Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{-5}\right) +\left(\frac{7}{-8}\right) +\left(\frac{8}{-3}\right)\\= \frac{-4}{5}- \frac{7}{8}-\frac{8}{3}\\=\frac{-96}{120}-\frac{105}{120}-\frac{320}{120}\\=\frac{-96-105-320}{120}\\=\frac{-521}{120}\)
2. \(+\left(\frac{9}{5}\right) +\left(\frac{5}{9}\right) -\left(\frac{-7}{-6}\right)\\= \frac{9}{5}+ \frac{5}{9}-\frac{7}{6}\\=\frac{162}{90}+\frac{50}{90}-\frac{105}{90}\\=\frac{162+50-105}{90}\\=\frac{107}{90}\)
3. \(+\left(\frac{9}{-7}\right) -\left(\frac{-4}{-4}\right) +\left(\frac{-3}{-5}\right)\\= \frac{-9}{7}- \frac{4}{4}+\frac{3}{5}\\=\frac{-9}{7}-\frac{1}{1}+\frac{3}{5}\\=\frac{-45}{35}-\frac{35}{35}+\frac{21}{35}\\=\frac{-45-35+21}{35}\\=\frac{-59}{35}\)
4. \(-\left(\frac{10}{7}\right) -\left(\frac{-2}{5}\right) +\left(\frac{-12}{-12}\right)\\= \frac{-10}{7}+ \frac{2}{5}+\frac{12}{12}\\=\frac{-10}{7}+\frac{2}{5}+\frac{1}{1}\\=\frac{-50}{35}+\frac{14}{35}+\frac{35}{35}\\=\frac{-50+14+35}{35}\\=\frac{-1}{35}\)
5. \(+\left(\frac{-4}{5}\right) +\left(\frac{9}{5}\right) -\left(\frac{-7}{-11}\right)\\= \frac{-4}{5}+ \frac{9}{5}-\frac{7}{11}\\=\frac{-44}{55}+\frac{99}{55}-\frac{35}{55}\\=\frac{-44+99-35}{55}\\=\frac{20}{55}\\=\frac{4}{11}\)
6. \(+\left(\frac{-10}{7}\right) -\left(\frac{10}{6}\right) +\left(\frac{-6}{10}\right)\\= \frac{-10}{7}- \frac{10}{6}-\frac{6}{10}\\=\frac{-10}{7}-\frac{5}{3}-\frac{3}{5}\\=\frac{-150}{105}-\frac{175}{105}-\frac{63}{105}\\=\frac{-150-175-63}{105}\\=\frac{-388}{105}\)
7. \(-\left(\frac{9}{8}\right) +\left(\frac{7}{7}\right) -\left(\frac{11}{3}\right)\\= \frac{-9}{8}+ \frac{7}{7}-\frac{11}{3}\\=\frac{-9}{8}+\frac{1}{1}-\frac{11}{3}\\=\frac{-27}{24}+\frac{24}{24}-\frac{88}{24}\\=\frac{-27+24-88}{24}\\=\frac{-91}{24}\)
8. \(+\left(\frac{7}{-8}\right) -\left(\frac{-2}{10}\right) +\left(\frac{6}{-4}\right)\\= \frac{-7}{8}+ \frac{2}{10}-\frac{6}{4}\\=\frac{-7}{8}+\frac{1}{5}-\frac{3}{2}\\=\frac{-35}{40}+\frac{8}{40}-\frac{60}{40}\\=\frac{-35+8-60}{40}\\=\frac{-87}{40}\)
9. \(+\left(\frac{7}{5}\right) -\left(\frac{-7}{8}\right) +\left(\frac{-8}{7}\right)\\= \frac{7}{5}+ \frac{7}{8}-\frac{8}{7}\\=\frac{392}{280}+\frac{245}{280}-\frac{320}{280}\\=\frac{392+245-320}{280}\\=\frac{317}{280}\)
10. \(+\left(\frac{10}{7}\right) +\left(\frac{-7}{-7}\right) -\left(\frac{-11}{-8}\right)\\= \frac{10}{7}+ \frac{7}{7}-\frac{11}{8}\\=\frac{10}{7}+\frac{1}{1}-\frac{11}{8}\\=\frac{80}{56}+\frac{56}{56}-\frac{77}{56}\\=\frac{80+56-77}{56}\\=\frac{59}{56}\)
11. \(-\left(\frac{-10}{7}\right) -\left(\frac{-4}{-6}\right) +\left(\frac{2}{3}\right)\\= \frac{10}{7}- \frac{4}{6}+\frac{2}{3}\\=\frac{10}{7}-\frac{2}{3}+\frac{2}{3}\\=\frac{30}{21}-\frac{14}{21}+\frac{14}{21}\\=\frac{30-14+14}{21}\\=\frac{30}{21}\\=\frac{10}{7}\)
12. \(-\left(\frac{-9}{-2}\right) -\left(\frac{2}{6}\right) -\left(\frac{-9}{-3}\right)\\= \frac{-9}{2}- \frac{2}{6}-\frac{9}{3}\\=\frac{-9}{2}-\frac{1}{3}-\frac{3}{1}\\=\frac{-27}{6}-\frac{2}{6}-\frac{18}{6}\\=\frac{-27-2-18}{6}\\=\frac{-47}{6}\)