Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{5}\right) +\left(\frac{-10}{4}\right) -\left(\frac{-4}{-9}\right)\\= \frac{-8}{5}- \frac{10}{4}-\frac{4}{9}\\=\frac{-8}{5}-\frac{5}{2}-\frac{4}{9}\\=\frac{-144}{90}-\frac{225}{90}-\frac{40}{90}\\=\frac{-144-225-40}{90}\\=\frac{-409}{90}\)
2. \(+\left(\frac{-10}{7}\right) -\left(\frac{-2}{8}\right) -\left(\frac{-3}{-6}\right)\\= \frac{-10}{7}+ \frac{2}{8}-\frac{3}{6}\\=\frac{-10}{7}+\frac{1}{4}-\frac{1}{2}\\=\frac{-40}{28}+\frac{7}{28}-\frac{14}{28}\\=\frac{-40+7-14}{28}\\=\frac{-47}{28}\)
3. \(+\left(\frac{2}{7}\right) -\left(\frac{-8}{-8}\right) -\left(\frac{4}{12}\right)\\= \frac{2}{7}- \frac{8}{8}-\frac{4}{12}\\=\frac{2}{7}-\frac{1}{1}-\frac{1}{3}\\=\frac{6}{21}-\frac{21}{21}-\frac{7}{21}\\=\frac{6-21-7}{21}\\=\frac{-22}{21}\)
4. \(-\left(\frac{4}{9}\right) -\left(\frac{-5}{5}\right) +\left(\frac{6}{4}\right)\\= \frac{-4}{9}+ \frac{5}{5}+\frac{6}{4}\\=\frac{-4}{9}+\frac{1}{1}+\frac{3}{2}\\=\frac{-8}{18}+\frac{18}{18}+\frac{27}{18}\\=\frac{-8+18+27}{18}\\=\frac{37}{18}\)
5. \(+\left(\frac{4}{-9}\right) -\left(\frac{7}{-10}\right) -\left(\frac{10}{3}\right)\\= \frac{-4}{9}+ \frac{7}{10}-\frac{10}{3}\\=\frac{-40}{90}+\frac{63}{90}-\frac{300}{90}\\=\frac{-40+63-300}{90}\\=\frac{-277}{90}\)
6. \(+\left(\frac{6}{-5}\right) +\left(\frac{-9}{-9}\right) +\left(\frac{5}{6}\right)\\= \frac{-6}{5}+ \frac{9}{9}+\frac{5}{6}\\=\frac{-6}{5}+\frac{1}{1}+\frac{5}{6}\\=\frac{-36}{30}+\frac{30}{30}+\frac{25}{30}\\=\frac{-36+30+25}{30}\\=\frac{19}{30}\)
7. \(-\left(\frac{7}{-8}\right) +\left(\frac{-9}{7}\right) +\left(\frac{-2}{2}\right)\\= \frac{7}{8}- \frac{9}{7}-\frac{2}{2}\\=\frac{7}{8}-\frac{9}{7}-\frac{1}{1}\\=\frac{49}{56}-\frac{72}{56}-\frac{56}{56}\\=\frac{49-72-56}{56}\\=\frac{-79}{56}\)
8. \(-\left(\frac{-2}{9}\right) +\left(\frac{2}{2}\right) -\left(\frac{2}{9}\right)\\= \frac{2}{9}+ \frac{2}{2}-\frac{2}{9}\\=\frac{2}{9}+\frac{1}{1}-\frac{2}{9}\\=\frac{2+1-2}{9}\\=\frac{1}{9}\)
9. \(-\left(\frac{4}{-7}\right) -\left(\frac{9}{-2}\right) -\left(\frac{11}{4}\right)\\= \frac{4}{7}+ \frac{9}{2}-\frac{11}{4}\\=\frac{16}{28}+\frac{126}{28}-\frac{77}{28}\\=\frac{16+126-77}{28}\\=\frac{65}{28}\)
10. \(+\left(\frac{-5}{-8}\right) -\left(\frac{-6}{6}\right) -\left(\frac{6}{-9}\right)\\= \frac{5}{8}+ \frac{6}{6}+\frac{6}{9}\\=\frac{5}{8}+\frac{1}{1}+\frac{2}{3}\\=\frac{15}{24}+\frac{24}{24}+\frac{16}{24}\\=\frac{15+24+16}{24}\\=\frac{55}{24}\)
11. \(-\left(\frac{7}{-2}\right) -\left(\frac{3}{-9}\right) +\left(\frac{-8}{-5}\right)\\= \frac{7}{2}+ \frac{3}{9}+\frac{8}{5}\\=\frac{7}{2}+\frac{1}{3}+\frac{8}{5}\\=\frac{105}{30}+\frac{10}{30}+\frac{48}{30}\\=\frac{105+10+48}{30}\\=\frac{163}{30}\)
12. \(+\left(\frac{2}{5}\right) -\left(\frac{-2}{-8}\right) +\left(\frac{8}{-12}\right)\\= \frac{2}{5}- \frac{2}{8}-\frac{8}{12}\\=\frac{2}{5}-\frac{1}{4}-\frac{2}{3}\\=\frac{24}{60}-\frac{15}{60}-\frac{40}{60}\\=\frac{24-15-40}{60}\\=\frac{-31}{60}\)