Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{-7}\right) -\left(\frac{-9}{-3}\right) +\left(\frac{-5}{-12}\right)\\= \frac{10}{7}- \frac{9}{3}+\frac{5}{12}\\=\frac{10}{7}-\frac{3}{1}+\frac{5}{12}\\=\frac{120}{84}-\frac{252}{84}+\frac{35}{84}\\=\frac{120-252+35}{84}\\=\frac{-97}{84}\)
2. \(-\left(\frac{-9}{7}\right) -\left(\frac{-4}{-4}\right) -\left(\frac{2}{8}\right)\\= \frac{9}{7}- \frac{4}{4}-\frac{2}{8}\\=\frac{9}{7}-\frac{1}{1}-\frac{1}{4}\\=\frac{36}{28}-\frac{28}{28}-\frac{7}{28}\\=\frac{36-28-7}{28}\\=\frac{1}{28}\)
3. \(-\left(\frac{10}{3}\right) -\left(\frac{10}{-2}\right) +\left(\frac{10}{-5}\right)\\= \frac{-10}{3}+ \frac{10}{2}-\frac{10}{5}\\=\frac{-10}{3}+\frac{5}{1}-\frac{2}{1}\\=\frac{-10+5-2}{3}\\=\frac{-7}{3}\)
4. \(+\left(\frac{-3}{4}\right) +\left(\frac{6}{-9}\right) +\left(\frac{-12}{5}\right)\\= \frac{-3}{4}- \frac{6}{9}-\frac{12}{5}\\=\frac{-3}{4}-\frac{2}{3}-\frac{12}{5}\\=\frac{-45}{60}-\frac{40}{60}-\frac{144}{60}\\=\frac{-45-40-144}{60}\\=\frac{-229}{60}\)
5. \(+\left(\frac{-10}{3}\right) +\left(\frac{5}{5}\right) -\left(\frac{3}{10}\right)\\= \frac{-10}{3}+ \frac{5}{5}-\frac{3}{10}\\=\frac{-10}{3}+\frac{1}{1}-\frac{3}{10}\\=\frac{-100}{30}+\frac{30}{30}-\frac{9}{30}\\=\frac{-100+30-9}{30}\\=\frac{-79}{30}\)
6. \(+\left(\frac{-5}{6}\right) -\left(\frac{10}{10}\right) -\left(\frac{-10}{-3}\right)\\= \frac{-5}{6}- \frac{10}{10}-\frac{10}{3}\\=\frac{-5}{6}-\frac{1}{1}-\frac{10}{3}\\=\frac{-5-1-10}{6}\\=\frac{-16}{6}\\=\frac{-8}{3}\)
7. \(+\left(\frac{8}{3}\right) +\left(\frac{9}{-8}\right) +\left(\frac{-12}{10}\right)\\= \frac{8}{3}- \frac{9}{8}-\frac{12}{10}\\=\frac{8}{3}-\frac{9}{8}-\frac{6}{5}\\=\frac{320}{120}-\frac{135}{120}-\frac{144}{120}\\=\frac{320-135-144}{120}\\=\frac{41}{120}\)
8. \(+\left(\frac{10}{3}\right) -\left(\frac{7}{6}\right) +\left(\frac{-5}{3}\right)\\= \frac{10}{3}- \frac{7}{6}-\frac{5}{3}\\=\frac{20}{6}-\frac{7}{6}-\frac{10}{6}\\=\frac{20-7-10}{6}\\=\frac{3}{6}\\=\frac{1}{2}\)
9. \(-\left(\frac{-5}{2}\right) +\left(\frac{-10}{-10}\right) -\left(\frac{-6}{-10}\right)\\= \frac{5}{2}+ \frac{10}{10}-\frac{6}{10}\\=\frac{5}{2}+\frac{1}{1}-\frac{3}{5}\\=\frac{25}{10}+\frac{10}{10}-\frac{6}{10}\\=\frac{25+10-6}{10}\\=\frac{29}{10}\)
10. \(+\left(\frac{3}{-2}\right) +\left(\frac{-6}{-2}\right) -\left(\frac{2}{-6}\right)\\= \frac{-3}{2}+ \frac{6}{2}+\frac{2}{6}\\=\frac{-3}{2}+\frac{3}{1}+\frac{1}{3}\\=\frac{-9}{6}+\frac{18}{6}+\frac{2}{6}\\=\frac{-9+18+2}{6}\\=\frac{11}{6}\)
11. \(+\left(\frac{-7}{-9}\right) -\left(\frac{7}{-10}\right) -\left(\frac{-11}{-7}\right)\\= \frac{7}{9}+ \frac{7}{10}-\frac{11}{7}\\=\frac{490}{630}+\frac{441}{630}-\frac{990}{630}\\=\frac{490+441-990}{630}\\=\frac{-59}{630}\)
12. \(+\left(\frac{6}{5}\right) +\left(\frac{3}{-5}\right) +\left(\frac{11}{-2}\right)\\= \frac{6}{5}- \frac{3}{5}-\frac{11}{2}\\=\frac{12}{10}-\frac{6}{10}-\frac{55}{10}\\=\frac{12-6-55}{10}\\=\frac{-49}{10}\)