Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{6}{-5}\right) -\left(\frac{-5}{-2}\right) +\left(\frac{-12}{8}\right)\\= \frac{-6}{5}- \frac{5}{2}-\frac{12}{8}\\=\frac{-6}{5}-\frac{5}{2}-\frac{3}{2}\\=\frac{-12}{10}-\frac{25}{10}-\frac{15}{10}\\=\frac{-12-25-15}{10}\\=\frac{-52}{10}\\=\frac{-26}{5}\)
2. \(+\left(\frac{7}{2}\right) -\left(\frac{-6}{-9}\right) -\left(\frac{2}{-7}\right)\\= \frac{7}{2}- \frac{6}{9}+\frac{2}{7}\\=\frac{7}{2}-\frac{2}{3}+\frac{2}{7}\\=\frac{147}{42}-\frac{28}{42}+\frac{12}{42}\\=\frac{147-28+12}{42}\\=\frac{131}{42}\)
3. \(-\left(\frac{-6}{-5}\right) -\left(\frac{3}{10}\right) -\left(\frac{-7}{-7}\right)\\= \frac{-6}{5}- \frac{3}{10}-\frac{7}{7}\\=\frac{-6}{5}-\frac{3}{10}-\frac{1}{1}\\=\frac{-12}{10}-\frac{3}{10}-\frac{10}{10}\\=\frac{-12-3-10}{10}\\=\frac{-25}{10}\\=\frac{-5}{2}\)
4. \(-\left(\frac{-6}{-7}\right) +\left(\frac{6}{-5}\right) +\left(\frac{-8}{6}\right)\\= \frac{-6}{7}- \frac{6}{5}-\frac{8}{6}\\=\frac{-6}{7}-\frac{6}{5}-\frac{4}{3}\\=\frac{-90}{105}-\frac{126}{105}-\frac{140}{105}\\=\frac{-90-126-140}{105}\\=\frac{-356}{105}\)
5. \(-\left(\frac{5}{3}\right) -\left(\frac{10}{7}\right) +\left(\frac{3}{-10}\right)\\= \frac{-5}{3}- \frac{10}{7}-\frac{3}{10}\\=\frac{-350}{210}-\frac{300}{210}-\frac{63}{210}\\=\frac{-350-300-63}{210}\\=\frac{-713}{210}\)
6. \(-\left(\frac{3}{-2}\right) -\left(\frac{-3}{8}\right) -\left(\frac{11}{2}\right)\\= \frac{3}{2}+ \frac{3}{8}-\frac{11}{2}\\=\frac{12}{8}+\frac{3}{8}-\frac{44}{8}\\=\frac{12+3-44}{8}\\=\frac{-29}{8}\)
7. \(-\left(\frac{-8}{3}\right) +\left(\frac{8}{-7}\right) +\left(\frac{-11}{-8}\right)\\= \frac{8}{3}- \frac{8}{7}+\frac{11}{8}\\=\frac{448}{168}-\frac{192}{168}+\frac{231}{168}\\=\frac{448-192+231}{168}\\=\frac{487}{168}\)
8. \(-\left(\frac{7}{-8}\right) -\left(\frac{-7}{3}\right) +\left(\frac{-3}{-2}\right)\\= \frac{7}{8}+ \frac{7}{3}+\frac{3}{2}\\=\frac{21}{24}+\frac{56}{24}+\frac{36}{24}\\=\frac{21+56+36}{24}\\=\frac{113}{24}\)
9. \(+\left(\frac{5}{-9}\right) -\left(\frac{-4}{4}\right) -\left(\frac{8}{-7}\right)\\= \frac{-5}{9}+ \frac{4}{4}+\frac{8}{7}\\=\frac{-5}{9}+\frac{1}{1}+\frac{8}{7}\\=\frac{-35}{63}+\frac{63}{63}+\frac{72}{63}\\=\frac{-35+63+72}{63}\\=\frac{100}{63}\)
10. \(+\left(\frac{8}{7}\right) +\left(\frac{7}{-5}\right) -\left(\frac{-9}{-9}\right)\\= \frac{8}{7}- \frac{7}{5}-\frac{9}{9}\\=\frac{8}{7}-\frac{7}{5}-\frac{1}{1}\\=\frac{40}{35}-\frac{49}{35}-\frac{35}{35}\\=\frac{40-49-35}{35}\\=\frac{-44}{35}\)
11. \(+\left(\frac{-8}{7}\right) +\left(\frac{2}{-8}\right) +\left(\frac{3}{-11}\right)\\= \frac{-8}{7}- \frac{2}{8}-\frac{3}{11}\\=\frac{-8}{7}-\frac{1}{4}-\frac{3}{11}\\=\frac{-352}{308}-\frac{77}{308}-\frac{84}{308}\\=\frac{-352-77-84}{308}\\=\frac{-513}{308}\)
12. \(+\left(\frac{9}{8}\right) +\left(\frac{8}{3}\right) +\left(\frac{-10}{-3}\right)\\= \frac{9}{8}+ \frac{8}{3}+\frac{10}{3}\\=\frac{27}{24}+\frac{64}{24}+\frac{80}{24}\\=\frac{27+64+80}{24}\\=\frac{171}{24}\\=\frac{57}{8}\)