Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{4}\right) -\left(\frac{-10}{9}\right) +\left(\frac{-5}{3}\right)\\= \frac{-7}{4}+ \frac{10}{9}-\frac{5}{3}\\=\frac{-63}{36}+\frac{40}{36}-\frac{60}{36}\\=\frac{-63+40-60}{36}\\=\frac{-83}{36}\)
2. \(+\left(\frac{5}{-2}\right) -\left(\frac{-6}{-4}\right) -\left(\frac{6}{-8}\right)\\= \frac{-5}{2}- \frac{6}{4}+\frac{6}{8}\\=\frac{-5}{2}-\frac{3}{2}+\frac{3}{4}\\=\frac{-10}{4}-\frac{6}{4}+\frac{3}{4}\\=\frac{-10-6+3}{4}\\=\frac{-13}{4}\)
3. \(+\left(\frac{-4}{5}\right) +\left(\frac{7}{10}\right) +\left(\frac{3}{-6}\right)\\= \frac{-4}{5}+ \frac{7}{10}-\frac{3}{6}\\=\frac{-4}{5}+\frac{7}{10}-\frac{1}{2}\\=\frac{-8}{10}+\frac{7}{10}-\frac{5}{10}\\=\frac{-8+7-5}{10}\\=\frac{-6}{10}\\=\frac{-3}{5}\)
4. \(-\left(\frac{-10}{9}\right) -\left(\frac{-2}{7}\right) -\left(\frac{-3}{-2}\right)\\= \frac{10}{9}+ \frac{2}{7}-\frac{3}{2}\\=\frac{140}{126}+\frac{36}{126}-\frac{189}{126}\\=\frac{140+36-189}{126}\\=\frac{-13}{126}\)
5. \(+\left(\frac{2}{-7}\right) -\left(\frac{-8}{6}\right) -\left(\frac{-2}{6}\right)\\= \frac{-2}{7}+ \frac{8}{6}+\frac{2}{6}\\=\frac{-2}{7}+\frac{4}{3}+\frac{1}{3}\\=\frac{-6}{21}+\frac{28}{21}+\frac{7}{21}\\=\frac{-6+28+7}{21}\\=\frac{29}{21}\)
6. \(-\left(\frac{-9}{-5}\right) -\left(\frac{-5}{5}\right) -\left(\frac{-7}{9}\right)\\= \frac{-9}{5}+ \frac{5}{5}+\frac{7}{9}\\=\frac{-9}{5}+\frac{1}{1}+\frac{7}{9}\\=\frac{-81}{45}+\frac{45}{45}+\frac{35}{45}\\=\frac{-81+45+35}{45}\\=\frac{-1}{45}\)
7. \(-\left(\frac{-4}{7}\right) -\left(\frac{-8}{8}\right) +\left(\frac{-8}{7}\right)\\= \frac{4}{7}+ \frac{8}{8}-\frac{8}{7}\\=\frac{4}{7}+\frac{1}{1}-\frac{8}{7}\\=\frac{4+1-8}{7}\\=\frac{-3}{7}\)
8. \(+\left(\frac{-8}{5}\right) -\left(\frac{-6}{-9}\right) +\left(\frac{-9}{12}\right)\\= \frac{-8}{5}- \frac{6}{9}-\frac{9}{12}\\=\frac{-8}{5}-\frac{2}{3}-\frac{3}{4}\\=\frac{-96}{60}-\frac{40}{60}-\frac{45}{60}\\=\frac{-96-40-45}{60}\\=\frac{-181}{60}\)
9. \(+\left(\frac{-2}{-3}\right) -\left(\frac{7}{4}\right) -\left(\frac{-6}{-8}\right)\\= \frac{2}{3}- \frac{7}{4}-\frac{6}{8}\\=\frac{2}{3}-\frac{7}{4}-\frac{3}{4}\\=\frac{8}{12}-\frac{21}{12}-\frac{9}{12}\\=\frac{8-21-9}{12}\\=\frac{-22}{12}\\=\frac{-11}{6}\)
10. \(+\left(\frac{4}{3}\right) +\left(\frac{-2}{4}\right) +\left(\frac{6}{-9}\right)\\= \frac{4}{3}- \frac{2}{4}-\frac{6}{9}\\=\frac{4}{3}-\frac{1}{2}-\frac{2}{3}\\=\frac{8}{6}-\frac{3}{6}-\frac{4}{6}\\=\frac{8-3-4}{6}\\=\frac{1}{6}\)
11. \(-\left(\frac{3}{-7}\right) +\left(\frac{2}{8}\right) -\left(\frac{-8}{9}\right)\\= \frac{3}{7}+ \frac{2}{8}+\frac{8}{9}\\=\frac{3}{7}+\frac{1}{4}+\frac{8}{9}\\=\frac{108}{252}+\frac{63}{252}+\frac{224}{252}\\=\frac{108+63+224}{252}\\=\frac{395}{252}\)
12. \(-\left(\frac{3}{-2}\right) +\left(\frac{-9}{5}\right) +\left(\frac{-3}{9}\right)\\= \frac{3}{2}- \frac{9}{5}-\frac{3}{9}\\=\frac{3}{2}-\frac{9}{5}-\frac{1}{3}\\=\frac{45}{30}-\frac{54}{30}-\frac{10}{30}\\=\frac{45-54-10}{30}\\=\frac{-19}{30}\)