Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{3}\right) -\left(\frac{-4}{-8}\right) +\left(\frac{-12}{-11}\right)\\= \frac{-5}{3}- \frac{4}{8}+\frac{12}{11}\\=\frac{-5}{3}-\frac{1}{2}+\frac{12}{11}\\=\frac{-110}{66}-\frac{33}{66}+\frac{72}{66}\\=\frac{-110-33+72}{66}\\=\frac{-71}{66}\)
2. \(+\left(\frac{4}{3}\right) +\left(\frac{-4}{9}\right) +\left(\frac{-12}{12}\right)\\= \frac{4}{3}- \frac{4}{9}-\frac{12}{12}\\=\frac{4}{3}-\frac{4}{9}-\frac{1}{1}\\=\frac{12}{9}-\frac{4}{9}-\frac{9}{9}\\=\frac{12-4-9}{9}\\=\frac{-1}{9}\)
3. \(+\left(\frac{-5}{4}\right) +\left(\frac{-6}{8}\right) +\left(\frac{8}{7}\right)\\= \frac{-5}{4}- \frac{6}{8}+\frac{8}{7}\\=\frac{-5}{4}-\frac{3}{4}+\frac{8}{7}\\=\frac{-35}{28}-\frac{21}{28}+\frac{32}{28}\\=\frac{-35-21+32}{28}\\=\frac{-24}{28}\\=\frac{-6}{7}\)
4. \(-\left(\frac{9}{-7}\right) -\left(\frac{-7}{-8}\right) +\left(\frac{-4}{-12}\right)\\= \frac{9}{7}- \frac{7}{8}+\frac{4}{12}\\=\frac{9}{7}-\frac{7}{8}+\frac{1}{3}\\=\frac{216}{168}-\frac{147}{168}+\frac{56}{168}\\=\frac{216-147+56}{168}\\=\frac{125}{168}\)
5. \(+\left(\frac{8}{3}\right) +\left(\frac{2}{-5}\right) -\left(\frac{-3}{-11}\right)\\= \frac{8}{3}- \frac{2}{5}-\frac{3}{11}\\=\frac{440}{165}-\frac{66}{165}-\frac{45}{165}\\=\frac{440-66-45}{165}\\=\frac{329}{165}\)
6. \(-\left(\frac{5}{-6}\right) +\left(\frac{3}{5}\right) -\left(\frac{3}{-2}\right)\\= \frac{5}{6}+ \frac{3}{5}+\frac{3}{2}\\=\frac{25}{30}+\frac{18}{30}+\frac{45}{30}\\=\frac{25+18+45}{30}\\=\frac{88}{30}\\=\frac{44}{15}\)
7. \(-\left(\frac{4}{9}\right) -\left(\frac{-6}{-7}\right) -\left(\frac{3}{-4}\right)\\= \frac{-4}{9}- \frac{6}{7}+\frac{3}{4}\\=\frac{-112}{252}-\frac{216}{252}+\frac{189}{252}\\=\frac{-112-216+189}{252}\\=\frac{-139}{252}\)
8. \(-\left(\frac{7}{5}\right) +\left(\frac{-8}{-10}\right) +\left(\frac{-9}{-9}\right)\\= \frac{-7}{5}+ \frac{8}{10}+\frac{9}{9}\\=\frac{-7}{5}+\frac{4}{5}+\frac{1}{1}\\=\frac{-7+4+1}{5}\\=\frac{-2}{5}\)
9. \(+\left(\frac{-6}{-5}\right) +\left(\frac{6}{8}\right) +\left(\frac{4}{-4}\right)\\= \frac{6}{5}+ \frac{6}{8}-\frac{4}{4}\\=\frac{6}{5}+\frac{3}{4}-\frac{1}{1}\\=\frac{24}{20}+\frac{15}{20}-\frac{20}{20}\\=\frac{24+15-20}{20}\\=\frac{19}{20}\)
10. \(-\left(\frac{7}{9}\right) +\left(\frac{-3}{-6}\right) +\left(\frac{-4}{-11}\right)\\= \frac{-7}{9}+ \frac{3}{6}+\frac{4}{11}\\=\frac{-7}{9}+\frac{1}{2}+\frac{4}{11}\\=\frac{-154}{198}+\frac{99}{198}+\frac{72}{198}\\=\frac{-154+99+72}{198}\\=\frac{17}{198}\)
11. \(+\left(\frac{-3}{-8}\right) -\left(\frac{5}{7}\right) -\left(\frac{-12}{4}\right)\\= \frac{3}{8}- \frac{5}{7}+\frac{12}{4}\\=\frac{3}{8}-\frac{5}{7}+\frac{3}{1}\\=\frac{21}{56}-\frac{40}{56}+\frac{168}{56}\\=\frac{21-40+168}{56}\\=\frac{149}{56}\)
12. \(+\left(\frac{10}{7}\right) +\left(\frac{5}{-8}\right) -\left(\frac{-9}{-3}\right)\\= \frac{10}{7}- \frac{5}{8}-\frac{9}{3}\\=\frac{10}{7}-\frac{5}{8}-\frac{3}{1}\\=\frac{80}{56}-\frac{35}{56}-\frac{168}{56}\\=\frac{80-35-168}{56}\\=\frac{-123}{56}\)