Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-8}{3}\right) +\left(\frac{-4}{-3}\right) -\left(\frac{-8}{-8}\right)\\= \frac{8}{3}+ \frac{4}{3}-\frac{8}{8}\\=\frac{8}{3}+\frac{4}{3}-\frac{1}{1}\\=\frac{8+4-1}{3}\\=\frac{11}{3}\)
2. \(-\left(\frac{5}{8}\right) -\left(\frac{-8}{6}\right) -\left(\frac{-4}{-11}\right)\\= \frac{-5}{8}+ \frac{8}{6}-\frac{4}{11}\\=\frac{-5}{8}+\frac{4}{3}-\frac{4}{11}\\=\frac{-165}{264}+\frac{352}{264}-\frac{96}{264}\\=\frac{-165+352-96}{264}\\=\frac{91}{264}\)
3. \(-\left(\frac{5}{2}\right) +\left(\frac{-6}{10}\right) +\left(\frac{-11}{-10}\right)\\= \frac{-5}{2}- \frac{6}{10}+\frac{11}{10}\\=\frac{-5}{2}-\frac{3}{5}+\frac{11}{10}\\=\frac{-25}{10}-\frac{6}{10}+\frac{11}{10}\\=\frac{-25-6+11}{10}\\=\frac{-20}{10}\\=\frac{-2}{1}\)
4. \(-\left(\frac{-3}{-8}\right) -\left(\frac{-10}{-10}\right) +\left(\frac{10}{-9}\right)\\= \frac{-3}{8}- \frac{10}{10}-\frac{10}{9}\\=\frac{-3}{8}-\frac{1}{1}-\frac{10}{9}\\=\frac{-27}{72}-\frac{72}{72}-\frac{80}{72}\\=\frac{-27-72-80}{72}\\=\frac{-179}{72}\)
5. \(-\left(\frac{2}{-3}\right) -\left(\frac{-4}{4}\right) -\left(\frac{-3}{4}\right)\\= \frac{2}{3}+ \frac{4}{4}+\frac{3}{4}\\=\frac{2}{3}+\frac{1}{1}+\frac{3}{4}\\=\frac{8}{12}+\frac{12}{12}+\frac{9}{12}\\=\frac{8+12+9}{12}\\=\frac{29}{12}\)
6. \(+\left(\frac{4}{-7}\right) -\left(\frac{-6}{6}\right) +\left(\frac{-10}{5}\right)\\= \frac{-4}{7}+ \frac{6}{6}-\frac{10}{5}\\=\frac{-4}{7}+\frac{1}{1}-\frac{2}{1}\\=\frac{-4+1-2}{7}\\=\frac{-5}{7}\)
7. \(-\left(\frac{6}{-5}\right) -\left(\frac{3}{9}\right) -\left(\frac{-6}{11}\right)\\= \frac{6}{5}- \frac{3}{9}+\frac{6}{11}\\=\frac{6}{5}-\frac{1}{3}+\frac{6}{11}\\=\frac{198}{165}-\frac{55}{165}+\frac{90}{165}\\=\frac{198-55+90}{165}\\=\frac{233}{165}\)
8. \(+\left(\frac{2}{-5}\right) -\left(\frac{-4}{-6}\right) +\left(\frac{-4}{2}\right)\\= \frac{-2}{5}- \frac{4}{6}-\frac{4}{2}\\=\frac{-2}{5}-\frac{2}{3}-\frac{2}{1}\\=\frac{-6}{15}-\frac{10}{15}-\frac{30}{15}\\=\frac{-6-10-30}{15}\\=\frac{-46}{15}\)
9. \(-\left(\frac{-3}{2}\right) -\left(\frac{10}{-5}\right) +\left(\frac{2}{-8}\right)\\= \frac{3}{2}+ \frac{10}{5}-\frac{2}{8}\\=\frac{3}{2}+\frac{2}{1}-\frac{1}{4}\\=\frac{6}{4}+\frac{8}{4}-\frac{1}{4}\\=\frac{6+8-1}{4}\\=\frac{13}{4}\)
10. \(+\left(\frac{5}{-2}\right) +\left(\frac{2}{-6}\right) -\left(\frac{8}{-9}\right)\\= \frac{-5}{2}- \frac{2}{6}+\frac{8}{9}\\=\frac{-5}{2}-\frac{1}{3}+\frac{8}{9}\\=\frac{-45}{18}-\frac{6}{18}+\frac{16}{18}\\=\frac{-45-6+16}{18}\\=\frac{-35}{18}\)
11. \(+\left(\frac{-6}{-7}\right) -\left(\frac{4}{-2}\right) +\left(\frac{10}{-12}\right)\\= \frac{6}{7}+ \frac{4}{2}-\frac{10}{12}\\=\frac{6}{7}+\frac{2}{1}-\frac{5}{6}\\=\frac{36}{42}+\frac{84}{42}-\frac{35}{42}\\=\frac{36+84-35}{42}\\=\frac{85}{42}\)
12. \(-\left(\frac{-7}{2}\right) -\left(\frac{6}{-5}\right) +\left(\frac{-8}{11}\right)\\= \frac{7}{2}+ \frac{6}{5}-\frac{8}{11}\\=\frac{385}{110}+\frac{132}{110}-\frac{80}{110}\\=\frac{385+132-80}{110}\\=\frac{437}{110}\)