Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{-5}\right) +\left(\frac{8}{-9}\right) +\left(\frac{-2}{-4}\right)\\= \frac{-6}{5}- \frac{8}{9}+\frac{2}{4}\\=\frac{-6}{5}-\frac{8}{9}+\frac{1}{2}\\=\frac{-108}{90}-\frac{80}{90}+\frac{45}{90}\\=\frac{-108-80+45}{90}\\=\frac{-143}{90}\)
2. \(-\left(\frac{3}{2}\right) -\left(\frac{-4}{-2}\right) +\left(\frac{9}{-10}\right)\\= \frac{-3}{2}- \frac{4}{2}-\frac{9}{10}\\=\frac{-3}{2}-\frac{2}{1}-\frac{9}{10}\\=\frac{-15}{10}-\frac{20}{10}-\frac{9}{10}\\=\frac{-15-20-9}{10}\\=\frac{-44}{10}\\=\frac{-22}{5}\)
3. \(-\left(\frac{-8}{3}\right) +\left(\frac{-5}{-7}\right) -\left(\frac{4}{11}\right)\\= \frac{8}{3}+ \frac{5}{7}-\frac{4}{11}\\=\frac{616}{231}+\frac{165}{231}-\frac{84}{231}\\=\frac{616+165-84}{231}\\=\frac{697}{231}\)
4. \(+\left(\frac{-8}{-9}\right) -\left(\frac{-9}{6}\right) -\left(\frac{7}{3}\right)\\= \frac{8}{9}+ \frac{9}{6}-\frac{7}{3}\\=\frac{8}{9}+\frac{3}{2}-\frac{7}{3}\\=\frac{16}{18}+\frac{27}{18}-\frac{42}{18}\\=\frac{16+27-42}{18}\\=\frac{1}{18}\)
5. \(+\left(\frac{-6}{-5}\right) -\left(\frac{8}{-2}\right) -\left(\frac{-8}{-4}\right)\\= \frac{6}{5}+ \frac{8}{2}-\frac{8}{4}\\=\frac{6}{5}+\frac{4}{1}-\frac{2}{1}\\=\frac{6+4-2}{5}\\=\frac{8}{5}\)
6. \(-\left(\frac{-4}{3}\right) -\left(\frac{8}{5}\right) -\left(\frac{-10}{-12}\right)\\= \frac{4}{3}- \frac{8}{5}-\frac{10}{12}\\=\frac{4}{3}-\frac{8}{5}-\frac{5}{6}\\=\frac{40}{30}-\frac{48}{30}-\frac{25}{30}\\=\frac{40-48-25}{30}\\=\frac{-33}{30}\\=\frac{-11}{10}\)
7. \(-\left(\frac{8}{3}\right) +\left(\frac{9}{7}\right) -\left(\frac{12}{-4}\right)\\= \frac{-8}{3}+ \frac{9}{7}+\frac{12}{4}\\=\frac{-8}{3}+\frac{9}{7}+\frac{3}{1}\\=\frac{-56}{21}+\frac{27}{21}+\frac{63}{21}\\=\frac{-56+27+63}{21}\\=\frac{34}{21}\)
8. \(+\left(\frac{-10}{-3}\right) -\left(\frac{5}{-6}\right) +\left(\frac{7}{-4}\right)\\= \frac{10}{3}+ \frac{5}{6}-\frac{7}{4}\\=\frac{40}{12}+\frac{10}{12}-\frac{21}{12}\\=\frac{40+10-21}{12}\\=\frac{29}{12}\)
9. \(+\left(\frac{7}{6}\right) +\left(\frac{3}{3}\right) +\left(\frac{-6}{-12}\right)\\= \frac{7}{6}+ \frac{3}{3}+\frac{6}{12}\\=\frac{7}{6}+\frac{1}{1}+\frac{1}{2}\\=\frac{7+1+1}{6}\\=\frac{9}{6}\\=\frac{3}{2}\)
10. \(-\left(\frac{-2}{-5}\right) -\left(\frac{3}{5}\right) -\left(\frac{2}{5}\right)\\= \frac{-2}{5}- \frac{3}{5}-\frac{2}{5}\\=\frac{-2-3-2}{5}\\=\frac{-7}{5}\)
11. \(-\left(\frac{-9}{2}\right) +\left(\frac{-10}{-2}\right) +\left(\frac{4}{-6}\right)\\= \frac{9}{2}+ \frac{10}{2}-\frac{4}{6}\\=\frac{9}{2}+\frac{5}{1}-\frac{2}{3}\\=\frac{27}{6}+\frac{30}{6}-\frac{4}{6}\\=\frac{27+30-4}{6}\\=\frac{53}{6}\)
12. \(+\left(\frac{3}{-2}\right) -\left(\frac{9}{4}\right) +\left(\frac{10}{-4}\right)\\= \frac{-3}{2}- \frac{9}{4}-\frac{10}{4}\\=\frac{-3}{2}-\frac{9}{4}-\frac{5}{2}\\=\frac{-6}{4}-\frac{9}{4}-\frac{10}{4}\\=\frac{-6-9-10}{4}\\=\frac{-25}{4}\)