Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{7}\right) +\left(\frac{3}{-7}\right) -\left(\frac{-12}{-3}\right)\\= \frac{-10}{7}- \frac{3}{7}-\frac{12}{3}\\=\frac{-10}{7}-\frac{3}{7}-\frac{4}{1}\\=\frac{-10-3-4}{7}\\=\frac{-17}{7}\)
2. \(-\left(\frac{-7}{-4}\right) +\left(\frac{-8}{7}\right) -\left(\frac{-11}{12}\right)\\= \frac{-7}{4}- \frac{8}{7}+\frac{11}{12}\\=\frac{-147}{84}-\frac{96}{84}+\frac{77}{84}\\=\frac{-147-96+77}{84}\\=\frac{-166}{84}\\=\frac{-83}{42}\)
3. \(-\left(\frac{-5}{9}\right) +\left(\frac{6}{8}\right) +\left(\frac{-5}{-6}\right)\\= \frac{5}{9}+ \frac{6}{8}+\frac{5}{6}\\=\frac{5}{9}+\frac{3}{4}+\frac{5}{6}\\=\frac{20}{36}+\frac{27}{36}+\frac{30}{36}\\=\frac{20+27+30}{36}\\=\frac{77}{36}\)
4. \(+\left(\frac{-4}{-9}\right) +\left(\frac{-6}{-8}\right) +\left(\frac{11}{-9}\right)\\= \frac{4}{9}+ \frac{6}{8}-\frac{11}{9}\\=\frac{4}{9}+\frac{3}{4}-\frac{11}{9}\\=\frac{16}{36}+\frac{27}{36}-\frac{44}{36}\\=\frac{16+27-44}{36}\\=\frac{-1}{36}\)
5. \(-\left(\frac{-9}{-2}\right) +\left(\frac{-4}{-8}\right) +\left(\frac{5}{6}\right)\\= \frac{-9}{2}+ \frac{4}{8}+\frac{5}{6}\\=\frac{-9}{2}+\frac{1}{2}+\frac{5}{6}\\=\frac{-27}{6}+\frac{3}{6}+\frac{5}{6}\\=\frac{-27+3+5}{6}\\=\frac{-19}{6}\)
6. \(+\left(\frac{-5}{-7}\right) +\left(\frac{5}{-3}\right) +\left(\frac{11}{-3}\right)\\= \frac{5}{7}- \frac{5}{3}-\frac{11}{3}\\=\frac{15}{21}-\frac{35}{21}-\frac{77}{21}\\=\frac{15-35-77}{21}\\=\frac{-97}{21}\)
7. \(+\left(\frac{-7}{-8}\right) -\left(\frac{-2}{-4}\right) -\left(\frac{4}{8}\right)\\= \frac{7}{8}- \frac{2}{4}-\frac{4}{8}\\=\frac{7}{8}-\frac{1}{2}-\frac{1}{2}\\=\frac{7-1-1}{8}\\=\frac{5}{8}\)
8. \(-\left(\frac{8}{-3}\right) -\left(\frac{-10}{8}\right) -\left(\frac{6}{2}\right)\\= \frac{8}{3}+ \frac{10}{8}-\frac{6}{2}\\=\frac{8}{3}+\frac{5}{4}-\frac{3}{1}\\=\frac{32}{12}+\frac{15}{12}-\frac{36}{12}\\=\frac{32+15-36}{12}\\=\frac{11}{12}\)
9. \(-\left(\frac{-5}{-6}\right) -\left(\frac{-2}{2}\right) -\left(\frac{4}{-12}\right)\\= \frac{-5}{6}+ \frac{2}{2}+\frac{4}{12}\\=\frac{-5}{6}+\frac{1}{1}+\frac{1}{3}\\=\frac{-5+1+1}{6}\\=\frac{-3}{6}\\=\frac{-1}{2}\)
10. \(+\left(\frac{7}{8}\right) -\left(\frac{-3}{5}\right) +\left(\frac{9}{-3}\right)\\= \frac{7}{8}+ \frac{3}{5}-\frac{9}{3}\\=\frac{7}{8}+\frac{3}{5}-\frac{3}{1}\\=\frac{35}{40}+\frac{24}{40}-\frac{120}{40}\\=\frac{35+24-120}{40}\\=\frac{-61}{40}\)
11. \(+\left(\frac{-8}{-5}\right) -\left(\frac{6}{-8}\right) +\left(\frac{9}{-12}\right)\\= \frac{8}{5}+ \frac{6}{8}-\frac{9}{12}\\=\frac{8}{5}+\frac{3}{4}-\frac{3}{4}\\=\frac{32}{20}+\frac{15}{20}-\frac{15}{20}\\=\frac{32+15-15}{20}\\=\frac{32}{20}\\=\frac{8}{5}\)
12. \(-\left(\frac{6}{5}\right) -\left(\frac{-2}{-7}\right) +\left(\frac{-6}{7}\right)\\= \frac{-6}{5}- \frac{2}{7}-\frac{6}{7}\\=\frac{-42}{35}-\frac{10}{35}-\frac{30}{35}\\=\frac{-42-10-30}{35}\\=\frac{-82}{35}\)