5. \(+\left(\frac{15}{-13}\right)-\left(\frac{-11}{-13}\right)\\= \frac{-15}{13}-\frac{11}{13}\\=\frac{-15-11}{13}\\=\frac{-26}{13}\\=\frac{-2}{1}\)
6. \(+\left(\frac{3}{5}\right)-\left(\frac{-7}{2}\right)\\= \frac{3}{5}+\frac{7}{2}\\=\frac{6}{10}+\frac{35}{10}\\=\frac{6+35}{10}\\=\frac{41}{10}\)
7. \(+\left(\frac{-4}{13}\right)-\left(\frac{-5}{-6}\right)\\= \frac{-4}{13}-\frac{5}{6}\\=\frac{-24}{78}-\frac{65}{78}\\=\frac{-24-65}{78}\\=\frac{-89}{78}\)
8. \(+\left(\frac{-10}{7}\right)+\left(\frac{4}{-3}\right)\\= \frac{-10}{7}-\frac{4}{3}\\=\frac{-30}{21}-\frac{28}{21}\\=\frac{-30-28}{21}\\=\frac{-58}{21}\)
9. \(+\left(\frac{-15}{11}\right)-\left(\frac{-14}{-3}\right)\\= \frac{-15}{11}-\frac{14}{3}\\=\frac{-45}{33}-\frac{154}{33}\\=\frac{-45-154}{33}\\=\frac{-199}{33}\)
10. \(+\left(\frac{4}{3}\right)-\left(\frac{12}{-7}\right)\\= \frac{4}{3}+\frac{12}{7}\\=\frac{28}{21}+\frac{36}{21}\\=\frac{28+36}{21}\\=\frac{64}{21}\)
11. \(-\left(\frac{3}{-13}\right)+\left(\frac{4}{-11}\right)\\= \frac{3}{13}-\frac{4}{11}\\=\frac{33}{143}-\frac{52}{143}\\=\frac{33-52}{143}\\=\frac{-19}{143}\)
12. \(-\left(\frac{-6}{5}\right)+\left(\frac{-2}{11}\right)\\= \frac{6}{5}-\frac{2}{11}\\=\frac{66}{55}-\frac{10}{55}\\=\frac{66-10}{55}\\=\frac{56}{55}\)