Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{8}{-5}\right) -\left(\frac{-2}{-6}\right) -\left(\frac{11}{3}\right)\\= \frac{-8}{5}- \frac{2}{6}-\frac{11}{3}\\=\frac{-8}{5}-\frac{1}{3}-\frac{11}{3}\\=\frac{-24}{15}-\frac{5}{15}-\frac{55}{15}\\=\frac{-24-5-55}{15}\\=\frac{-84}{15}\\=\frac{-28}{5}\)
2. \(+\left(\frac{-3}{7}\right) +\left(\frac{-4}{-2}\right) -\left(\frac{-2}{2}\right)\\= \frac{-3}{7}+ \frac{4}{2}+\frac{2}{2}\\=\frac{-3}{7}+\frac{2}{1}+\frac{1}{1}\\=\frac{-3+2+1}{7}\\=\frac{0}{7}\\=\frac{0}{1}\)
3. \(+\left(\frac{5}{8}\right) -\left(\frac{4}{6}\right) -\left(\frac{-2}{-7}\right)\\= \frac{5}{8}- \frac{4}{6}-\frac{2}{7}\\=\frac{5}{8}-\frac{2}{3}-\frac{2}{7}\\=\frac{105}{168}-\frac{112}{168}-\frac{48}{168}\\=\frac{105-112-48}{168}\\=\frac{-55}{168}\)
4. \(-\left(\frac{-8}{-3}\right) +\left(\frac{6}{-2}\right) +\left(\frac{2}{-11}\right)\\= \frac{-8}{3}- \frac{6}{2}-\frac{2}{11}\\=\frac{-8}{3}-\frac{3}{1}-\frac{2}{11}\\=\frac{-88}{33}-\frac{99}{33}-\frac{6}{33}\\=\frac{-88-99-6}{33}\\=\frac{-193}{33}\)
5. \(-\left(\frac{10}{7}\right) -\left(\frac{8}{-8}\right) -\left(\frac{8}{10}\right)\\= \frac{-10}{7}+ \frac{8}{8}-\frac{8}{10}\\=\frac{-10}{7}+\frac{1}{1}-\frac{4}{5}\\=\frac{-50}{35}+\frac{35}{35}-\frac{28}{35}\\=\frac{-50+35-28}{35}\\=\frac{-43}{35}\)
6. \(-\left(\frac{-7}{-4}\right) -\left(\frac{-8}{-3}\right) +\left(\frac{2}{-7}\right)\\= \frac{-7}{4}- \frac{8}{3}-\frac{2}{7}\\=\frac{-147}{84}-\frac{224}{84}-\frac{24}{84}\\=\frac{-147-224-24}{84}\\=\frac{-395}{84}\)
7. \(+\left(\frac{9}{4}\right) +\left(\frac{-3}{-4}\right) +\left(\frac{10}{12}\right)\\= \frac{9}{4}+ \frac{3}{4}+\frac{10}{12}\\=\frac{9}{4}+\frac{3}{4}+\frac{5}{6}\\=\frac{27}{12}+\frac{9}{12}+\frac{10}{12}\\=\frac{27+9+10}{12}\\=\frac{46}{12}\\=\frac{23}{6}\)
8. \(-\left(\frac{-9}{-5}\right) -\left(\frac{-3}{4}\right) +\left(\frac{-6}{6}\right)\\= \frac{-9}{5}+ \frac{3}{4}-\frac{6}{6}\\=\frac{-9}{5}+\frac{3}{4}-\frac{1}{1}\\=\frac{-36}{20}+\frac{15}{20}-\frac{20}{20}\\=\frac{-36+15-20}{20}\\=\frac{-41}{20}\)
9. \(+\left(\frac{-7}{4}\right) +\left(\frac{-3}{4}\right) -\left(\frac{8}{-9}\right)\\= \frac{-7}{4}- \frac{3}{4}+\frac{8}{9}\\=\frac{-63}{36}-\frac{27}{36}+\frac{32}{36}\\=\frac{-63-27+32}{36}\\=\frac{-58}{36}\\=\frac{-29}{18}\)
10. \(-\left(\frac{-5}{6}\right) -\left(\frac{5}{8}\right) +\left(\frac{-11}{7}\right)\\= \frac{5}{6}- \frac{5}{8}-\frac{11}{7}\\=\frac{140}{168}-\frac{105}{168}-\frac{264}{168}\\=\frac{140-105-264}{168}\\=\frac{-229}{168}\)
11. \(-\left(\frac{6}{5}\right) -\left(\frac{-9}{3}\right) -\left(\frac{-8}{12}\right)\\= \frac{-6}{5}+ \frac{9}{3}+\frac{8}{12}\\=\frac{-6}{5}+\frac{3}{1}+\frac{2}{3}\\=\frac{-18}{15}+\frac{45}{15}+\frac{10}{15}\\=\frac{-18+45+10}{15}\\=\frac{37}{15}\)
12. \(-\left(\frac{5}{-2}\right) -\left(\frac{9}{7}\right) +\left(\frac{-7}{11}\right)\\= \frac{5}{2}- \frac{9}{7}-\frac{7}{11}\\=\frac{385}{154}-\frac{198}{154}-\frac{98}{154}\\=\frac{385-198-98}{154}\\=\frac{89}{154}\)