Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-12}{5}\right)-\left(\frac{-15}{-4}\right)\\= \frac{12}{5}-\frac{15}{4}\\=\frac{48}{20}-\frac{75}{20}\\=\frac{48-75}{20}\\=\frac{-27}{20}\)
2. \(+\left(\frac{-10}{9}\right)+\left(\frac{7}{4}\right)\\= \frac{-10}{9}+\frac{7}{4}\\=\frac{-40}{36}+\frac{63}{36}\\=\frac{-40+63}{36}\\=\frac{23}{36}\)
3. \(+\left(\frac{-8}{7}\right)-\left(\frac{-10}{3}\right)\\= \frac{-8}{7}+\frac{10}{3}\\=\frac{-24}{21}+\frac{70}{21}\\=\frac{-24+70}{21}\\=\frac{46}{21}\)
4. \(+\left(\frac{-6}{11}\right)-\left(\frac{-10}{-3}\right)\\= \frac{-6}{11}-\frac{10}{3}\\=\frac{-18}{33}-\frac{110}{33}\\=\frac{-18-110}{33}\\=\frac{-128}{33}\)
5. \(+\left(\frac{-14}{-9}\right)-\left(\frac{5}{14}\right)\\= \frac{14}{9}-\frac{5}{14}\\=\frac{196}{126}-\frac{45}{126}\\=\frac{196-45}{126}\\=\frac{151}{126}\)
6. \(-\left(\frac{7}{-6}\right)-\left(\frac{-5}{14}\right)\\= \frac{7}{6}+\frac{5}{14}\\=\frac{49}{42}+\frac{15}{42}\\=\frac{49+15}{42}\\=\frac{64}{42}\\=\frac{32}{21}\)
7. \(+\left(\frac{10}{-9}\right)-\left(\frac{5}{2}\right)\\= \frac{-10}{9}-\frac{5}{2}\\=\frac{-20}{18}-\frac{45}{18}\\=\frac{-20-45}{18}\\=\frac{-65}{18}\)
8. \(-\left(\frac{-9}{-8}\right)-\left(\frac{2}{7}\right)\\= \frac{-9}{8}-\frac{2}{7}\\=\frac{-63}{56}-\frac{16}{56}\\=\frac{-63-16}{56}\\=\frac{-79}{56}\)
9. \(+\left(\frac{10}{11}\right)+\left(\frac{-15}{8}\right)\\= \frac{10}{11}-\frac{15}{8}\\=\frac{80}{88}-\frac{165}{88}\\=\frac{80-165}{88}\\=\frac{-85}{88}\)
10. \(+\left(\frac{-2}{9}\right)+\left(\frac{-2}{-9}\right)\\= \frac{-2}{9}+\frac{2}{9}\\=\frac{-2+2}{9}\\=\frac{0}{9}\\=\frac{0}{1}\)
11. \(-\left(\frac{6}{-7}\right)+\left(\frac{8}{-9}\right)\\= \frac{6}{7}-\frac{8}{9}\\=\frac{54}{63}-\frac{56}{63}\\=\frac{54-56}{63}\\=\frac{-2}{63}\)
12. \(-\left(\frac{-6}{5}\right)-\left(\frac{11}{14}\right)\\= \frac{6}{5}-\frac{11}{14}\\=\frac{84}{70}-\frac{55}{70}\\=\frac{84-55}{70}\\=\frac{29}{70}\)