Breuken haakjesregel (reeks 1)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{12}{-5}\right)-\left(\frac{5}{-13}\right)\\= \frac{-12}{5}+\frac{5}{13}\\=\frac{-156}{65}+\frac{25}{65}\\=\frac{-156+25}{65}\\=\frac{-131}{65}\)
2. \(+\left(\frac{-8}{13}\right)-\left(\frac{-15}{7}\right)\\= \frac{-8}{13}+\frac{15}{7}\\=\frac{-56}{91}+\frac{195}{91}\\=\frac{-56+195}{91}\\=\frac{139}{91}\)
3. \(-\left(\frac{3}{-7}\right)+\left(\frac{8}{5}\right)\\= \frac{3}{7}+\frac{8}{5}\\=\frac{15}{35}+\frac{56}{35}\\=\frac{15+56}{35}\\=\frac{71}{35}\)
4. \(+\left(\frac{-4}{9}\right)-\left(\frac{9}{-13}\right)\\= \frac{-4}{9}+\frac{9}{13}\\=\frac{-52}{117}+\frac{81}{117}\\=\frac{-52+81}{117}\\=\frac{29}{117}\)
5. \(-\left(\frac{-13}{-14}\right)-\left(\frac{-8}{3}\right)\\= \frac{-13}{14}+\frac{8}{3}\\=\frac{-39}{42}+\frac{112}{42}\\=\frac{-39+112}{42}\\=\frac{73}{42}\)
6. \(+\left(\frac{9}{-14}\right)+\left(\frac{4}{3}\right)\\= \frac{-9}{14}+\frac{4}{3}\\=\frac{-27}{42}+\frac{56}{42}\\=\frac{-27+56}{42}\\=\frac{29}{42}\)
7. \(-\left(\frac{15}{-2}\right)-\left(\frac{2}{-7}\right)\\= \frac{15}{2}+\frac{2}{7}\\=\frac{105}{14}+\frac{4}{14}\\=\frac{105+4}{14}\\=\frac{109}{14}\)
8. \(-\left(\frac{11}{6}\right)+\left(\frac{-14}{5}\right)\\= \frac{-11}{6}-\frac{14}{5}\\=\frac{-55}{30}-\frac{84}{30}\\=\frac{-55-84}{30}\\=\frac{-139}{30}\)
9. \(-\left(\frac{-5}{-6}\right)-\left(\frac{-15}{13}\right)\\= \frac{-5}{6}+\frac{15}{13}\\=\frac{-65}{78}+\frac{90}{78}\\=\frac{-65+90}{78}\\=\frac{25}{78}\)
10. \(+\left(\frac{-14}{-9}\right)+\left(\frac{-15}{4}\right)\\= \frac{14}{9}-\frac{15}{4}\\=\frac{56}{36}-\frac{135}{36}\\=\frac{56-135}{36}\\=\frac{-79}{36}\)
11. \(-\left(\frac{-11}{6}\right)+\left(\frac{9}{-10}\right)\\= \frac{11}{6}-\frac{9}{10}\\=\frac{55}{30}-\frac{27}{30}\\=\frac{55-27}{30}\\=\frac{28}{30}\\=\frac{14}{15}\)
12. \(+\left(\frac{-14}{13}\right)+\left(\frac{-10}{-7}\right)\\= \frac{-14}{13}+\frac{10}{7}\\=\frac{-98}{91}+\frac{130}{91}\\=\frac{-98+130}{91}\\=\frac{32}{91}\)