Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{2}\right)+\left(\frac{-12}{11}\right)\\= \frac{5}{2}-\frac{12}{11}\\=\frac{55}{22}-\frac{24}{22}\\=\frac{55-24}{22}\\=\frac{31}{22}\)
2. \(+\left(\frac{5}{11}\right)-\left(\frac{-5}{-4}\right)\\= \frac{5}{11}-\frac{5}{4}\\=\frac{20}{44}-\frac{55}{44}\\=\frac{20-55}{44}\\=\frac{-35}{44}\)
3. \(-\left(\frac{-14}{-5}\right)+\left(\frac{-6}{11}\right)\\= \frac{-14}{5}-\frac{6}{11}\\=\frac{-154}{55}-\frac{30}{55}\\=\frac{-154-30}{55}\\=\frac{-184}{55}\)
4. \(-\left(\frac{5}{2}\right)+\left(\frac{11}{8}\right)\\= \frac{-5}{2}+\frac{11}{8}\\=\frac{-20}{8}+\frac{11}{8}\\=\frac{-20+11}{8}\\=\frac{-9}{8}\)
5. \(+\left(\frac{-15}{8}\right)+\left(\frac{3}{-13}\right)\\= \frac{-15}{8}-\frac{3}{13}\\=\frac{-195}{104}-\frac{24}{104}\\=\frac{-195-24}{104}\\=\frac{-219}{104}\)
6. \(-\left(\frac{5}{-6}\right)+\left(\frac{-2}{-11}\right)\\= \frac{5}{6}+\frac{2}{11}\\=\frac{55}{66}+\frac{12}{66}\\=\frac{55+12}{66}\\=\frac{67}{66}\)
7. \(+\left(\frac{15}{-8}\right)+\left(\frac{7}{10}\right)\\= \frac{-15}{8}+\frac{7}{10}\\=\frac{-75}{40}+\frac{28}{40}\\=\frac{-75+28}{40}\\=\frac{-47}{40}\)
8. \(+\left(\frac{10}{-3}\right)+\left(\frac{14}{-13}\right)\\= \frac{-10}{3}-\frac{14}{13}\\=\frac{-130}{39}-\frac{42}{39}\\=\frac{-130-42}{39}\\=\frac{-172}{39}\)
9. \(-\left(\frac{15}{4}\right)+\left(\frac{11}{12}\right)\\= \frac{-15}{4}+\frac{11}{12}\\=\frac{-45}{12}+\frac{11}{12}\\=\frac{-45+11}{12}\\=\frac{-34}{12}\\=\frac{-17}{6}\)
10. \(-\left(\frac{10}{11}\right)-\left(\frac{13}{-14}\right)\\= \frac{-10}{11}+\frac{13}{14}\\=\frac{-140}{154}+\frac{143}{154}\\=\frac{-140+143}{154}\\=\frac{3}{154}\)
11. \(+\left(\frac{-15}{-11}\right)-\left(\frac{4}{5}\right)\\= \frac{15}{11}-\frac{4}{5}\\=\frac{75}{55}-\frac{44}{55}\\=\frac{75-44}{55}\\=\frac{31}{55}\)
12. \(-\left(\frac{-2}{13}\right)+\left(\frac{15}{13}\right)\\= \frac{2}{13}+\frac{15}{13}\\=\frac{2+15}{13}\\=\frac{17}{13}\)