Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{2}\right) -\left(\frac{8}{9}\right) +\left(\frac{4}{-12}\right)\\= \frac{-9}{2}- \frac{8}{9}-\frac{4}{12}\\=\frac{-9}{2}-\frac{8}{9}-\frac{1}{3}\\=\frac{-81}{18}-\frac{16}{18}-\frac{6}{18}\\=\frac{-81-16-6}{18}\\=\frac{-103}{18}\)
2. \(-\left(\frac{-9}{-8}\right) -\left(\frac{-2}{-4}\right) +\left(\frac{2}{-8}\right)\\= \frac{-9}{8}- \frac{2}{4}-\frac{2}{8}\\=\frac{-9}{8}-\frac{1}{2}-\frac{1}{4}\\=\frac{-9-1-1}{8}\\=\frac{-11}{8}\)
3. \(+\left(\frac{-3}{-7}\right) -\left(\frac{-6}{9}\right) +\left(\frac{8}{10}\right)\\= \frac{3}{7}+ \frac{6}{9}+\frac{8}{10}\\=\frac{3}{7}+\frac{2}{3}+\frac{4}{5}\\=\frac{45}{105}+\frac{70}{105}+\frac{84}{105}\\=\frac{45+70+84}{105}\\=\frac{199}{105}\)
4. \(-\left(\frac{-8}{-9}\right) +\left(\frac{10}{4}\right) +\left(\frac{-7}{-6}\right)\\= \frac{-8}{9}+ \frac{10}{4}+\frac{7}{6}\\=\frac{-8}{9}+\frac{5}{2}+\frac{7}{6}\\=\frac{-16}{18}+\frac{45}{18}+\frac{21}{18}\\=\frac{-16+45+21}{18}\\=\frac{50}{18}\\=\frac{25}{9}\)
5. \(-\left(\frac{8}{-3}\right) -\left(\frac{-10}{-6}\right) -\left(\frac{-6}{-3}\right)\\= \frac{8}{3}- \frac{10}{6}-\frac{6}{3}\\=\frac{8}{3}-\frac{5}{3}-\frac{2}{1}\\=\frac{8-5-2}{3}\\=\frac{1}{3}\)
6. \(-\left(\frac{-7}{8}\right) -\left(\frac{-2}{-3}\right) +\left(\frac{7}{9}\right)\\= \frac{7}{8}- \frac{2}{3}+\frac{7}{9}\\=\frac{63}{72}-\frac{48}{72}+\frac{56}{72}\\=\frac{63-48+56}{72}\\=\frac{71}{72}\)
7. \(-\left(\frac{-8}{-3}\right) +\left(\frac{-10}{-6}\right) -\left(\frac{-9}{10}\right)\\= \frac{-8}{3}+ \frac{10}{6}+\frac{9}{10}\\=\frac{-8}{3}+\frac{5}{3}+\frac{9}{10}\\=\frac{-80}{30}+\frac{50}{30}+\frac{27}{30}\\=\frac{-80+50+27}{30}\\=\frac{-3}{30}\\=\frac{-1}{10}\)
8. \(-\left(\frac{-4}{9}\right) +\left(\frac{-9}{-10}\right) +\left(\frac{12}{-3}\right)\\= \frac{4}{9}+ \frac{9}{10}-\frac{12}{3}\\=\frac{4}{9}+\frac{9}{10}-\frac{4}{1}\\=\frac{40}{90}+\frac{81}{90}-\frac{360}{90}\\=\frac{40+81-360}{90}\\=\frac{-239}{90}\)
9. \(-\left(\frac{-5}{-2}\right) -\left(\frac{3}{7}\right) +\left(\frac{2}{-9}\right)\\= \frac{-5}{2}- \frac{3}{7}-\frac{2}{9}\\=\frac{-315}{126}-\frac{54}{126}-\frac{28}{126}\\=\frac{-315-54-28}{126}\\=\frac{-397}{126}\)
10. \(-\left(\frac{-8}{-7}\right) +\left(\frac{-5}{-9}\right) -\left(\frac{-2}{8}\right)\\= \frac{-8}{7}+ \frac{5}{9}+\frac{2}{8}\\=\frac{-8}{7}+\frac{5}{9}+\frac{1}{4}\\=\frac{-288}{252}+\frac{140}{252}+\frac{63}{252}\\=\frac{-288+140+63}{252}\\=\frac{-85}{252}\)
11. \(+\left(\frac{5}{-4}\right) +\left(\frac{-3}{-4}\right) +\left(\frac{-10}{11}\right)\\= \frac{-5}{4}+ \frac{3}{4}-\frac{10}{11}\\=\frac{-55}{44}+\frac{33}{44}-\frac{40}{44}\\=\frac{-55+33-40}{44}\\=\frac{-62}{44}\\=\frac{-31}{22}\)
12. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-2}{-2}\right) -\left(\frac{12}{3}\right)\\= \frac{-6}{5}- \frac{2}{2}-\frac{12}{3}\\=\frac{-6}{5}-\frac{1}{1}-\frac{4}{1}\\=\frac{-6-1-4}{5}\\=\frac{-11}{5}\)