Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{7}\right) -\left(\frac{-9}{-6}\right) -\left(\frac{3}{3}\right)\\= \frac{6}{7}- \frac{9}{6}-\frac{3}{3}\\=\frac{6}{7}-\frac{3}{2}-\frac{1}{1}\\=\frac{12}{14}-\frac{21}{14}-\frac{14}{14}\\=\frac{12-21-14}{14}\\=\frac{-23}{14}\)
2. \(+\left(\frac{-5}{-2}\right) +\left(\frac{-2}{-3}\right) -\left(\frac{-5}{11}\right)\\= \frac{5}{2}+ \frac{2}{3}+\frac{5}{11}\\=\frac{165}{66}+\frac{44}{66}+\frac{30}{66}\\=\frac{165+44+30}{66}\\=\frac{239}{66}\)
3. \(+\left(\frac{4}{-3}\right) +\left(\frac{-7}{4}\right) -\left(\frac{5}{6}\right)\\= \frac{-4}{3}- \frac{7}{4}-\frac{5}{6}\\=\frac{-16}{12}-\frac{21}{12}-\frac{10}{12}\\=\frac{-16-21-10}{12}\\=\frac{-47}{12}\)
4. \(-\left(\frac{-7}{9}\right) +\left(\frac{-10}{-9}\right) +\left(\frac{10}{7}\right)\\= \frac{7}{9}+ \frac{10}{9}+\frac{10}{7}\\=\frac{49}{63}+\frac{70}{63}+\frac{90}{63}\\=\frac{49+70+90}{63}\\=\frac{209}{63}\)
5. \(+\left(\frac{-2}{7}\right) -\left(\frac{-8}{-7}\right) +\left(\frac{9}{-12}\right)\\= \frac{-2}{7}- \frac{8}{7}-\frac{9}{12}\\=\frac{-2}{7}-\frac{8}{7}-\frac{3}{4}\\=\frac{-8}{28}-\frac{32}{28}-\frac{21}{28}\\=\frac{-8-32-21}{28}\\=\frac{-61}{28}\)
6. \(+\left(\frac{2}{-9}\right) -\left(\frac{-3}{7}\right) +\left(\frac{4}{-2}\right)\\= \frac{-2}{9}+ \frac{3}{7}-\frac{4}{2}\\=\frac{-2}{9}+\frac{3}{7}-\frac{2}{1}\\=\frac{-14}{63}+\frac{27}{63}-\frac{126}{63}\\=\frac{-14+27-126}{63}\\=\frac{-113}{63}\)
7. \(+\left(\frac{2}{-3}\right) +\left(\frac{-5}{-8}\right) -\left(\frac{8}{9}\right)\\= \frac{-2}{3}+ \frac{5}{8}-\frac{8}{9}\\=\frac{-48}{72}+\frac{45}{72}-\frac{64}{72}\\=\frac{-48+45-64}{72}\\=\frac{-67}{72}\)
8. \(-\left(\frac{-2}{3}\right) -\left(\frac{-2}{-2}\right) -\left(\frac{2}{-2}\right)\\= \frac{2}{3}- \frac{2}{2}+\frac{2}{2}\\=\frac{2}{3}-\frac{1}{1}+\frac{1}{1}\\=\frac{2-1+1}{3}\\=\frac{2}{3}\)
9. \(-\left(\frac{-10}{7}\right) +\left(\frac{-5}{3}\right) +\left(\frac{-12}{3}\right)\\= \frac{10}{7}- \frac{5}{3}-\frac{12}{3}\\=\frac{10}{7}-\frac{5}{3}-\frac{4}{1}\\=\frac{30}{21}-\frac{35}{21}-\frac{84}{21}\\=\frac{30-35-84}{21}\\=\frac{-89}{21}\)
10. \(+\left(\frac{5}{4}\right) -\left(\frac{8}{-4}\right) +\left(\frac{-3}{-10}\right)\\= \frac{5}{4}+ \frac{8}{4}+\frac{3}{10}\\=\frac{5}{4}+\frac{2}{1}+\frac{3}{10}\\=\frac{25}{20}+\frac{40}{20}+\frac{6}{20}\\=\frac{25+40+6}{20}\\=\frac{71}{20}\)
11. \(-\left(\frac{6}{-5}\right) +\left(\frac{5}{-4}\right) +\left(\frac{12}{10}\right)\\= \frac{6}{5}- \frac{5}{4}+\frac{12}{10}\\=\frac{6}{5}-\frac{5}{4}+\frac{6}{5}\\=\frac{24}{20}-\frac{25}{20}+\frac{24}{20}\\=\frac{24-25+24}{20}\\=\frac{23}{20}\)
12. \(+\left(\frac{-7}{-8}\right) +\left(\frac{-7}{-5}\right) +\left(\frac{-3}{-3}\right)\\= \frac{7}{8}+ \frac{7}{5}+\frac{3}{3}\\=\frac{7}{8}+\frac{7}{5}+\frac{1}{1}\\=\frac{35}{40}+\frac{56}{40}+\frac{40}{40}\\=\frac{35+56+40}{40}\\=\frac{131}{40}\)