Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{-9}\right)-\left(\frac{13}{-6}\right)\\= \frac{-10}{9}+\frac{13}{6}\\=\frac{-20}{18}+\frac{39}{18}\\=\frac{-20+39}{18}\\=\frac{19}{18}\)
2. \(+\left(\frac{-8}{-7}\right)-\left(\frac{11}{4}\right)\\= \frac{8}{7}-\frac{11}{4}\\=\frac{32}{28}-\frac{77}{28}\\=\frac{32-77}{28}\\=\frac{-45}{28}\)
3. \(+\left(\frac{15}{-13}\right)+\left(\frac{12}{5}\right)\\= \frac{-15}{13}+\frac{12}{5}\\=\frac{-75}{65}+\frac{156}{65}\\=\frac{-75+156}{65}\\=\frac{81}{65}\)
4. \(+\left(\frac{-7}{3}\right)-\left(\frac{10}{-3}\right)\\= \frac{-7}{3}+\frac{10}{3}\\=\frac{-7+10}{3}\\=\frac{3}{3}\\=\frac{1}{1}\)
5. \(+\left(\frac{5}{-12}\right)+\left(\frac{-4}{-7}\right)\\= \frac{-5}{12}+\frac{4}{7}\\=\frac{-35}{84}+\frac{48}{84}\\=\frac{-35+48}{84}\\=\frac{13}{84}\)
6. \(+\left(\frac{-8}{-13}\right)+\left(\frac{-13}{14}\right)\\= \frac{8}{13}-\frac{13}{14}\\=\frac{112}{182}-\frac{169}{182}\\=\frac{112-169}{182}\\=\frac{-57}{182}\)
7. \(-\left(\frac{3}{4}\right)-\left(\frac{-2}{-7}\right)\\= \frac{-3}{4}-\frac{2}{7}\\=\frac{-21}{28}-\frac{8}{28}\\=\frac{-21-8}{28}\\=\frac{-29}{28}\)
8. \(-\left(\frac{-6}{5}\right)+\left(\frac{-12}{5}\right)\\= \frac{6}{5}-\frac{12}{5}\\=\frac{6-12}{5}\\=\frac{-6}{5}\)
9. \(-\left(\frac{-15}{2}\right)+\left(\frac{9}{4}\right)\\= \frac{15}{2}+\frac{9}{4}\\=\frac{30}{4}+\frac{9}{4}\\=\frac{30+9}{4}\\=\frac{39}{4}\)
10. \(-\left(\frac{-3}{-8}\right)+\left(\frac{6}{5}\right)\\= \frac{-3}{8}+\frac{6}{5}\\=\frac{-15}{40}+\frac{48}{40}\\=\frac{-15+48}{40}\\=\frac{33}{40}\)
11. \(-\left(\frac{-12}{-7}\right)-\left(\frac{-8}{9}\right)\\= \frac{-12}{7}+\frac{8}{9}\\=\frac{-108}{63}+\frac{56}{63}\\=\frac{-108+56}{63}\\=\frac{-52}{63}\)
12. \(+\left(\frac{-13}{4}\right)-\left(\frac{-14}{-9}\right)\\= \frac{-13}{4}-\frac{14}{9}\\=\frac{-117}{36}-\frac{56}{36}\\=\frac{-117-56}{36}\\=\frac{-173}{36}\)