Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{10}{3}\right) +\left(\frac{10}{-8}\right) -\left(\frac{-5}{-8}\right)\\= \frac{10}{3}- \frac{10}{8}-\frac{5}{8}\\=\frac{10}{3}-\frac{5}{4}-\frac{5}{8}\\=\frac{80}{24}-\frac{30}{24}-\frac{15}{24}\\=\frac{80-30-15}{24}\\=\frac{35}{24}\)
2. \(-\left(\frac{8}{-5}\right) -\left(\frac{4}{-5}\right) -\left(\frac{-6}{-3}\right)\\= \frac{8}{5}+ \frac{4}{5}-\frac{6}{3}\\=\frac{8}{5}+\frac{4}{5}-\frac{2}{1}\\=\frac{8+4-2}{5}\\=\frac{10}{5}\\=\frac{2}{1}\)
3. \(-\left(\frac{5}{2}\right) -\left(\frac{4}{-3}\right) +\left(\frac{12}{9}\right)\\= \frac{-5}{2}+ \frac{4}{3}+\frac{12}{9}\\=\frac{-5}{2}+\frac{4}{3}+\frac{4}{3}\\=\frac{-15}{6}+\frac{8}{6}+\frac{8}{6}\\=\frac{-15+8+8}{6}\\=\frac{1}{6}\)
4. \(+\left(\frac{-7}{8}\right) -\left(\frac{-7}{-5}\right) +\left(\frac{5}{11}\right)\\= \frac{-7}{8}- \frac{7}{5}+\frac{5}{11}\\=\frac{-385}{440}-\frac{616}{440}+\frac{200}{440}\\=\frac{-385-616+200}{440}\\=\frac{-801}{440}\)
5. \(+\left(\frac{7}{-8}\right) -\left(\frac{8}{5}\right) +\left(\frac{-12}{11}\right)\\= \frac{-7}{8}- \frac{8}{5}-\frac{12}{11}\\=\frac{-385}{440}-\frac{704}{440}-\frac{480}{440}\\=\frac{-385-704-480}{440}\\=\frac{-1569}{440}\)
6. \(-\left(\frac{-5}{-6}\right) +\left(\frac{-10}{10}\right) +\left(\frac{12}{-10}\right)\\= \frac{-5}{6}- \frac{10}{10}-\frac{12}{10}\\=\frac{-5}{6}-\frac{1}{1}-\frac{6}{5}\\=\frac{-25}{30}-\frac{30}{30}-\frac{36}{30}\\=\frac{-25-30-36}{30}\\=\frac{-91}{30}\)
7. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-6}{-8}\right) +\left(\frac{-6}{-5}\right)\\= \frac{6}{5}+ \frac{6}{8}+\frac{6}{5}\\=\frac{6}{5}+\frac{3}{4}+\frac{6}{5}\\=\frac{24}{20}+\frac{15}{20}+\frac{24}{20}\\=\frac{24+15+24}{20}\\=\frac{63}{20}\)
8. \(+\left(\frac{3}{-7}\right) -\left(\frac{-3}{7}\right) -\left(\frac{-4}{11}\right)\\= \frac{-3}{7}+ \frac{3}{7}+\frac{4}{11}\\=\frac{-33}{77}+\frac{33}{77}+\frac{28}{77}\\=\frac{-33+33+28}{77}\\=\frac{28}{77}\\=\frac{4}{11}\)
9. \(-\left(\frac{-7}{-3}\right) -\left(\frac{8}{-2}\right) -\left(\frac{7}{10}\right)\\= \frac{-7}{3}+ \frac{8}{2}-\frac{7}{10}\\=\frac{-7}{3}+\frac{4}{1}-\frac{7}{10}\\=\frac{-70}{30}+\frac{120}{30}-\frac{21}{30}\\=\frac{-70+120-21}{30}\\=\frac{29}{30}\)
10. \(+\left(\frac{4}{-3}\right) -\left(\frac{3}{-7}\right) +\left(\frac{-10}{4}\right)\\= \frac{-4}{3}+ \frac{3}{7}-\frac{10}{4}\\=\frac{-4}{3}+\frac{3}{7}-\frac{5}{2}\\=\frac{-56}{42}+\frac{18}{42}-\frac{105}{42}\\=\frac{-56+18-105}{42}\\=\frac{-143}{42}\)
11. \(+\left(\frac{5}{-3}\right) +\left(\frac{6}{-2}\right) -\left(\frac{-2}{-6}\right)\\= \frac{-5}{3}- \frac{6}{2}-\frac{2}{6}\\=\frac{-5}{3}-\frac{3}{1}-\frac{1}{3}\\=\frac{-5-3-1}{3}\\=\frac{-9}{3}\\=\frac{-3}{1}\)
12. \(+\left(\frac{10}{9}\right) +\left(\frac{-6}{-10}\right) +\left(\frac{-3}{-5}\right)\\= \frac{10}{9}+ \frac{6}{10}+\frac{3}{5}\\=\frac{10}{9}+\frac{3}{5}+\frac{3}{5}\\=\frac{50}{45}+\frac{27}{45}+\frac{27}{45}\\=\frac{50+27+27}{45}\\=\frac{104}{45}\)