Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-7}{-2}\right)-\left(\frac{-7}{-4}\right)\\= \frac{-7}{2}-\frac{7}{4}\\=\frac{-14}{4}-\frac{7}{4}\\=\frac{-14-7}{4}\\=\frac{-21}{4}\)
2. \(+\left(\frac{-15}{11}\right)-\left(\frac{-6}{-11}\right)\\= \frac{-15}{11}-\frac{6}{11}\\=\frac{-15-6}{11}\\=\frac{-21}{11}\)
3. \(-\left(\frac{-4}{-7}\right)+\left(\frac{13}{-10}\right)\\= \frac{-4}{7}-\frac{13}{10}\\=\frac{-40}{70}-\frac{91}{70}\\=\frac{-40-91}{70}\\=\frac{-131}{70}\)
4. \(+\left(\frac{-7}{-4}\right)+\left(\frac{11}{-13}\right)\\= \frac{7}{4}-\frac{11}{13}\\=\frac{91}{52}-\frac{44}{52}\\=\frac{91-44}{52}\\=\frac{47}{52}\)
5. \(-\left(\frac{-13}{2}\right)+\left(\frac{-4}{3}\right)\\= \frac{13}{2}-\frac{4}{3}\\=\frac{39}{6}-\frac{8}{6}\\=\frac{39-8}{6}\\=\frac{31}{6}\)
6. \(+\left(\frac{13}{2}\right)+\left(\frac{12}{11}\right)\\= \frac{13}{2}+\frac{12}{11}\\=\frac{143}{22}+\frac{24}{22}\\=\frac{143+24}{22}\\=\frac{167}{22}\)
7. \(-\left(\frac{-7}{-3}\right)-\left(\frac{-9}{14}\right)\\= \frac{-7}{3}+\frac{9}{14}\\=\frac{-98}{42}+\frac{27}{42}\\=\frac{-98+27}{42}\\=\frac{-71}{42}\)
8. \(-\left(\frac{3}{4}\right)-\left(\frac{10}{7}\right)\\= \frac{-3}{4}-\frac{10}{7}\\=\frac{-21}{28}-\frac{40}{28}\\=\frac{-21-40}{28}\\=\frac{-61}{28}\)
9. \(-\left(\frac{-15}{7}\right)+\left(\frac{-13}{-3}\right)\\= \frac{15}{7}+\frac{13}{3}\\=\frac{45}{21}+\frac{91}{21}\\=\frac{45+91}{21}\\=\frac{136}{21}\)
10. \(-\left(\frac{10}{-13}\right)+\left(\frac{3}{14}\right)\\= \frac{10}{13}+\frac{3}{14}\\=\frac{140}{182}+\frac{39}{182}\\=\frac{140+39}{182}\\=\frac{179}{182}\)
11. \(+\left(\frac{9}{4}\right)-\left(\frac{-9}{4}\right)\\= \frac{9}{4}+\frac{9}{4}\\=\frac{9+9}{4}\\=\frac{18}{4}\\=\frac{9}{2}\)
12. \(+\left(\frac{-2}{-9}\right)-\left(\frac{-9}{2}\right)\\= \frac{2}{9}+\frac{9}{2}\\=\frac{4}{18}+\frac{81}{18}\\=\frac{4+81}{18}\\=\frac{85}{18}\)