Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{-2}\right) -\left(\frac{-2}{5}\right) +\left(\frac{-3}{-5}\right)\\= \frac{7}{2}+ \frac{2}{5}+\frac{3}{5}\\=\frac{35}{10}+\frac{4}{10}+\frac{6}{10}\\=\frac{35+4+6}{10}\\=\frac{45}{10}\\=\frac{9}{2}\)
2. \(-\left(\frac{9}{-5}\right) +\left(\frac{-7}{4}\right) -\left(\frac{7}{6}\right)\\= \frac{9}{5}- \frac{7}{4}-\frac{7}{6}\\=\frac{108}{60}-\frac{105}{60}-\frac{70}{60}\\=\frac{108-105-70}{60}\\=\frac{-67}{60}\)
3. \(-\left(\frac{-10}{-9}\right) -\left(\frac{9}{10}\right) -\left(\frac{3}{-8}\right)\\= \frac{-10}{9}- \frac{9}{10}+\frac{3}{8}\\=\frac{-400}{360}-\frac{324}{360}+\frac{135}{360}\\=\frac{-400-324+135}{360}\\=\frac{-589}{360}\)
4. \(+\left(\frac{-4}{-3}\right) -\left(\frac{-4}{-7}\right) +\left(\frac{5}{-3}\right)\\= \frac{4}{3}- \frac{4}{7}-\frac{5}{3}\\=\frac{28}{21}-\frac{12}{21}-\frac{35}{21}\\=\frac{28-12-35}{21}\\=\frac{-19}{21}\)
5. \(+\left(\frac{-2}{3}\right) -\left(\frac{-7}{-3}\right) +\left(\frac{2}{12}\right)\\= \frac{-2}{3}- \frac{7}{3}+\frac{2}{12}\\=\frac{-2}{3}-\frac{7}{3}+\frac{1}{6}\\=\frac{-4}{6}-\frac{14}{6}+\frac{1}{6}\\=\frac{-4-14+1}{6}\\=\frac{-17}{6}\)
6. \(-\left(\frac{5}{-2}\right) -\left(\frac{-5}{10}\right) -\left(\frac{-6}{6}\right)\\= \frac{5}{2}+ \frac{5}{10}+\frac{6}{6}\\=\frac{5}{2}+\frac{1}{2}+\frac{1}{1}\\=\frac{5+1+1}{2}\\=\frac{7}{2}\)
7. \(-\left(\frac{3}{8}\right) +\left(\frac{-10}{8}\right) -\left(\frac{-8}{12}\right)\\= \frac{-3}{8}- \frac{10}{8}+\frac{8}{12}\\=\frac{-3}{8}-\frac{5}{4}+\frac{2}{3}\\=\frac{-9}{24}-\frac{30}{24}+\frac{16}{24}\\=\frac{-9-30+16}{24}\\=\frac{-23}{24}\)
8. \(+\left(\frac{6}{-5}\right) -\left(\frac{6}{6}\right) -\left(\frac{3}{3}\right)\\= \frac{-6}{5}- \frac{6}{6}-\frac{3}{3}\\=\frac{-6}{5}-\frac{1}{1}-\frac{1}{1}\\=\frac{-6-1-1}{5}\\=\frac{-8}{5}\)
9. \(-\left(\frac{5}{-4}\right) +\left(\frac{-5}{7}\right) -\left(\frac{8}{-8}\right)\\= \frac{5}{4}- \frac{5}{7}+\frac{8}{8}\\=\frac{5}{4}-\frac{5}{7}+\frac{1}{1}\\=\frac{35}{28}-\frac{20}{28}+\frac{28}{28}\\=\frac{35-20+28}{28}\\=\frac{43}{28}\)
10. \(+\left(\frac{4}{3}\right) -\left(\frac{6}{-8}\right) +\left(\frac{-4}{-6}\right)\\= \frac{4}{3}+ \frac{6}{8}+\frac{4}{6}\\=\frac{4}{3}+\frac{3}{4}+\frac{2}{3}\\=\frac{16}{12}+\frac{9}{12}+\frac{8}{12}\\=\frac{16+9+8}{12}\\=\frac{33}{12}\\=\frac{11}{4}\)
11. \(-\left(\frac{7}{8}\right) +\left(\frac{2}{-7}\right) -\left(\frac{-6}{5}\right)\\= \frac{-7}{8}- \frac{2}{7}+\frac{6}{5}\\=\frac{-245}{280}-\frac{80}{280}+\frac{336}{280}\\=\frac{-245-80+336}{280}\\=\frac{11}{280}\)
12. \(-\left(\frac{5}{-7}\right) -\left(\frac{-2}{3}\right) +\left(\frac{-3}{4}\right)\\= \frac{5}{7}+ \frac{2}{3}-\frac{3}{4}\\=\frac{60}{84}+\frac{56}{84}-\frac{63}{84}\\=\frac{60+56-63}{84}\\=\frac{53}{84}\)