Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-14}{9}\right)+\left(\frac{-9}{14}\right)\\= \frac{-14}{9}-\frac{9}{14}\\=\frac{-196}{126}-\frac{81}{126}\\=\frac{-196-81}{126}\\=\frac{-277}{126}\)
2. \(+\left(\frac{12}{-7}\right)-\left(\frac{13}{7}\right)\\= \frac{-12}{7}-\frac{13}{7}\\=\frac{-12-13}{7}\\=\frac{-25}{7}\)
3. \(+\left(\frac{2}{9}\right)-\left(\frac{-12}{5}\right)\\= \frac{2}{9}+\frac{12}{5}\\=\frac{10}{45}+\frac{108}{45}\\=\frac{10+108}{45}\\=\frac{118}{45}\)
4. \(-\left(\frac{8}{-7}\right)+\left(\frac{-4}{-9}\right)\\= \frac{8}{7}+\frac{4}{9}\\=\frac{72}{63}+\frac{28}{63}\\=\frac{72+28}{63}\\=\frac{100}{63}\)
5. \(+\left(\frac{8}{-9}\right)+\left(\frac{-3}{10}\right)\\= \frac{-8}{9}-\frac{3}{10}\\=\frac{-80}{90}-\frac{27}{90}\\=\frac{-80-27}{90}\\=\frac{-107}{90}\)
6. \(+\left(\frac{5}{2}\right)+\left(\frac{7}{9}\right)\\= \frac{5}{2}+\frac{7}{9}\\=\frac{45}{18}+\frac{14}{18}\\=\frac{45+14}{18}\\=\frac{59}{18}\)
7. \(-\left(\frac{-12}{-5}\right)+\left(\frac{-2}{7}\right)\\= \frac{-12}{5}-\frac{2}{7}\\=\frac{-84}{35}-\frac{10}{35}\\=\frac{-84-10}{35}\\=\frac{-94}{35}\)
8. \(-\left(\frac{14}{-9}\right)+\left(\frac{-15}{-8}\right)\\= \frac{14}{9}+\frac{15}{8}\\=\frac{112}{72}+\frac{135}{72}\\=\frac{112+135}{72}\\=\frac{247}{72}\)
9. \(-\left(\frac{-8}{5}\right)-\left(\frac{-4}{7}\right)\\= \frac{8}{5}+\frac{4}{7}\\=\frac{56}{35}+\frac{20}{35}\\=\frac{56+20}{35}\\=\frac{76}{35}\)
10. \(-\left(\frac{3}{7}\right)-\left(\frac{10}{3}\right)\\= \frac{-3}{7}-\frac{10}{3}\\=\frac{-9}{21}-\frac{70}{21}\\=\frac{-9-70}{21}\\=\frac{-79}{21}\)
11. \(+\left(\frac{-14}{3}\right)-\left(\frac{-12}{-5}\right)\\= \frac{-14}{3}-\frac{12}{5}\\=\frac{-70}{15}-\frac{36}{15}\\=\frac{-70-36}{15}\\=\frac{-106}{15}\)
12. \(-\left(\frac{-4}{-3}\right)-\left(\frac{-10}{3}\right)\\= \frac{-4}{3}+\frac{10}{3}\\=\frac{-4+10}{3}\\=\frac{6}{3}\\=\frac{2}{1}\)