Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{3}\right) -\left(\frac{-7}{-9}\right) +\left(\frac{-7}{-12}\right)\\= \frac{2}{3}- \frac{7}{9}+\frac{7}{12}\\=\frac{24}{36}-\frac{28}{36}+\frac{21}{36}\\=\frac{24-28+21}{36}\\=\frac{17}{36}\)
2. \(-\left(\frac{-8}{-3}\right) +\left(\frac{8}{-9}\right) -\left(\frac{4}{6}\right)\\= \frac{-8}{3}- \frac{8}{9}-\frac{4}{6}\\=\frac{-8}{3}-\frac{8}{9}-\frac{2}{3}\\=\frac{-24}{9}-\frac{8}{9}-\frac{6}{9}\\=\frac{-24-8-6}{9}\\=\frac{-38}{9}\)
3. \(-\left(\frac{10}{-3}\right) -\left(\frac{-10}{-7}\right) +\left(\frac{4}{2}\right)\\= \frac{10}{3}- \frac{10}{7}+\frac{4}{2}\\=\frac{10}{3}-\frac{10}{7}+\frac{2}{1}\\=\frac{70}{21}-\frac{30}{21}+\frac{42}{21}\\=\frac{70-30+42}{21}\\=\frac{82}{21}\)
4. \(-\left(\frac{-8}{-7}\right) -\left(\frac{4}{-3}\right) +\left(\frac{3}{6}\right)\\= \frac{-8}{7}+ \frac{4}{3}+\frac{3}{6}\\=\frac{-8}{7}+\frac{4}{3}+\frac{1}{2}\\=\frac{-48}{42}+\frac{56}{42}+\frac{21}{42}\\=\frac{-48+56+21}{42}\\=\frac{29}{42}\)
5. \(-\left(\frac{-8}{-5}\right) +\left(\frac{-6}{8}\right) -\left(\frac{-4}{5}\right)\\= \frac{-8}{5}- \frac{6}{8}+\frac{4}{5}\\=\frac{-8}{5}-\frac{3}{4}+\frac{4}{5}\\=\frac{-32}{20}-\frac{15}{20}+\frac{16}{20}\\=\frac{-32-15+16}{20}\\=\frac{-31}{20}\)
6. \(-\left(\frac{4}{7}\right) +\left(\frac{-5}{-5}\right) -\left(\frac{3}{-9}\right)\\= \frac{-4}{7}+ \frac{5}{5}+\frac{3}{9}\\=\frac{-4}{7}+\frac{1}{1}+\frac{1}{3}\\=\frac{-12}{21}+\frac{21}{21}+\frac{7}{21}\\=\frac{-12+21+7}{21}\\=\frac{16}{21}\)
7. \(-\left(\frac{-3}{-2}\right) -\left(\frac{2}{-4}\right) -\left(\frac{3}{7}\right)\\= \frac{-3}{2}+ \frac{2}{4}-\frac{3}{7}\\=\frac{-3}{2}+\frac{1}{2}-\frac{3}{7}\\=\frac{-21}{14}+\frac{7}{14}-\frac{6}{14}\\=\frac{-21+7-6}{14}\\=\frac{-20}{14}\\=\frac{-10}{7}\)
8. \(-\left(\frac{7}{-6}\right) -\left(\frac{6}{-10}\right) +\left(\frac{-9}{10}\right)\\= \frac{7}{6}+ \frac{6}{10}-\frac{9}{10}\\=\frac{7}{6}+\frac{3}{5}-\frac{9}{10}\\=\frac{35}{30}+\frac{18}{30}-\frac{27}{30}\\=\frac{35+18-27}{30}\\=\frac{26}{30}\\=\frac{13}{15}\)
9. \(-\left(\frac{-5}{6}\right) +\left(\frac{-6}{-6}\right) +\left(\frac{-2}{-8}\right)\\= \frac{5}{6}+ \frac{6}{6}+\frac{2}{8}\\=\frac{5}{6}+\frac{1}{1}+\frac{1}{4}\\=\frac{10}{12}+\frac{12}{12}+\frac{3}{12}\\=\frac{10+12+3}{12}\\=\frac{25}{12}\)
10. \(+\left(\frac{2}{3}\right) -\left(\frac{-8}{-8}\right) -\left(\frac{4}{10}\right)\\= \frac{2}{3}- \frac{8}{8}-\frac{4}{10}\\=\frac{2}{3}-\frac{1}{1}-\frac{2}{5}\\=\frac{10}{15}-\frac{15}{15}-\frac{6}{15}\\=\frac{10-15-6}{15}\\=\frac{-11}{15}\)
11. \(-\left(\frac{-4}{5}\right) -\left(\frac{6}{6}\right) +\left(\frac{-12}{9}\right)\\= \frac{4}{5}- \frac{6}{6}-\frac{12}{9}\\=\frac{4}{5}-\frac{1}{1}-\frac{4}{3}\\=\frac{12}{15}-\frac{15}{15}-\frac{20}{15}\\=\frac{12-15-20}{15}\\=\frac{-23}{15}\)
12. \(+\left(\frac{2}{5}\right) -\left(\frac{-9}{5}\right) -\left(\frac{-4}{4}\right)\\= \frac{2}{5}+ \frac{9}{5}+\frac{4}{4}\\=\frac{2}{5}+\frac{9}{5}+\frac{1}{1}\\=\frac{2+9+1}{5}\\=\frac{12}{5}\)