Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{-2}\right) -\left(\frac{-6}{-2}\right) +\left(\frac{12}{3}\right)\\= \frac{7}{2}- \frac{6}{2}+\frac{12}{3}\\=\frac{7}{2}-\frac{3}{1}+\frac{4}{1}\\=\frac{7-3+4}{2}\\=\frac{8}{2}\\=\frac{4}{1}\)
2. \(+\left(\frac{6}{7}\right) -\left(\frac{7}{6}\right) +\left(\frac{-5}{5}\right)\\= \frac{6}{7}- \frac{7}{6}-\frac{5}{5}\\=\frac{6}{7}-\frac{7}{6}-\frac{1}{1}\\=\frac{36}{42}-\frac{49}{42}-\frac{42}{42}\\=\frac{36-49-42}{42}\\=\frac{-55}{42}\)
3. \(-\left(\frac{3}{-5}\right) -\left(\frac{5}{-2}\right) +\left(\frac{-5}{-12}\right)\\= \frac{3}{5}+ \frac{5}{2}+\frac{5}{12}\\=\frac{36}{60}+\frac{150}{60}+\frac{25}{60}\\=\frac{36+150+25}{60}\\=\frac{211}{60}\)
4. \(+\left(\frac{-8}{3}\right) -\left(\frac{-5}{-3}\right) -\left(\frac{-6}{4}\right)\\= \frac{-8}{3}- \frac{5}{3}+\frac{6}{4}\\=\frac{-8}{3}-\frac{5}{3}+\frac{3}{2}\\=\frac{-16}{6}-\frac{10}{6}+\frac{9}{6}\\=\frac{-16-10+9}{6}\\=\frac{-17}{6}\)
5. \(-\left(\frac{9}{5}\right) +\left(\frac{8}{8}\right) +\left(\frac{9}{-11}\right)\\= \frac{-9}{5}+ \frac{8}{8}-\frac{9}{11}\\=\frac{-9}{5}+\frac{1}{1}-\frac{9}{11}\\=\frac{-99}{55}+\frac{55}{55}-\frac{45}{55}\\=\frac{-99+55-45}{55}\\=\frac{-89}{55}\)
6. \(+\left(\frac{2}{7}\right) +\left(\frac{6}{9}\right) +\left(\frac{-11}{-7}\right)\\= \frac{2}{7}+ \frac{6}{9}+\frac{11}{7}\\=\frac{2}{7}+\frac{2}{3}+\frac{11}{7}\\=\frac{6}{21}+\frac{14}{21}+\frac{33}{21}\\=\frac{6+14+33}{21}\\=\frac{53}{21}\)
7. \(-\left(\frac{-4}{-7}\right) +\left(\frac{-9}{-9}\right) +\left(\frac{-5}{10}\right)\\= \frac{-4}{7}+ \frac{9}{9}-\frac{5}{10}\\=\frac{-4}{7}+\frac{1}{1}-\frac{1}{2}\\=\frac{-8}{14}+\frac{14}{14}-\frac{7}{14}\\=\frac{-8+14-7}{14}\\=\frac{-1}{14}\)
8. \(+\left(\frac{-10}{3}\right) +\left(\frac{-6}{-10}\right) -\left(\frac{-6}{11}\right)\\= \frac{-10}{3}+ \frac{6}{10}+\frac{6}{11}\\=\frac{-10}{3}+\frac{3}{5}+\frac{6}{11}\\=\frac{-550}{165}+\frac{99}{165}+\frac{90}{165}\\=\frac{-550+99+90}{165}\\=\frac{-361}{165}\)
9. \(-\left(\frac{-10}{-7}\right) -\left(\frac{-6}{-7}\right) -\left(\frac{11}{-6}\right)\\= \frac{-10}{7}- \frac{6}{7}+\frac{11}{6}\\=\frac{-60}{42}-\frac{36}{42}+\frac{77}{42}\\=\frac{-60-36+77}{42}\\=\frac{-19}{42}\)
10. \(+\left(\frac{3}{7}\right) -\left(\frac{-8}{-2}\right) -\left(\frac{8}{-10}\right)\\= \frac{3}{7}- \frac{8}{2}+\frac{8}{10}\\=\frac{3}{7}-\frac{4}{1}+\frac{4}{5}\\=\frac{15}{35}-\frac{140}{35}+\frac{28}{35}\\=\frac{15-140+28}{35}\\=\frac{-97}{35}\)
11. \(-\left(\frac{3}{-2}\right) +\left(\frac{7}{-6}\right) -\left(\frac{-8}{-5}\right)\\= \frac{3}{2}- \frac{7}{6}-\frac{8}{5}\\=\frac{45}{30}-\frac{35}{30}-\frac{48}{30}\\=\frac{45-35-48}{30}\\=\frac{-38}{30}\\=\frac{-19}{15}\)
12. \(+\left(\frac{3}{-8}\right) +\left(\frac{-5}{2}\right) +\left(\frac{-9}{-5}\right)\\= \frac{-3}{8}- \frac{5}{2}+\frac{9}{5}\\=\frac{-15}{40}-\frac{100}{40}+\frac{72}{40}\\=\frac{-15-100+72}{40}\\=\frac{-43}{40}\)