Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{-5}\right) -\left(\frac{5}{-9}\right) -\left(\frac{2}{10}\right)\\= \frac{4}{5}+ \frac{5}{9}-\frac{2}{10}\\=\frac{4}{5}+\frac{5}{9}-\frac{1}{5}\\=\frac{36}{45}+\frac{25}{45}-\frac{9}{45}\\=\frac{36+25-9}{45}\\=\frac{52}{45}\)
2. \(+\left(\frac{10}{7}\right) -\left(\frac{2}{5}\right) +\left(\frac{-2}{5}\right)\\= \frac{10}{7}- \frac{2}{5}-\frac{2}{5}\\=\frac{50}{35}-\frac{14}{35}-\frac{14}{35}\\=\frac{50-14-14}{35}\\=\frac{22}{35}\)
3. \(-\left(\frac{5}{7}\right) -\left(\frac{-6}{5}\right) +\left(\frac{-8}{-8}\right)\\= \frac{-5}{7}+ \frac{6}{5}+\frac{8}{8}\\=\frac{-5}{7}+\frac{6}{5}+\frac{1}{1}\\=\frac{-25}{35}+\frac{42}{35}+\frac{35}{35}\\=\frac{-25+42+35}{35}\\=\frac{52}{35}\)
4. \(+\left(\frac{-5}{-2}\right) -\left(\frac{-9}{-9}\right) -\left(\frac{11}{-2}\right)\\= \frac{5}{2}- \frac{9}{9}+\frac{11}{2}\\=\frac{5}{2}-\frac{1}{1}+\frac{11}{2}\\=\frac{5-1+11}{2}\\=\frac{15}{2}\)
5. \(-\left(\frac{-4}{-9}\right) -\left(\frac{-6}{6}\right) -\left(\frac{8}{-12}\right)\\= \frac{-4}{9}+ \frac{6}{6}+\frac{8}{12}\\=\frac{-4}{9}+\frac{1}{1}+\frac{2}{3}\\=\frac{-4+1+2}{9}\\=\frac{-1}{9}\)
6. \(+\left(\frac{8}{-7}\right) +\left(\frac{4}{-8}\right) -\left(\frac{3}{8}\right)\\= \frac{-8}{7}- \frac{4}{8}-\frac{3}{8}\\=\frac{-8}{7}-\frac{1}{2}-\frac{3}{8}\\=\frac{-64}{56}-\frac{28}{56}-\frac{21}{56}\\=\frac{-64-28-21}{56}\\=\frac{-113}{56}\)
7. \(+\left(\frac{-7}{9}\right) -\left(\frac{-9}{-7}\right) -\left(\frac{-5}{-4}\right)\\= \frac{-7}{9}- \frac{9}{7}-\frac{5}{4}\\=\frac{-196}{252}-\frac{324}{252}-\frac{315}{252}\\=\frac{-196-324-315}{252}\\=\frac{-835}{252}\)
8. \(+\left(\frac{6}{5}\right) -\left(\frac{6}{-6}\right) +\left(\frac{5}{12}\right)\\= \frac{6}{5}+ \frac{6}{6}+\frac{5}{12}\\=\frac{6}{5}+\frac{1}{1}+\frac{5}{12}\\=\frac{72}{60}+\frac{60}{60}+\frac{25}{60}\\=\frac{72+60+25}{60}\\=\frac{157}{60}\)
9. \(-\left(\frac{10}{-3}\right) -\left(\frac{-6}{-3}\right) -\left(\frac{7}{6}\right)\\= \frac{10}{3}- \frac{6}{3}-\frac{7}{6}\\=\frac{10}{3}-\frac{2}{1}-\frac{7}{6}\\=\frac{20}{6}-\frac{12}{6}-\frac{7}{6}\\=\frac{20-12-7}{6}\\=\frac{1}{6}\)
10. \(-\left(\frac{-8}{9}\right) -\left(\frac{9}{6}\right) +\left(\frac{4}{11}\right)\\= \frac{8}{9}- \frac{9}{6}+\frac{4}{11}\\=\frac{8}{9}-\frac{3}{2}+\frac{4}{11}\\=\frac{176}{198}-\frac{297}{198}+\frac{72}{198}\\=\frac{176-297+72}{198}\\=\frac{-49}{198}\)
11. \(+\left(\frac{-10}{7}\right) +\left(\frac{9}{7}\right) +\left(\frac{8}{11}\right)\\= \frac{-10}{7}+ \frac{9}{7}+\frac{8}{11}\\=\frac{-110}{77}+\frac{99}{77}+\frac{56}{77}\\=\frac{-110+99+56}{77}\\=\frac{45}{77}\)
12. \(-\left(\frac{3}{-4}\right) +\left(\frac{5}{8}\right) +\left(\frac{-12}{3}\right)\\= \frac{3}{4}+ \frac{5}{8}-\frac{12}{3}\\=\frac{3}{4}+\frac{5}{8}-\frac{4}{1}\\=\frac{6}{8}+\frac{5}{8}-\frac{32}{8}\\=\frac{6+5-32}{8}\\=\frac{-21}{8}\)