Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{-3}\right) -\left(\frac{6}{3}\right) -\left(\frac{-6}{2}\right)\\= \frac{2}{3}- \frac{6}{3}+\frac{6}{2}\\=\frac{2}{3}-\frac{2}{1}+\frac{3}{1}\\=\frac{2-2+3}{3}\\=\frac{3}{3}\\=\frac{1}{1}\)
2. \(-\left(\frac{3}{7}\right) +\left(\frac{3}{6}\right) +\left(\frac{4}{-7}\right)\\= \frac{-3}{7}+ \frac{3}{6}-\frac{4}{7}\\=\frac{-3}{7}+\frac{1}{2}-\frac{4}{7}\\=\frac{-6}{14}+\frac{7}{14}-\frac{8}{14}\\=\frac{-6+7-8}{14}\\=\frac{-7}{14}\\=\frac{-1}{2}\)
3. \(-\left(\frac{3}{4}\right) +\left(\frac{10}{-5}\right) -\left(\frac{-4}{-10}\right)\\= \frac{-3}{4}- \frac{10}{5}-\frac{4}{10}\\=\frac{-3}{4}-\frac{2}{1}-\frac{2}{5}\\=\frac{-15}{20}-\frac{40}{20}-\frac{8}{20}\\=\frac{-15-40-8}{20}\\=\frac{-63}{20}\)
4. \(-\left(\frac{-3}{-2}\right) +\left(\frac{8}{8}\right) -\left(\frac{4}{11}\right)\\= \frac{-3}{2}+ \frac{8}{8}-\frac{4}{11}\\=\frac{-3}{2}+\frac{1}{1}-\frac{4}{11}\\=\frac{-33}{22}+\frac{22}{22}-\frac{8}{22}\\=\frac{-33+22-8}{22}\\=\frac{-19}{22}\)
5. \(-\left(\frac{-10}{9}\right) -\left(\frac{9}{-3}\right) +\left(\frac{7}{11}\right)\\= \frac{10}{9}+ \frac{9}{3}+\frac{7}{11}\\=\frac{10}{9}+\frac{3}{1}+\frac{7}{11}\\=\frac{110}{99}+\frac{297}{99}+\frac{63}{99}\\=\frac{110+297+63}{99}\\=\frac{470}{99}\)
6. \(+\left(\frac{6}{5}\right) -\left(\frac{4}{8}\right) +\left(\frac{-2}{2}\right)\\= \frac{6}{5}- \frac{4}{8}-\frac{2}{2}\\=\frac{6}{5}-\frac{1}{2}-\frac{1}{1}\\=\frac{12}{10}-\frac{5}{10}-\frac{10}{10}\\=\frac{12-5-10}{10}\\=\frac{-3}{10}\)
7. \(-\left(\frac{5}{2}\right) -\left(\frac{-5}{7}\right) -\left(\frac{2}{-2}\right)\\= \frac{-5}{2}+ \frac{5}{7}+\frac{2}{2}\\=\frac{-5}{2}+\frac{5}{7}+\frac{1}{1}\\=\frac{-35}{14}+\frac{10}{14}+\frac{14}{14}\\=\frac{-35+10+14}{14}\\=\frac{-11}{14}\)
8. \(+\left(\frac{6}{-5}\right) +\left(\frac{-7}{7}\right) +\left(\frac{-3}{9}\right)\\= \frac{-6}{5}- \frac{7}{7}-\frac{3}{9}\\=\frac{-6}{5}-\frac{1}{1}-\frac{1}{3}\\=\frac{-18}{15}-\frac{15}{15}-\frac{5}{15}\\=\frac{-18-15-5}{15}\\=\frac{-38}{15}\)
9. \(-\left(\frac{-5}{9}\right) +\left(\frac{5}{2}\right) -\left(\frac{4}{8}\right)\\= \frac{5}{9}+ \frac{5}{2}-\frac{4}{8}\\=\frac{5}{9}+\frac{5}{2}-\frac{1}{2}\\=\frac{10}{18}+\frac{45}{18}-\frac{9}{18}\\=\frac{10+45-9}{18}\\=\frac{46}{18}\\=\frac{23}{9}\)
10. \(-\left(\frac{9}{2}\right) +\left(\frac{-2}{10}\right) +\left(\frac{-11}{-12}\right)\\= \frac{-9}{2}- \frac{2}{10}+\frac{11}{12}\\=\frac{-9}{2}-\frac{1}{5}+\frac{11}{12}\\=\frac{-270}{60}-\frac{12}{60}+\frac{55}{60}\\=\frac{-270-12+55}{60}\\=\frac{-227}{60}\)
11. \(-\left(\frac{5}{8}\right) +\left(\frac{-10}{-6}\right) +\left(\frac{11}{-5}\right)\\= \frac{-5}{8}+ \frac{10}{6}-\frac{11}{5}\\=\frac{-5}{8}+\frac{5}{3}-\frac{11}{5}\\=\frac{-75}{120}+\frac{200}{120}-\frac{264}{120}\\=\frac{-75+200-264}{120}\\=\frac{-139}{120}\)
12. \(-\left(\frac{-9}{-8}\right) -\left(\frac{7}{2}\right) -\left(\frac{-12}{-11}\right)\\= \frac{-9}{8}- \frac{7}{2}-\frac{12}{11}\\=\frac{-99}{88}-\frac{308}{88}-\frac{96}{88}\\=\frac{-99-308-96}{88}\\=\frac{-503}{88}\)