Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{4}\right) -\left(\frac{2}{-2}\right) -\left(\frac{-11}{8}\right)\\= \frac{5}{4}+ \frac{2}{2}+\frac{11}{8}\\=\frac{5}{4}+\frac{1}{1}+\frac{11}{8}\\=\frac{10}{8}+\frac{8}{8}+\frac{11}{8}\\=\frac{10+8+11}{8}\\=\frac{29}{8}\)
2. \(+\left(\frac{4}{-5}\right) +\left(\frac{7}{6}\right) -\left(\frac{5}{10}\right)\\= \frac{-4}{5}+ \frac{7}{6}-\frac{5}{10}\\=\frac{-4}{5}+\frac{7}{6}-\frac{1}{2}\\=\frac{-24}{30}+\frac{35}{30}-\frac{15}{30}\\=\frac{-24+35-15}{30}\\=\frac{-4}{30}\\=\frac{-2}{15}\)
3. \(-\left(\frac{7}{-9}\right) -\left(\frac{-4}{-9}\right) -\left(\frac{-11}{-3}\right)\\= \frac{7}{9}- \frac{4}{9}-\frac{11}{3}\\=\frac{7-4-11}{9}\\=\frac{-8}{9}\)
4. \(+\left(\frac{-3}{-2}\right) +\left(\frac{9}{-2}\right) -\left(\frac{-10}{-7}\right)\\= \frac{3}{2}- \frac{9}{2}-\frac{10}{7}\\=\frac{21}{14}-\frac{63}{14}-\frac{20}{14}\\=\frac{21-63-20}{14}\\=\frac{-62}{14}\\=\frac{-31}{7}\)
5. \(-\left(\frac{-2}{-9}\right) -\left(\frac{9}{6}\right) -\left(\frac{-10}{-4}\right)\\= \frac{-2}{9}- \frac{9}{6}-\frac{10}{4}\\=\frac{-2}{9}-\frac{3}{2}-\frac{5}{2}\\=\frac{-4}{18}-\frac{27}{18}-\frac{45}{18}\\=\frac{-4-27-45}{18}\\=\frac{-76}{18}\\=\frac{-38}{9}\)
6. \(+\left(\frac{-4}{7}\right) -\left(\frac{6}{10}\right) +\left(\frac{3}{3}\right)\\= \frac{-4}{7}- \frac{6}{10}+\frac{3}{3}\\=\frac{-4}{7}-\frac{3}{5}+\frac{1}{1}\\=\frac{-20}{35}-\frac{21}{35}+\frac{35}{35}\\=\frac{-20-21+35}{35}\\=\frac{-6}{35}\)
7. \(+\left(\frac{-5}{-4}\right) +\left(\frac{-6}{-8}\right) +\left(\frac{4}{4}\right)\\= \frac{5}{4}+ \frac{6}{8}+\frac{4}{4}\\=\frac{5}{4}+\frac{3}{4}+\frac{1}{1}\\=\frac{5+3+1}{4}\\=\frac{9}{4}\)
8. \(-\left(\frac{6}{5}\right) +\left(\frac{9}{-6}\right) +\left(\frac{3}{-9}\right)\\= \frac{-6}{5}- \frac{9}{6}-\frac{3}{9}\\=\frac{-6}{5}-\frac{3}{2}-\frac{1}{3}\\=\frac{-36}{30}-\frac{45}{30}-\frac{10}{30}\\=\frac{-36-45-10}{30}\\=\frac{-91}{30}\)
9. \(-\left(\frac{-7}{8}\right) +\left(\frac{2}{-10}\right) +\left(\frac{-10}{10}\right)\\= \frac{7}{8}- \frac{2}{10}-\frac{10}{10}\\=\frac{7}{8}-\frac{1}{5}-\frac{1}{1}\\=\frac{35}{40}-\frac{8}{40}-\frac{40}{40}\\=\frac{35-8-40}{40}\\=\frac{-13}{40}\)
10. \(-\left(\frac{-3}{-2}\right) -\left(\frac{-8}{-7}\right) -\left(\frac{-10}{-4}\right)\\= \frac{-3}{2}- \frac{8}{7}-\frac{10}{4}\\=\frac{-3}{2}-\frac{8}{7}-\frac{5}{2}\\=\frac{-21}{14}-\frac{16}{14}-\frac{35}{14}\\=\frac{-21-16-35}{14}\\=\frac{-72}{14}\\=\frac{-36}{7}\)
11. \(+\left(\frac{-3}{-2}\right) -\left(\frac{-4}{-5}\right) +\left(\frac{5}{2}\right)\\= \frac{3}{2}- \frac{4}{5}+\frac{5}{2}\\=\frac{15}{10}-\frac{8}{10}+\frac{25}{10}\\=\frac{15-8+25}{10}\\=\frac{32}{10}\\=\frac{16}{5}\)
12. \(+\left(\frac{-3}{8}\right) -\left(\frac{-6}{3}\right) -\left(\frac{12}{5}\right)\\= \frac{-3}{8}+ \frac{6}{3}-\frac{12}{5}\\=\frac{-3}{8}+\frac{2}{1}-\frac{12}{5}\\=\frac{-15}{40}+\frac{80}{40}-\frac{96}{40}\\=\frac{-15+80-96}{40}\\=\frac{-31}{40}\)