Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{-6}\right) +\left(\frac{-3}{-8}\right) -\left(\frac{-2}{9}\right)\\= \frac{5}{6}+ \frac{3}{8}+\frac{2}{9}\\=\frac{60}{72}+\frac{27}{72}+\frac{16}{72}\\=\frac{60+27+16}{72}\\=\frac{103}{72}\)
2. \(+\left(\frac{2}{3}\right) +\left(\frac{-9}{-5}\right) +\left(\frac{10}{-2}\right)\\= \frac{2}{3}+ \frac{9}{5}-\frac{10}{2}\\=\frac{2}{3}+\frac{9}{5}-\frac{5}{1}\\=\frac{10}{15}+\frac{27}{15}-\frac{75}{15}\\=\frac{10+27-75}{15}\\=\frac{-38}{15}\)
3. \(-\left(\frac{4}{5}\right) -\left(\frac{10}{4}\right) -\left(\frac{-11}{-10}\right)\\= \frac{-4}{5}- \frac{10}{4}-\frac{11}{10}\\=\frac{-4}{5}-\frac{5}{2}-\frac{11}{10}\\=\frac{-8}{10}-\frac{25}{10}-\frac{11}{10}\\=\frac{-8-25-11}{10}\\=\frac{-44}{10}\\=\frac{-22}{5}\)
4. \(-\left(\frac{2}{9}\right) -\left(\frac{4}{10}\right) -\left(\frac{2}{-5}\right)\\= \frac{-2}{9}- \frac{4}{10}+\frac{2}{5}\\=\frac{-2}{9}-\frac{2}{5}+\frac{2}{5}\\=\frac{-10}{45}-\frac{18}{45}+\frac{18}{45}\\=\frac{-10-18+18}{45}\\=\frac{-10}{45}\\=\frac{-2}{9}\)
5. \(-\left(\frac{-2}{3}\right) +\left(\frac{9}{9}\right) +\left(\frac{12}{2}\right)\\= \frac{2}{3}+ \frac{9}{9}+\frac{12}{2}\\=\frac{2}{3}+\frac{1}{1}+\frac{6}{1}\\=\frac{2+1+6}{3}\\=\frac{9}{3}\\=\frac{3}{1}\)
6. \(+\left(\frac{5}{-6}\right) +\left(\frac{5}{-2}\right) -\left(\frac{9}{-5}\right)\\= \frac{-5}{6}- \frac{5}{2}+\frac{9}{5}\\=\frac{-25}{30}-\frac{75}{30}+\frac{54}{30}\\=\frac{-25-75+54}{30}\\=\frac{-46}{30}\\=\frac{-23}{15}\)
7. \(-\left(\frac{6}{5}\right) +\left(\frac{-6}{-5}\right) +\left(\frac{-11}{2}\right)\\= \frac{-6}{5}+ \frac{6}{5}-\frac{11}{2}\\=\frac{-12}{10}+\frac{12}{10}-\frac{55}{10}\\=\frac{-12+12-55}{10}\\=\frac{-55}{10}\\=\frac{-11}{2}\)
8. \(+\left(\frac{-3}{-2}\right) +\left(\frac{-5}{-3}\right) -\left(\frac{-11}{11}\right)\\= \frac{3}{2}+ \frac{5}{3}+\frac{11}{11}\\=\frac{3}{2}+\frac{5}{3}+\frac{1}{1}\\=\frac{9}{6}+\frac{10}{6}+\frac{6}{6}\\=\frac{9+10+6}{6}\\=\frac{25}{6}\)
9. \(+\left(\frac{-8}{-7}\right) +\left(\frac{-5}{2}\right) +\left(\frac{3}{-9}\right)\\= \frac{8}{7}- \frac{5}{2}-\frac{3}{9}\\=\frac{8}{7}-\frac{5}{2}-\frac{1}{3}\\=\frac{48}{42}-\frac{105}{42}-\frac{14}{42}\\=\frac{48-105-14}{42}\\=\frac{-71}{42}\)
10. \(+\left(\frac{4}{-7}\right) +\left(\frac{2}{7}\right) +\left(\frac{-6}{-7}\right)\\= \frac{-4}{7}+ \frac{2}{7}+\frac{6}{7}\\=\frac{-4+2+6}{7}\\=\frac{4}{7}\)
11. \(+\left(\frac{5}{-4}\right) -\left(\frac{-8}{10}\right) +\left(\frac{7}{-12}\right)\\= \frac{-5}{4}+ \frac{8}{10}-\frac{7}{12}\\=\frac{-5}{4}+\frac{4}{5}-\frac{7}{12}\\=\frac{-75}{60}+\frac{48}{60}-\frac{35}{60}\\=\frac{-75+48-35}{60}\\=\frac{-62}{60}\\=\frac{-31}{30}\)
12. \(-\left(\frac{-8}{-3}\right) +\left(\frac{8}{2}\right) +\left(\frac{-4}{-10}\right)\\= \frac{-8}{3}+ \frac{8}{2}+\frac{4}{10}\\=\frac{-8}{3}+\frac{4}{1}+\frac{2}{5}\\=\frac{-40}{15}+\frac{60}{15}+\frac{6}{15}\\=\frac{-40+60+6}{15}\\=\frac{26}{15}\)