Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{-3}\right) -\left(\frac{2}{-10}\right) +\left(\frac{-7}{7}\right)\\= \frac{-4}{3}+ \frac{2}{10}-\frac{7}{7}\\=\frac{-4}{3}+\frac{1}{5}-\frac{1}{1}\\=\frac{-20}{15}+\frac{3}{15}-\frac{15}{15}\\=\frac{-20+3-15}{15}\\=\frac{-32}{15}\)
2. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-4}{10}\right) +\left(\frac{-4}{12}\right)\\= \frac{6}{5}+ \frac{4}{10}-\frac{4}{12}\\=\frac{6}{5}+\frac{2}{5}-\frac{1}{3}\\=\frac{18}{15}+\frac{6}{15}-\frac{5}{15}\\=\frac{18+6-5}{15}\\=\frac{19}{15}\)
3. \(-\left(\frac{-6}{-7}\right) +\left(\frac{-3}{2}\right) +\left(\frac{3}{9}\right)\\= \frac{-6}{7}- \frac{3}{2}+\frac{3}{9}\\=\frac{-6}{7}-\frac{3}{2}+\frac{1}{3}\\=\frac{-36}{42}-\frac{63}{42}+\frac{14}{42}\\=\frac{-36-63+14}{42}\\=\frac{-85}{42}\)
4. \(-\left(\frac{7}{-2}\right) +\left(\frac{8}{5}\right) -\left(\frac{2}{8}\right)\\= \frac{7}{2}+ \frac{8}{5}-\frac{2}{8}\\=\frac{7}{2}+\frac{8}{5}-\frac{1}{4}\\=\frac{70}{20}+\frac{32}{20}-\frac{5}{20}\\=\frac{70+32-5}{20}\\=\frac{97}{20}\)
5. \(+\left(\frac{-3}{4}\right) +\left(\frac{-10}{5}\right) -\left(\frac{-12}{-2}\right)\\= \frac{-3}{4}- \frac{10}{5}-\frac{12}{2}\\=\frac{-3}{4}-\frac{2}{1}-\frac{6}{1}\\=\frac{-3-2-6}{4}\\=\frac{-11}{4}\)
6. \(-\left(\frac{-10}{-7}\right) +\left(\frac{6}{-7}\right) -\left(\frac{-2}{10}\right)\\= \frac{-10}{7}- \frac{6}{7}+\frac{2}{10}\\=\frac{-10}{7}-\frac{6}{7}+\frac{1}{5}\\=\frac{-50}{35}-\frac{30}{35}+\frac{7}{35}\\=\frac{-50-30+7}{35}\\=\frac{-73}{35}\)
7. \(-\left(\frac{-2}{3}\right) -\left(\frac{5}{-7}\right) +\left(\frac{4}{8}\right)\\= \frac{2}{3}+ \frac{5}{7}+\frac{4}{8}\\=\frac{2}{3}+\frac{5}{7}+\frac{1}{2}\\=\frac{28}{42}+\frac{30}{42}+\frac{21}{42}\\=\frac{28+30+21}{42}\\=\frac{79}{42}\)
8. \(+\left(\frac{-8}{9}\right) +\left(\frac{6}{3}\right) +\left(\frac{2}{-5}\right)\\= \frac{-8}{9}+ \frac{6}{3}-\frac{2}{5}\\=\frac{-8}{9}+\frac{2}{1}-\frac{2}{5}\\=\frac{-40}{45}+\frac{90}{45}-\frac{18}{45}\\=\frac{-40+90-18}{45}\\=\frac{32}{45}\)
9. \(-\left(\frac{-4}{-9}\right) +\left(\frac{9}{4}\right) -\left(\frac{-7}{-8}\right)\\= \frac{-4}{9}+ \frac{9}{4}-\frac{7}{8}\\=\frac{-32}{72}+\frac{162}{72}-\frac{63}{72}\\=\frac{-32+162-63}{72}\\=\frac{67}{72}\)
10. \(-\left(\frac{2}{-5}\right) -\left(\frac{3}{4}\right) +\left(\frac{5}{-2}\right)\\= \frac{2}{5}- \frac{3}{4}-\frac{5}{2}\\=\frac{8}{20}-\frac{15}{20}-\frac{50}{20}\\=\frac{8-15-50}{20}\\=\frac{-57}{20}\)
11. \(-\left(\frac{8}{-5}\right) -\left(\frac{-6}{2}\right) +\left(\frac{5}{4}\right)\\= \frac{8}{5}+ \frac{6}{2}+\frac{5}{4}\\=\frac{8}{5}+\frac{3}{1}+\frac{5}{4}\\=\frac{32}{20}+\frac{60}{20}+\frac{25}{20}\\=\frac{32+60+25}{20}\\=\frac{117}{20}\)
12. \(-\left(\frac{2}{-3}\right) +\left(\frac{-8}{2}\right) +\left(\frac{-11}{-4}\right)\\= \frac{2}{3}- \frac{8}{2}+\frac{11}{4}\\=\frac{2}{3}-\frac{4}{1}+\frac{11}{4}\\=\frac{8}{12}-\frac{48}{12}+\frac{33}{12}\\=\frac{8-48+33}{12}\\=\frac{-7}{12}\)