Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-8}{7}\right) +\left(\frac{7}{-6}\right) +\left(\frac{3}{-10}\right)\\= \frac{8}{7}- \frac{7}{6}-\frac{3}{10}\\=\frac{240}{210}-\frac{245}{210}-\frac{63}{210}\\=\frac{240-245-63}{210}\\=\frac{-68}{210}\\=\frac{-34}{105}\)
2. \(-\left(\frac{3}{2}\right) +\left(\frac{2}{-3}\right) -\left(\frac{-9}{-7}\right)\\= \frac{-3}{2}- \frac{2}{3}-\frac{9}{7}\\=\frac{-63}{42}-\frac{28}{42}-\frac{54}{42}\\=\frac{-63-28-54}{42}\\=\frac{-145}{42}\)
3. \(-\left(\frac{-10}{7}\right) +\left(\frac{-9}{-10}\right) -\left(\frac{11}{9}\right)\\= \frac{10}{7}+ \frac{9}{10}-\frac{11}{9}\\=\frac{900}{630}+\frac{567}{630}-\frac{770}{630}\\=\frac{900+567-770}{630}\\=\frac{697}{630}\)
4. \(-\left(\frac{2}{5}\right) +\left(\frac{-4}{2}\right) +\left(\frac{-11}{-4}\right)\\= \frac{-2}{5}- \frac{4}{2}+\frac{11}{4}\\=\frac{-2}{5}-\frac{2}{1}+\frac{11}{4}\\=\frac{-8}{20}-\frac{40}{20}+\frac{55}{20}\\=\frac{-8-40+55}{20}\\=\frac{7}{20}\)
5. \(-\left(\frac{-6}{5}\right) +\left(\frac{-2}{-2}\right) -\left(\frac{10}{8}\right)\\= \frac{6}{5}+ \frac{2}{2}-\frac{10}{8}\\=\frac{6}{5}+\frac{1}{1}-\frac{5}{4}\\=\frac{24}{20}+\frac{20}{20}-\frac{25}{20}\\=\frac{24+20-25}{20}\\=\frac{19}{20}\)
6. \(-\left(\frac{7}{-8}\right) +\left(\frac{-5}{-4}\right) +\left(\frac{-10}{10}\right)\\= \frac{7}{8}+ \frac{5}{4}-\frac{10}{10}\\=\frac{7}{8}+\frac{5}{4}-\frac{1}{1}\\=\frac{7+5-1}{8}\\=\frac{11}{8}\)
7. \(-\left(\frac{7}{-9}\right) +\left(\frac{-10}{-6}\right) -\left(\frac{3}{3}\right)\\= \frac{7}{9}+ \frac{10}{6}-\frac{3}{3}\\=\frac{7}{9}+\frac{5}{3}-\frac{1}{1}\\=\frac{7+5-1}{9}\\=\frac{11}{9}\)
8. \(+\left(\frac{-2}{-3}\right) +\left(\frac{-3}{6}\right) +\left(\frac{-4}{-9}\right)\\= \frac{2}{3}- \frac{3}{6}+\frac{4}{9}\\=\frac{2}{3}-\frac{1}{2}+\frac{4}{9}\\=\frac{12}{18}-\frac{9}{18}+\frac{8}{18}\\=\frac{12-9+8}{18}\\=\frac{11}{18}\)
9. \(+\left(\frac{2}{3}\right) -\left(\frac{-4}{-6}\right) +\left(\frac{3}{8}\right)\\= \frac{2}{3}- \frac{4}{6}+\frac{3}{8}\\=\frac{2}{3}-\frac{2}{3}+\frac{3}{8}\\=\frac{16}{24}-\frac{16}{24}+\frac{9}{24}\\=\frac{16-16+9}{24}\\=\frac{9}{24}\\=\frac{3}{8}\)
10. \(-\left(\frac{-7}{-2}\right) -\left(\frac{-6}{9}\right) +\left(\frac{-9}{-11}\right)\\= \frac{-7}{2}+ \frac{6}{9}+\frac{9}{11}\\=\frac{-7}{2}+\frac{2}{3}+\frac{9}{11}\\=\frac{-231}{66}+\frac{44}{66}+\frac{54}{66}\\=\frac{-231+44+54}{66}\\=\frac{-133}{66}\)
11. \(-\left(\frac{5}{-6}\right) -\left(\frac{7}{-2}\right) -\left(\frac{-3}{5}\right)\\= \frac{5}{6}+ \frac{7}{2}+\frac{3}{5}\\=\frac{25}{30}+\frac{105}{30}+\frac{18}{30}\\=\frac{25+105+18}{30}\\=\frac{148}{30}\\=\frac{74}{15}\)
12. \(+\left(\frac{-2}{-3}\right) -\left(\frac{-3}{-8}\right) +\left(\frac{11}{-8}\right)\\= \frac{2}{3}- \frac{3}{8}-\frac{11}{8}\\=\frac{16}{24}-\frac{9}{24}-\frac{33}{24}\\=\frac{16-9-33}{24}\\=\frac{-26}{24}\\=\frac{-13}{12}\)