Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{-7}\right) -\left(\frac{6}{-7}\right) +\left(\frac{-10}{7}\right)\\= \frac{-6}{7}+ \frac{6}{7}-\frac{10}{7}\\=\frac{-6+6-10}{7}\\=\frac{-10}{7}\)
2. \(-\left(\frac{-8}{9}\right) +\left(\frac{-4}{3}\right) +\left(\frac{2}{-3}\right)\\= \frac{8}{9}- \frac{4}{3}-\frac{2}{3}\\=\frac{8-4-2}{9}\\=\frac{2}{9}\)
3. \(-\left(\frac{10}{-7}\right) -\left(\frac{-5}{7}\right) -\left(\frac{-4}{-5}\right)\\= \frac{10}{7}+ \frac{5}{7}-\frac{4}{5}\\=\frac{50}{35}+\frac{25}{35}-\frac{28}{35}\\=\frac{50+25-28}{35}\\=\frac{47}{35}\)
4. \(+\left(\frac{-9}{-2}\right) -\left(\frac{-4}{-3}\right) +\left(\frac{4}{-8}\right)\\= \frac{9}{2}- \frac{4}{3}-\frac{4}{8}\\=\frac{9}{2}-\frac{4}{3}-\frac{1}{2}\\=\frac{27}{6}-\frac{8}{6}-\frac{3}{6}\\=\frac{27-8-3}{6}\\=\frac{16}{6}\\=\frac{8}{3}\)
5. \(-\left(\frac{-7}{-9}\right) -\left(\frac{6}{4}\right) +\left(\frac{9}{11}\right)\\= \frac{-7}{9}- \frac{6}{4}+\frac{9}{11}\\=\frac{-7}{9}-\frac{3}{2}+\frac{9}{11}\\=\frac{-154}{198}-\frac{297}{198}+\frac{162}{198}\\=\frac{-154-297+162}{198}\\=\frac{-289}{198}\)
6. \(-\left(\frac{7}{6}\right) +\left(\frac{5}{5}\right) -\left(\frac{-5}{-3}\right)\\= \frac{-7}{6}+ \frac{5}{5}-\frac{5}{3}\\=\frac{-7}{6}+\frac{1}{1}-\frac{5}{3}\\=\frac{-7+1-5}{6}\\=\frac{-11}{6}\)
7. \(-\left(\frac{-3}{-2}\right) +\left(\frac{9}{-5}\right) -\left(\frac{-3}{12}\right)\\= \frac{-3}{2}- \frac{9}{5}+\frac{3}{12}\\=\frac{-3}{2}-\frac{9}{5}+\frac{1}{4}\\=\frac{-30}{20}-\frac{36}{20}+\frac{5}{20}\\=\frac{-30-36+5}{20}\\=\frac{-61}{20}\)
8. \(-\left(\frac{2}{-9}\right) +\left(\frac{8}{7}\right) +\left(\frac{-3}{-5}\right)\\= \frac{2}{9}+ \frac{8}{7}+\frac{3}{5}\\=\frac{70}{315}+\frac{360}{315}+\frac{189}{315}\\=\frac{70+360+189}{315}\\=\frac{619}{315}\)
9. \(-\left(\frac{6}{5}\right) +\left(\frac{4}{9}\right) +\left(\frac{5}{-11}\right)\\= \frac{-6}{5}+ \frac{4}{9}-\frac{5}{11}\\=\frac{-594}{495}+\frac{220}{495}-\frac{225}{495}\\=\frac{-594+220-225}{495}\\=\frac{-599}{495}\)
10. \(-\left(\frac{-2}{-3}\right) -\left(\frac{-7}{-9}\right) -\left(\frac{-8}{-12}\right)\\= \frac{-2}{3}- \frac{7}{9}-\frac{8}{12}\\=\frac{-2}{3}-\frac{7}{9}-\frac{2}{3}\\=\frac{-6}{9}-\frac{7}{9}-\frac{6}{9}\\=\frac{-6-7-6}{9}\\=\frac{-19}{9}\)
11. \(+\left(\frac{7}{-8}\right) +\left(\frac{-7}{-7}\right) +\left(\frac{-11}{-3}\right)\\= \frac{-7}{8}+ \frac{7}{7}+\frac{11}{3}\\=\frac{-7}{8}+\frac{1}{1}+\frac{11}{3}\\=\frac{-21}{24}+\frac{24}{24}+\frac{88}{24}\\=\frac{-21+24+88}{24}\\=\frac{91}{24}\)
12. \(+\left(\frac{-4}{-3}\right) -\left(\frac{-6}{10}\right) -\left(\frac{-5}{-5}\right)\\= \frac{4}{3}+ \frac{6}{10}-\frac{5}{5}\\=\frac{4}{3}+\frac{3}{5}-\frac{1}{1}\\=\frac{20}{15}+\frac{9}{15}-\frac{15}{15}\\=\frac{20+9-15}{15}\\=\frac{14}{15}\)