Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{15}{2}\right)-\left(\frac{-5}{-2}\right)\\= \frac{15}{2}-\frac{5}{2}\\=\frac{15-5}{2}\\=\frac{10}{2}\\=\frac{5}{1}\)
2. \(+\left(\frac{11}{7}\right)+\left(\frac{2}{-5}\right)\\= \frac{11}{7}-\frac{2}{5}\\=\frac{55}{35}-\frac{14}{35}\\=\frac{55-14}{35}\\=\frac{41}{35}\)
3. \(-\left(\frac{14}{-3}\right)+\left(\frac{-6}{-5}\right)\\= \frac{14}{3}+\frac{6}{5}\\=\frac{70}{15}+\frac{18}{15}\\=\frac{70+18}{15}\\=\frac{88}{15}\)
4. \(-\left(\frac{-15}{-2}\right)-\left(\frac{-2}{-3}\right)\\= \frac{-15}{2}-\frac{2}{3}\\=\frac{-45}{6}-\frac{4}{6}\\=\frac{-45-4}{6}\\=\frac{-49}{6}\)
5. \(-\left(\frac{3}{-4}\right)-\left(\frac{8}{-3}\right)\\= \frac{3}{4}+\frac{8}{3}\\=\frac{9}{12}+\frac{32}{12}\\=\frac{9+32}{12}\\=\frac{41}{12}\)
6. \(+\left(\frac{-2}{-7}\right)+\left(\frac{12}{5}\right)\\= \frac{2}{7}+\frac{12}{5}\\=\frac{10}{35}+\frac{84}{35}\\=\frac{10+84}{35}\\=\frac{94}{35}\)
7. \(-\left(\frac{-15}{11}\right)-\left(\frac{13}{-5}\right)\\= \frac{15}{11}+\frac{13}{5}\\=\frac{75}{55}+\frac{143}{55}\\=\frac{75+143}{55}\\=\frac{218}{55}\)
8. \(-\left(\frac{4}{-5}\right)+\left(\frac{8}{3}\right)\\= \frac{4}{5}+\frac{8}{3}\\=\frac{12}{15}+\frac{40}{15}\\=\frac{12+40}{15}\\=\frac{52}{15}\)
9. \(-\left(\frac{14}{3}\right)-\left(\frac{-10}{13}\right)\\= \frac{-14}{3}+\frac{10}{13}\\=\frac{-182}{39}+\frac{30}{39}\\=\frac{-182+30}{39}\\=\frac{-152}{39}\)
10. \(-\left(\frac{4}{-9}\right)-\left(\frac{-14}{-9}\right)\\= \frac{4}{9}-\frac{14}{9}\\=\frac{4-14}{9}\\=\frac{-10}{9}\)
11. \(+\left(\frac{13}{2}\right)+\left(\frac{12}{-13}\right)\\= \frac{13}{2}-\frac{12}{13}\\=\frac{169}{26}-\frac{24}{26}\\=\frac{169-24}{26}\\=\frac{145}{26}\)
12. \(+\left(\frac{-2}{5}\right)-\left(\frac{-12}{5}\right)\\= \frac{-2}{5}+\frac{12}{5}\\=\frac{-2+12}{5}\\=\frac{10}{5}\\=\frac{2}{1}\)