Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-7}\right)-\left(\frac{10}{-7}\right)\\= \frac{10}{7}+\frac{10}{7}\\=\frac{10+10}{7}\\=\frac{20}{7}\)
2. \(+\left(\frac{-2}{-7}\right)+\left(\frac{-15}{8}\right)\\= \frac{2}{7}-\frac{15}{8}\\=\frac{16}{56}-\frac{105}{56}\\=\frac{16-105}{56}\\=\frac{-89}{56}\)
3. \(-\left(\frac{6}{-13}\right)-\left(\frac{-15}{7}\right)\\= \frac{6}{13}+\frac{15}{7}\\=\frac{42}{91}+\frac{195}{91}\\=\frac{42+195}{91}\\=\frac{237}{91}\)
4. \(+\left(\frac{-14}{-3}\right)+\left(\frac{5}{3}\right)\\= \frac{14}{3}+\frac{5}{3}\\=\frac{14+5}{3}\\=\frac{19}{3}\)
5. \(-\left(\frac{3}{-13}\right)+\left(\frac{-4}{7}\right)\\= \frac{3}{13}-\frac{4}{7}\\=\frac{21}{91}-\frac{52}{91}\\=\frac{21-52}{91}\\=\frac{-31}{91}\)
6. \(-\left(\frac{9}{-8}\right)-\left(\frac{-3}{-11}\right)\\= \frac{9}{8}-\frac{3}{11}\\=\frac{99}{88}-\frac{24}{88}\\=\frac{99-24}{88}\\=\frac{75}{88}\)
7. \(+\left(\frac{8}{3}\right)+\left(\frac{5}{-11}\right)\\= \frac{8}{3}-\frac{5}{11}\\=\frac{88}{33}-\frac{15}{33}\\=\frac{88-15}{33}\\=\frac{73}{33}\)
8. \(+\left(\frac{-14}{3}\right)+\left(\frac{-3}{-4}\right)\\= \frac{-14}{3}+\frac{3}{4}\\=\frac{-56}{12}+\frac{9}{12}\\=\frac{-56+9}{12}\\=\frac{-47}{12}\)
9. \(+\left(\frac{-11}{-4}\right)+\left(\frac{-7}{3}\right)\\= \frac{11}{4}-\frac{7}{3}\\=\frac{33}{12}-\frac{28}{12}\\=\frac{33-28}{12}\\=\frac{5}{12}\)
10. \(-\left(\frac{12}{5}\right)+\left(\frac{-8}{-7}\right)\\= \frac{-12}{5}+\frac{8}{7}\\=\frac{-84}{35}+\frac{40}{35}\\=\frac{-84+40}{35}\\=\frac{-44}{35}\)
11. \(-\left(\frac{-2}{-7}\right)+\left(\frac{4}{3}\right)\\= \frac{-2}{7}+\frac{4}{3}\\=\frac{-6}{21}+\frac{28}{21}\\=\frac{-6+28}{21}\\=\frac{22}{21}\)
12. \(+\left(\frac{-3}{-10}\right)+\left(\frac{12}{11}\right)\\= \frac{3}{10}+\frac{12}{11}\\=\frac{33}{110}+\frac{120}{110}\\=\frac{33+120}{110}\\=\frac{153}{110}\)