Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{-7}\right) -\left(\frac{3}{-9}\right) -\left(\frac{2}{-11}\right)\\= \frac{8}{7}+ \frac{3}{9}+\frac{2}{11}\\=\frac{8}{7}+\frac{1}{3}+\frac{2}{11}\\=\frac{264}{231}+\frac{77}{231}+\frac{42}{231}\\=\frac{264+77+42}{231}\\=\frac{383}{231}\)
2. \(+\left(\frac{-6}{-5}\right) -\left(\frac{7}{-8}\right) -\left(\frac{-2}{-8}\right)\\= \frac{6}{5}+ \frac{7}{8}-\frac{2}{8}\\=\frac{6}{5}+\frac{7}{8}-\frac{1}{4}\\=\frac{48}{40}+\frac{35}{40}-\frac{10}{40}\\=\frac{48+35-10}{40}\\=\frac{73}{40}\)
3. \(-\left(\frac{9}{2}\right) -\left(\frac{4}{2}\right) +\left(\frac{8}{-3}\right)\\= \frac{-9}{2}- \frac{4}{2}-\frac{8}{3}\\=\frac{-9}{2}-\frac{2}{1}-\frac{8}{3}\\=\frac{-27}{6}-\frac{12}{6}-\frac{16}{6}\\=\frac{-27-12-16}{6}\\=\frac{-55}{6}\)
4. \(-\left(\frac{-10}{-7}\right) -\left(\frac{4}{6}\right) +\left(\frac{6}{-6}\right)\\= \frac{-10}{7}- \frac{4}{6}-\frac{6}{6}\\=\frac{-10}{7}-\frac{2}{3}-\frac{1}{1}\\=\frac{-30}{21}-\frac{14}{21}-\frac{21}{21}\\=\frac{-30-14-21}{21}\\=\frac{-65}{21}\)
5. \(-\left(\frac{9}{7}\right) -\left(\frac{2}{-2}\right) +\left(\frac{-8}{-2}\right)\\= \frac{-9}{7}+ \frac{2}{2}+\frac{8}{2}\\=\frac{-9}{7}+\frac{1}{1}+\frac{4}{1}\\=\frac{-9+1+4}{7}\\=\frac{-4}{7}\)
6. \(+\left(\frac{-4}{-9}\right) +\left(\frac{9}{-3}\right) -\left(\frac{6}{12}\right)\\= \frac{4}{9}- \frac{9}{3}-\frac{6}{12}\\=\frac{4}{9}-\frac{3}{1}-\frac{1}{2}\\=\frac{8}{18}-\frac{54}{18}-\frac{9}{18}\\=\frac{8-54-9}{18}\\=\frac{-55}{18}\)
7. \(+\left(\frac{-4}{9}\right) -\left(\frac{-7}{4}\right) +\left(\frac{11}{-9}\right)\\= \frac{-4}{9}+ \frac{7}{4}-\frac{11}{9}\\=\frac{-16}{36}+\frac{63}{36}-\frac{44}{36}\\=\frac{-16+63-44}{36}\\=\frac{3}{36}\\=\frac{1}{12}\)
8. \(-\left(\frac{3}{-4}\right) -\left(\frac{8}{-9}\right) +\left(\frac{-7}{-3}\right)\\= \frac{3}{4}+ \frac{8}{9}+\frac{7}{3}\\=\frac{27}{36}+\frac{32}{36}+\frac{84}{36}\\=\frac{27+32+84}{36}\\=\frac{143}{36}\)
9. \(-\left(\frac{-10}{3}\right) -\left(\frac{6}{4}\right) +\left(\frac{7}{-2}\right)\\= \frac{10}{3}- \frac{6}{4}-\frac{7}{2}\\=\frac{10}{3}-\frac{3}{2}-\frac{7}{2}\\=\frac{20}{6}-\frac{9}{6}-\frac{21}{6}\\=\frac{20-9-21}{6}\\=\frac{-10}{6}\\=\frac{-5}{3}\)
10. \(-\left(\frac{4}{-5}\right) -\left(\frac{9}{-4}\right) +\left(\frac{3}{-11}\right)\\= \frac{4}{5}+ \frac{9}{4}-\frac{3}{11}\\=\frac{176}{220}+\frac{495}{220}-\frac{60}{220}\\=\frac{176+495-60}{220}\\=\frac{611}{220}\)
11. \(-\left(\frac{10}{7}\right) -\left(\frac{3}{-5}\right) -\left(\frac{-3}{5}\right)\\= \frac{-10}{7}+ \frac{3}{5}+\frac{3}{5}\\=\frac{-50}{35}+\frac{21}{35}+\frac{21}{35}\\=\frac{-50+21+21}{35}\\=\frac{-8}{35}\)
12. \(+\left(\frac{-6}{5}\right) -\left(\frac{5}{5}\right) -\left(\frac{-8}{-5}\right)\\= \frac{-6}{5}- \frac{5}{5}-\frac{8}{5}\\=\frac{-6}{5}-\frac{1}{1}-\frac{8}{5}\\=\frac{-6-1-8}{5}\\=\frac{-15}{5}\\=\frac{-3}{1}\)