Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{7}\right) -\left(\frac{2}{10}\right) -\left(\frac{-8}{-2}\right)\\= \frac{3}{7}- \frac{2}{10}-\frac{8}{2}\\=\frac{3}{7}-\frac{1}{5}-\frac{4}{1}\\=\frac{15}{35}-\frac{7}{35}-\frac{140}{35}\\=\frac{15-7-140}{35}\\=\frac{-132}{35}\)
2. \(-\left(\frac{6}{-5}\right) +\left(\frac{-7}{-6}\right) -\left(\frac{4}{-12}\right)\\= \frac{6}{5}+ \frac{7}{6}+\frac{4}{12}\\=\frac{6}{5}+\frac{7}{6}+\frac{1}{3}\\=\frac{36}{30}+\frac{35}{30}+\frac{10}{30}\\=\frac{36+35+10}{30}\\=\frac{81}{30}\\=\frac{27}{10}\)
3. \(-\left(\frac{2}{-5}\right) +\left(\frac{3}{4}\right) +\left(\frac{11}{-2}\right)\\= \frac{2}{5}+ \frac{3}{4}-\frac{11}{2}\\=\frac{8}{20}+\frac{15}{20}-\frac{110}{20}\\=\frac{8+15-110}{20}\\=\frac{-87}{20}\)
4. \(+\left(\frac{-9}{-8}\right) -\left(\frac{10}{-5}\right) +\left(\frac{8}{5}\right)\\= \frac{9}{8}+ \frac{10}{5}+\frac{8}{5}\\=\frac{9}{8}+\frac{2}{1}+\frac{8}{5}\\=\frac{45}{40}+\frac{80}{40}+\frac{64}{40}\\=\frac{45+80+64}{40}\\=\frac{189}{40}\)
5. \(-\left(\frac{-6}{-7}\right) -\left(\frac{-9}{6}\right) -\left(\frac{5}{-3}\right)\\= \frac{-6}{7}+ \frac{9}{6}+\frac{5}{3}\\=\frac{-6}{7}+\frac{3}{2}+\frac{5}{3}\\=\frac{-36}{42}+\frac{63}{42}+\frac{70}{42}\\=\frac{-36+63+70}{42}\\=\frac{97}{42}\)
6. \(+\left(\frac{3}{2}\right) -\left(\frac{-7}{-7}\right) +\left(\frac{7}{11}\right)\\= \frac{3}{2}- \frac{7}{7}+\frac{7}{11}\\=\frac{3}{2}-\frac{1}{1}+\frac{7}{11}\\=\frac{33}{22}-\frac{22}{22}+\frac{14}{22}\\=\frac{33-22+14}{22}\\=\frac{25}{22}\)
7. \(+\left(\frac{4}{5}\right) -\left(\frac{10}{-5}\right) -\left(\frac{12}{-2}\right)\\= \frac{4}{5}+ \frac{10}{5}+\frac{12}{2}\\=\frac{4}{5}+\frac{2}{1}+\frac{6}{1}\\=\frac{4+2+6}{5}\\=\frac{12}{5}\)
8. \(+\left(\frac{3}{-2}\right) +\left(\frac{-6}{-7}\right) +\left(\frac{7}{-12}\right)\\= \frac{-3}{2}+ \frac{6}{7}-\frac{7}{12}\\=\frac{-126}{84}+\frac{72}{84}-\frac{49}{84}\\=\frac{-126+72-49}{84}\\=\frac{-103}{84}\)
9. \(-\left(\frac{-6}{5}\right) +\left(\frac{-5}{8}\right) -\left(\frac{6}{8}\right)\\= \frac{6}{5}- \frac{5}{8}-\frac{6}{8}\\=\frac{6}{5}-\frac{5}{8}-\frac{3}{4}\\=\frac{48}{40}-\frac{25}{40}-\frac{30}{40}\\=\frac{48-25-30}{40}\\=\frac{-7}{40}\)
10. \(+\left(\frac{8}{9}\right) -\left(\frac{3}{5}\right) -\left(\frac{-8}{-4}\right)\\= \frac{8}{9}- \frac{3}{5}-\frac{8}{4}\\=\frac{8}{9}-\frac{3}{5}-\frac{2}{1}\\=\frac{40}{45}-\frac{27}{45}-\frac{90}{45}\\=\frac{40-27-90}{45}\\=\frac{-77}{45}\)
11. \(-\left(\frac{-8}{9}\right) +\left(\frac{-9}{6}\right) +\left(\frac{9}{11}\right)\\= \frac{8}{9}- \frac{9}{6}+\frac{9}{11}\\=\frac{8}{9}-\frac{3}{2}+\frac{9}{11}\\=\frac{176}{198}-\frac{297}{198}+\frac{162}{198}\\=\frac{176-297+162}{198}\\=\frac{41}{198}\)
12. \(+\left(\frac{-9}{2}\right) +\left(\frac{10}{8}\right) -\left(\frac{-2}{-11}\right)\\= \frac{-9}{2}+ \frac{10}{8}-\frac{2}{11}\\=\frac{-9}{2}+\frac{5}{4}-\frac{2}{11}\\=\frac{-198}{44}+\frac{55}{44}-\frac{8}{44}\\=\frac{-198+55-8}{44}\\=\frac{-151}{44}\)