Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{-7}\right) -\left(\frac{6}{-8}\right) -\left(\frac{-4}{7}\right)\\= \frac{8}{7}+ \frac{6}{8}+\frac{4}{7}\\=\frac{8}{7}+\frac{3}{4}+\frac{4}{7}\\=\frac{32}{28}+\frac{21}{28}+\frac{16}{28}\\=\frac{32+21+16}{28}\\=\frac{69}{28}\)
2. \(+\left(\frac{-6}{-5}\right) +\left(\frac{6}{-5}\right) -\left(\frac{-12}{10}\right)\\= \frac{6}{5}- \frac{6}{5}+\frac{12}{10}\\=\frac{6}{5}-\frac{6}{5}+\frac{6}{5}\\=\frac{6-6+6}{5}\\=\frac{6}{5}\)
3. \(+\left(\frac{-6}{7}\right) +\left(\frac{9}{-3}\right) +\left(\frac{8}{-5}\right)\\= \frac{-6}{7}- \frac{9}{3}-\frac{8}{5}\\=\frac{-6}{7}-\frac{3}{1}-\frac{8}{5}\\=\frac{-30}{35}-\frac{105}{35}-\frac{56}{35}\\=\frac{-30-105-56}{35}\\=\frac{-191}{35}\)
4. \(+\left(\frac{-7}{-9}\right) -\left(\frac{7}{7}\right) -\left(\frac{4}{8}\right)\\= \frac{7}{9}- \frac{7}{7}-\frac{4}{8}\\=\frac{7}{9}-\frac{1}{1}-\frac{1}{2}\\=\frac{14}{18}-\frac{18}{18}-\frac{9}{18}\\=\frac{14-18-9}{18}\\=\frac{-13}{18}\)
5. \(+\left(\frac{-3}{7}\right) -\left(\frac{7}{10}\right) -\left(\frac{11}{-12}\right)\\= \frac{-3}{7}- \frac{7}{10}+\frac{11}{12}\\=\frac{-180}{420}-\frac{294}{420}+\frac{385}{420}\\=\frac{-180-294+385}{420}\\=\frac{-89}{420}\)
6. \(-\left(\frac{6}{-5}\right) -\left(\frac{-3}{-10}\right) +\left(\frac{3}{8}\right)\\= \frac{6}{5}- \frac{3}{10}+\frac{3}{8}\\=\frac{48}{40}-\frac{12}{40}+\frac{15}{40}\\=\frac{48-12+15}{40}\\=\frac{51}{40}\)
7. \(-\left(\frac{-9}{2}\right) +\left(\frac{-3}{4}\right) -\left(\frac{7}{-3}\right)\\= \frac{9}{2}- \frac{3}{4}+\frac{7}{3}\\=\frac{54}{12}-\frac{9}{12}+\frac{28}{12}\\=\frac{54-9+28}{12}\\=\frac{73}{12}\)
8. \(+\left(\frac{8}{5}\right) +\left(\frac{-2}{-6}\right) -\left(\frac{-5}{12}\right)\\= \frac{8}{5}+ \frac{2}{6}+\frac{5}{12}\\=\frac{8}{5}+\frac{1}{3}+\frac{5}{12}\\=\frac{96}{60}+\frac{20}{60}+\frac{25}{60}\\=\frac{96+20+25}{60}\\=\frac{141}{60}\\=\frac{47}{20}\)
9. \(-\left(\frac{-4}{3}\right) +\left(\frac{5}{5}\right) -\left(\frac{-4}{-8}\right)\\= \frac{4}{3}+ \frac{5}{5}-\frac{4}{8}\\=\frac{4}{3}+\frac{1}{1}-\frac{1}{2}\\=\frac{8}{6}+\frac{6}{6}-\frac{3}{6}\\=\frac{8+6-3}{6}\\=\frac{11}{6}\)
10. \(+\left(\frac{-3}{5}\right) -\left(\frac{-10}{5}\right) -\left(\frac{-2}{7}\right)\\= \frac{-3}{5}+ \frac{10}{5}+\frac{2}{7}\\=\frac{-3}{5}+\frac{2}{1}+\frac{2}{7}\\=\frac{-21}{35}+\frac{70}{35}+\frac{10}{35}\\=\frac{-21+70+10}{35}\\=\frac{59}{35}\)
11. \(+\left(\frac{2}{3}\right) -\left(\frac{-6}{8}\right) +\left(\frac{-8}{7}\right)\\= \frac{2}{3}+ \frac{6}{8}-\frac{8}{7}\\=\frac{2}{3}+\frac{3}{4}-\frac{8}{7}\\=\frac{56}{84}+\frac{63}{84}-\frac{96}{84}\\=\frac{56+63-96}{84}\\=\frac{23}{84}\)
12. \(-\left(\frac{-4}{3}\right) +\left(\frac{-4}{-6}\right) +\left(\frac{-3}{9}\right)\\= \frac{4}{3}+ \frac{4}{6}-\frac{3}{9}\\=\frac{4}{3}+\frac{2}{3}-\frac{1}{3}\\=\frac{4+2-1}{3}\\=\frac{5}{3}\)