Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{-7}\right) +\left(\frac{-7}{-6}\right) -\left(\frac{-12}{11}\right)\\= \frac{-4}{7}+ \frac{7}{6}+\frac{12}{11}\\=\frac{-264}{462}+\frac{539}{462}+\frac{504}{462}\\=\frac{-264+539+504}{462}\\=\frac{779}{462}\)
2. \(-\left(\frac{7}{8}\right) -\left(\frac{-2}{-3}\right) -\left(\frac{-4}{-2}\right)\\= \frac{-7}{8}- \frac{2}{3}-\frac{4}{2}\\=\frac{-7}{8}-\frac{2}{3}-\frac{2}{1}\\=\frac{-21}{24}-\frac{16}{24}-\frac{48}{24}\\=\frac{-21-16-48}{24}\\=\frac{-85}{24}\)
3. \(-\left(\frac{8}{5}\right) -\left(\frac{5}{4}\right) -\left(\frac{-12}{6}\right)\\= \frac{-8}{5}- \frac{5}{4}+\frac{12}{6}\\=\frac{-8}{5}-\frac{5}{4}+\frac{2}{1}\\=\frac{-32}{20}-\frac{25}{20}+\frac{40}{20}\\=\frac{-32-25+40}{20}\\=\frac{-17}{20}\)
4. \(-\left(\frac{7}{2}\right) +\left(\frac{-3}{-6}\right) -\left(\frac{-12}{2}\right)\\= \frac{-7}{2}+ \frac{3}{6}+\frac{12}{2}\\=\frac{-7}{2}+\frac{1}{2}+\frac{6}{1}\\=\frac{-7+1+6}{2}\\=\frac{0}{2}\\=\frac{0}{1}\)
5. \(-\left(\frac{4}{-3}\right) +\left(\frac{4}{3}\right) +\left(\frac{5}{-9}\right)\\= \frac{4}{3}+ \frac{4}{3}-\frac{5}{9}\\=\frac{12}{9}+\frac{12}{9}-\frac{5}{9}\\=\frac{12+12-5}{9}\\=\frac{19}{9}\)
6. \(+\left(\frac{10}{-3}\right) -\left(\frac{3}{-10}\right) -\left(\frac{6}{-5}\right)\\= \frac{-10}{3}+ \frac{3}{10}+\frac{6}{5}\\=\frac{-100}{30}+\frac{9}{30}+\frac{36}{30}\\=\frac{-100+9+36}{30}\\=\frac{-55}{30}\\=\frac{-11}{6}\)
7. \(-\left(\frac{-3}{7}\right) +\left(\frac{7}{2}\right) +\left(\frac{-12}{7}\right)\\= \frac{3}{7}+ \frac{7}{2}-\frac{12}{7}\\=\frac{6}{14}+\frac{49}{14}-\frac{24}{14}\\=\frac{6+49-24}{14}\\=\frac{31}{14}\)
8. \(-\left(\frac{-6}{-7}\right) -\left(\frac{-8}{-6}\right) +\left(\frac{3}{11}\right)\\= \frac{-6}{7}- \frac{8}{6}+\frac{3}{11}\\=\frac{-6}{7}-\frac{4}{3}+\frac{3}{11}\\=\frac{-198}{231}-\frac{308}{231}+\frac{63}{231}\\=\frac{-198-308+63}{231}\\=\frac{-443}{231}\)
9. \(+\left(\frac{-4}{-3}\right) +\left(\frac{10}{-6}\right) +\left(\frac{9}{-5}\right)\\= \frac{4}{3}- \frac{10}{6}-\frac{9}{5}\\=\frac{4}{3}-\frac{5}{3}-\frac{9}{5}\\=\frac{20}{15}-\frac{25}{15}-\frac{27}{15}\\=\frac{20-25-27}{15}\\=\frac{-32}{15}\)
10. \(-\left(\frac{-9}{4}\right) -\left(\frac{-9}{8}\right) -\left(\frac{2}{12}\right)\\= \frac{9}{4}+ \frac{9}{8}-\frac{2}{12}\\=\frac{9}{4}+\frac{9}{8}-\frac{1}{6}\\=\frac{54}{24}+\frac{27}{24}-\frac{4}{24}\\=\frac{54+27-4}{24}\\=\frac{77}{24}\)
11. \(-\left(\frac{-8}{-7}\right) -\left(\frac{9}{8}\right) +\left(\frac{8}{-10}\right)\\= \frac{-8}{7}- \frac{9}{8}-\frac{8}{10}\\=\frac{-8}{7}-\frac{9}{8}-\frac{4}{5}\\=\frac{-320}{280}-\frac{315}{280}-\frac{224}{280}\\=\frac{-320-315-224}{280}\\=\frac{-859}{280}\)
12. \(-\left(\frac{-2}{3}\right) +\left(\frac{9}{-8}\right) +\left(\frac{9}{-10}\right)\\= \frac{2}{3}- \frac{9}{8}-\frac{9}{10}\\=\frac{80}{120}-\frac{135}{120}-\frac{108}{120}\\=\frac{80-135-108}{120}\\=\frac{-163}{120}\)