Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{-3}\right) +\left(\frac{6}{6}\right) +\left(\frac{10}{4}\right)\\= \frac{2}{3}+ \frac{6}{6}+\frac{10}{4}\\=\frac{2}{3}+\frac{1}{1}+\frac{5}{2}\\=\frac{4}{6}+\frac{6}{6}+\frac{15}{6}\\=\frac{4+6+15}{6}\\=\frac{25}{6}\)
2. \(+\left(\frac{-4}{-3}\right) -\left(\frac{10}{-7}\right) -\left(\frac{-3}{11}\right)\\= \frac{4}{3}+ \frac{10}{7}+\frac{3}{11}\\=\frac{308}{231}+\frac{330}{231}+\frac{63}{231}\\=\frac{308+330+63}{231}\\=\frac{701}{231}\)
3. \(+\left(\frac{7}{2}\right) -\left(\frac{3}{-4}\right) +\left(\frac{-11}{-2}\right)\\= \frac{7}{2}+ \frac{3}{4}+\frac{11}{2}\\=\frac{14}{4}+\frac{3}{4}+\frac{22}{4}\\=\frac{14+3+22}{4}\\=\frac{39}{4}\)
4. \(+\left(\frac{4}{3}\right) +\left(\frac{-5}{8}\right) -\left(\frac{6}{3}\right)\\= \frac{4}{3}- \frac{5}{8}-\frac{6}{3}\\=\frac{4}{3}-\frac{5}{8}-\frac{2}{1}\\=\frac{32}{24}-\frac{15}{24}-\frac{48}{24}\\=\frac{32-15-48}{24}\\=\frac{-31}{24}\)
5. \(-\left(\frac{5}{8}\right) -\left(\frac{4}{7}\right) -\left(\frac{-5}{11}\right)\\= \frac{-5}{8}- \frac{4}{7}+\frac{5}{11}\\=\frac{-385}{616}-\frac{352}{616}+\frac{280}{616}\\=\frac{-385-352+280}{616}\\=\frac{-457}{616}\)
6. \(-\left(\frac{-2}{9}\right) -\left(\frac{-2}{7}\right) +\left(\frac{2}{-6}\right)\\= \frac{2}{9}+ \frac{2}{7}-\frac{2}{6}\\=\frac{2}{9}+\frac{2}{7}-\frac{1}{3}\\=\frac{14}{63}+\frac{18}{63}-\frac{21}{63}\\=\frac{14+18-21}{63}\\=\frac{11}{63}\)
7. \(-\left(\frac{-5}{6}\right) -\left(\frac{4}{3}\right) +\left(\frac{6}{5}\right)\\= \frac{5}{6}- \frac{4}{3}+\frac{6}{5}\\=\frac{25}{30}-\frac{40}{30}+\frac{36}{30}\\=\frac{25-40+36}{30}\\=\frac{21}{30}\\=\frac{7}{10}\)
8. \(+\left(\frac{9}{-2}\right) +\left(\frac{2}{-3}\right) +\left(\frac{11}{2}\right)\\= \frac{-9}{2}- \frac{2}{3}+\frac{11}{2}\\=\frac{-27}{6}-\frac{4}{6}+\frac{33}{6}\\=\frac{-27-4+33}{6}\\=\frac{2}{6}\\=\frac{1}{3}\)
9. \(-\left(\frac{2}{-3}\right) +\left(\frac{-6}{-8}\right) -\left(\frac{-2}{-9}\right)\\= \frac{2}{3}+ \frac{6}{8}-\frac{2}{9}\\=\frac{2}{3}+\frac{3}{4}-\frac{2}{9}\\=\frac{24}{36}+\frac{27}{36}-\frac{8}{36}\\=\frac{24+27-8}{36}\\=\frac{43}{36}\)
10. \(+\left(\frac{8}{7}\right) +\left(\frac{-6}{-9}\right) +\left(\frac{6}{12}\right)\\= \frac{8}{7}+ \frac{6}{9}+\frac{6}{12}\\=\frac{8}{7}+\frac{2}{3}+\frac{1}{2}\\=\frac{48}{42}+\frac{28}{42}+\frac{21}{42}\\=\frac{48+28+21}{42}\\=\frac{97}{42}\)
11. \(+\left(\frac{-5}{2}\right) -\left(\frac{-3}{8}\right) -\left(\frac{-11}{11}\right)\\= \frac{-5}{2}+ \frac{3}{8}+\frac{11}{11}\\=\frac{-5}{2}+\frac{3}{8}+\frac{1}{1}\\=\frac{-20}{8}+\frac{3}{8}+\frac{8}{8}\\=\frac{-20+3+8}{8}\\=\frac{-9}{8}\)
12. \(+\left(\frac{2}{-3}\right) +\left(\frac{-2}{10}\right) -\left(\frac{12}{-6}\right)\\= \frac{-2}{3}- \frac{2}{10}+\frac{12}{6}\\=\frac{-2}{3}-\frac{1}{5}+\frac{2}{1}\\=\frac{-10}{15}-\frac{3}{15}+\frac{30}{15}\\=\frac{-10-3+30}{15}\\=\frac{17}{15}\)