Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{9}\right) +\left(\frac{8}{-8}\right) +\left(\frac{-9}{6}\right)\\= \frac{-2}{9}- \frac{8}{8}-\frac{9}{6}\\=\frac{-2}{9}-\frac{1}{1}-\frac{3}{2}\\=\frac{-4}{18}-\frac{18}{18}-\frac{27}{18}\\=\frac{-4-18-27}{18}\\=\frac{-49}{18}\)
2. \(+\left(\frac{-8}{-7}\right) +\left(\frac{8}{-6}\right) +\left(\frac{-11}{-10}\right)\\= \frac{8}{7}- \frac{8}{6}+\frac{11}{10}\\=\frac{8}{7}-\frac{4}{3}+\frac{11}{10}\\=\frac{240}{210}-\frac{280}{210}+\frac{231}{210}\\=\frac{240-280+231}{210}\\=\frac{191}{210}\)
3. \(+\left(\frac{6}{5}\right) -\left(\frac{-5}{5}\right) -\left(\frac{12}{-9}\right)\\= \frac{6}{5}+ \frac{5}{5}+\frac{12}{9}\\=\frac{6}{5}+\frac{1}{1}+\frac{4}{3}\\=\frac{18}{15}+\frac{15}{15}+\frac{20}{15}\\=\frac{18+15+20}{15}\\=\frac{53}{15}\)
4. \(-\left(\frac{8}{5}\right) -\left(\frac{-5}{5}\right) -\left(\frac{7}{-2}\right)\\= \frac{-8}{5}+ \frac{5}{5}+\frac{7}{2}\\=\frac{-8}{5}+\frac{1}{1}+\frac{7}{2}\\=\frac{-16}{10}+\frac{10}{10}+\frac{35}{10}\\=\frac{-16+10+35}{10}\\=\frac{29}{10}\)
5. \(-\left(\frac{9}{7}\right) -\left(\frac{-2}{-3}\right) -\left(\frac{-6}{-2}\right)\\= \frac{-9}{7}- \frac{2}{3}-\frac{6}{2}\\=\frac{-9}{7}-\frac{2}{3}-\frac{3}{1}\\=\frac{-27}{21}-\frac{14}{21}-\frac{63}{21}\\=\frac{-27-14-63}{21}\\=\frac{-104}{21}\)
6. \(+\left(\frac{-2}{-7}\right) -\left(\frac{9}{2}\right) -\left(\frac{4}{-9}\right)\\= \frac{2}{7}- \frac{9}{2}+\frac{4}{9}\\=\frac{36}{126}-\frac{567}{126}+\frac{56}{126}\\=\frac{36-567+56}{126}\\=\frac{-475}{126}\)
7. \(+\left(\frac{-2}{-3}\right) -\left(\frac{-10}{-2}\right) -\left(\frac{2}{6}\right)\\= \frac{2}{3}- \frac{10}{2}-\frac{2}{6}\\=\frac{2}{3}-\frac{5}{1}-\frac{1}{3}\\=\frac{2-5-1}{3}\\=\frac{-4}{3}\)
8. \(+\left(\frac{-8}{-3}\right) -\left(\frac{7}{4}\right) +\left(\frac{11}{4}\right)\\= \frac{8}{3}- \frac{7}{4}+\frac{11}{4}\\=\frac{32}{12}-\frac{21}{12}+\frac{33}{12}\\=\frac{32-21+33}{12}\\=\frac{44}{12}\\=\frac{11}{3}\)
9. \(-\left(\frac{-2}{-7}\right) -\left(\frac{9}{4}\right) +\left(\frac{-8}{11}\right)\\= \frac{-2}{7}- \frac{9}{4}-\frac{8}{11}\\=\frac{-88}{308}-\frac{693}{308}-\frac{224}{308}\\=\frac{-88-693-224}{308}\\=\frac{-1005}{308}\)
10. \(+\left(\frac{-3}{7}\right) +\left(\frac{10}{-9}\right) +\left(\frac{-7}{-4}\right)\\= \frac{-3}{7}- \frac{10}{9}+\frac{7}{4}\\=\frac{-108}{252}-\frac{280}{252}+\frac{441}{252}\\=\frac{-108-280+441}{252}\\=\frac{53}{252}\)
11. \(+\left(\frac{2}{3}\right) -\left(\frac{-6}{-10}\right) +\left(\frac{9}{-5}\right)\\= \frac{2}{3}- \frac{6}{10}-\frac{9}{5}\\=\frac{2}{3}-\frac{3}{5}-\frac{9}{5}\\=\frac{10}{15}-\frac{9}{15}-\frac{27}{15}\\=\frac{10-9-27}{15}\\=\frac{-26}{15}\)
12. \(+\left(\frac{5}{6}\right) +\left(\frac{-8}{-5}\right) -\left(\frac{-12}{-12}\right)\\= \frac{5}{6}+ \frac{8}{5}-\frac{12}{12}\\=\frac{5}{6}+\frac{8}{5}-\frac{1}{1}\\=\frac{25}{30}+\frac{48}{30}-\frac{30}{30}\\=\frac{25+48-30}{30}\\=\frac{43}{30}\)