Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{-9}\right) +\left(\frac{2}{-9}\right) -\left(\frac{8}{12}\right)\\= \frac{4}{9}- \frac{2}{9}-\frac{8}{12}\\=\frac{4}{9}-\frac{2}{9}-\frac{2}{3}\\=\frac{4-2-2}{9}\\=\frac{0}{9}\\=\frac{0}{1}\)
2. \(+\left(\frac{-2}{9}\right) +\left(\frac{-3}{-10}\right) +\left(\frac{10}{-9}\right)\\= \frac{-2}{9}+ \frac{3}{10}-\frac{10}{9}\\=\frac{-20}{90}+\frac{27}{90}-\frac{100}{90}\\=\frac{-20+27-100}{90}\\=\frac{-93}{90}\\=\frac{-31}{30}\)
3. \(-\left(\frac{-7}{-2}\right) +\left(\frac{4}{7}\right) -\left(\frac{2}{-6}\right)\\= \frac{-7}{2}+ \frac{4}{7}+\frac{2}{6}\\=\frac{-7}{2}+\frac{4}{7}+\frac{1}{3}\\=\frac{-147}{42}+\frac{24}{42}+\frac{14}{42}\\=\frac{-147+24+14}{42}\\=\frac{-109}{42}\)
4. \(+\left(\frac{2}{-3}\right) +\left(\frac{-8}{2}\right) -\left(\frac{-10}{-10}\right)\\= \frac{-2}{3}- \frac{8}{2}-\frac{10}{10}\\=\frac{-2}{3}-\frac{4}{1}-\frac{1}{1}\\=\frac{-2-4-1}{3}\\=\frac{-7}{3}\)
5. \(-\left(\frac{-8}{-5}\right) +\left(\frac{4}{7}\right) -\left(\frac{-9}{4}\right)\\= \frac{-8}{5}+ \frac{4}{7}+\frac{9}{4}\\=\frac{-224}{140}+\frac{80}{140}+\frac{315}{140}\\=\frac{-224+80+315}{140}\\=\frac{171}{140}\)
6. \(-\left(\frac{4}{3}\right) -\left(\frac{5}{3}\right) -\left(\frac{8}{-8}\right)\\= \frac{-4}{3}- \frac{5}{3}+\frac{8}{8}\\=\frac{-4}{3}-\frac{5}{3}+\frac{1}{1}\\=\frac{-4-5+1}{3}\\=\frac{-8}{3}\)
7. \(-\left(\frac{7}{2}\right) +\left(\frac{7}{9}\right) +\left(\frac{8}{3}\right)\\= \frac{-7}{2}+ \frac{7}{9}+\frac{8}{3}\\=\frac{-63}{18}+\frac{14}{18}+\frac{48}{18}\\=\frac{-63+14+48}{18}\\=\frac{-1}{18}\)
8. \(+\left(\frac{-3}{-7}\right) +\left(\frac{-3}{-5}\right) +\left(\frac{-12}{-4}\right)\\= \frac{3}{7}+ \frac{3}{5}+\frac{12}{4}\\=\frac{3}{7}+\frac{3}{5}+\frac{3}{1}\\=\frac{15}{35}+\frac{21}{35}+\frac{105}{35}\\=\frac{15+21+105}{35}\\=\frac{141}{35}\)
9. \(+\left(\frac{10}{-7}\right) +\left(\frac{7}{-9}\right) -\left(\frac{7}{-3}\right)\\= \frac{-10}{7}- \frac{7}{9}+\frac{7}{3}\\=\frac{-90}{63}-\frac{49}{63}+\frac{147}{63}\\=\frac{-90-49+147}{63}\\=\frac{8}{63}\)
10. \(+\left(\frac{7}{9}\right) +\left(\frac{5}{-4}\right) -\left(\frac{11}{-11}\right)\\= \frac{7}{9}- \frac{5}{4}+\frac{11}{11}\\=\frac{7}{9}-\frac{5}{4}+\frac{1}{1}\\=\frac{28}{36}-\frac{45}{36}+\frac{36}{36}\\=\frac{28-45+36}{36}\\=\frac{19}{36}\)
11. \(+\left(\frac{-5}{2}\right) +\left(\frac{7}{10}\right) +\left(\frac{5}{-2}\right)\\= \frac{-5}{2}+ \frac{7}{10}-\frac{5}{2}\\=\frac{-25}{10}+\frac{7}{10}-\frac{25}{10}\\=\frac{-25+7-25}{10}\\=\frac{-43}{10}\)
12. \(+\left(\frac{-9}{7}\right) -\left(\frac{4}{8}\right) +\left(\frac{-10}{-6}\right)\\= \frac{-9}{7}- \frac{4}{8}+\frac{10}{6}\\=\frac{-9}{7}-\frac{1}{2}+\frac{5}{3}\\=\frac{-54}{42}-\frac{21}{42}+\frac{70}{42}\\=\frac{-54-21+70}{42}\\=\frac{-5}{42}\)