Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{12}{-7}\right)+\left(\frac{-4}{-9}\right)\\= \frac{12}{7}+\frac{4}{9}\\=\frac{108}{63}+\frac{28}{63}\\=\frac{108+28}{63}\\=\frac{136}{63}\)
2. \(-\left(\frac{9}{-13}\right)-\left(\frac{10}{-3}\right)\\= \frac{9}{13}+\frac{10}{3}\\=\frac{27}{39}+\frac{130}{39}\\=\frac{27+130}{39}\\=\frac{157}{39}\)
3. \(-\left(\frac{9}{-7}\right)+\left(\frac{11}{-10}\right)\\= \frac{9}{7}-\frac{11}{10}\\=\frac{90}{70}-\frac{77}{70}\\=\frac{90-77}{70}\\=\frac{13}{70}\)
4. \(-\left(\frac{-12}{-11}\right)-\left(\frac{-7}{10}\right)\\= \frac{-12}{11}+\frac{7}{10}\\=\frac{-120}{110}+\frac{77}{110}\\=\frac{-120+77}{110}\\=\frac{-43}{110}\)
5. \(-\left(\frac{-9}{-10}\right)-\left(\frac{10}{-11}\right)\\= \frac{-9}{10}+\frac{10}{11}\\=\frac{-99}{110}+\frac{100}{110}\\=\frac{-99+100}{110}\\=\frac{1}{110}\)
6. \(-\left(\frac{-8}{-5}\right)-\left(\frac{12}{-13}\right)\\= \frac{-8}{5}+\frac{12}{13}\\=\frac{-104}{65}+\frac{60}{65}\\=\frac{-104+60}{65}\\=\frac{-44}{65}\)
7. \(-\left(\frac{15}{11}\right)-\left(\frac{-4}{-9}\right)\\= \frac{-15}{11}-\frac{4}{9}\\=\frac{-135}{99}-\frac{44}{99}\\=\frac{-135-44}{99}\\=\frac{-179}{99}\)
8. \(-\left(\frac{-14}{9}\right)-\left(\frac{-8}{9}\right)\\= \frac{14}{9}+\frac{8}{9}\\=\frac{14+8}{9}\\=\frac{22}{9}\)
9. \(+\left(\frac{10}{-7}\right)+\left(\frac{-13}{-5}\right)\\= \frac{-10}{7}+\frac{13}{5}\\=\frac{-50}{35}+\frac{91}{35}\\=\frac{-50+91}{35}\\=\frac{41}{35}\)
10. \(-\left(\frac{7}{-9}\right)-\left(\frac{-3}{-11}\right)\\= \frac{7}{9}-\frac{3}{11}\\=\frac{77}{99}-\frac{27}{99}\\=\frac{77-27}{99}\\=\frac{50}{99}\)
11. \(-\left(\frac{7}{-4}\right)-\left(\frac{8}{7}\right)\\= \frac{7}{4}-\frac{8}{7}\\=\frac{49}{28}-\frac{32}{28}\\=\frac{49-32}{28}\\=\frac{17}{28}\)
12. \(+\left(\frac{11}{-6}\right)+\left(\frac{8}{3}\right)\\= \frac{-11}{6}+\frac{8}{3}\\=\frac{-11+8}{6}\\=\frac{-3}{6}\\=\frac{-1}{2}\)