Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{-5}\right) -\left(\frac{5}{-8}\right) -\left(\frac{5}{12}\right)\\= \frac{-6}{5}+ \frac{5}{8}-\frac{5}{12}\\=\frac{-144}{120}+\frac{75}{120}-\frac{50}{120}\\=\frac{-144+75-50}{120}\\=\frac{-119}{120}\)
2. \(-\left(\frac{-9}{-7}\right) -\left(\frac{-4}{-5}\right) -\left(\frac{-8}{4}\right)\\= \frac{-9}{7}- \frac{4}{5}+\frac{8}{4}\\=\frac{-9}{7}-\frac{4}{5}+\frac{2}{1}\\=\frac{-45}{35}-\frac{28}{35}+\frac{70}{35}\\=\frac{-45-28+70}{35}\\=\frac{-3}{35}\)
3. \(-\left(\frac{-3}{7}\right) +\left(\frac{-4}{6}\right) -\left(\frac{7}{3}\right)\\= \frac{3}{7}- \frac{4}{6}-\frac{7}{3}\\=\frac{3}{7}-\frac{2}{3}-\frac{7}{3}\\=\frac{9}{21}-\frac{14}{21}-\frac{49}{21}\\=\frac{9-14-49}{21}\\=\frac{-54}{21}\\=\frac{-18}{7}\)
4. \(+\left(\frac{-5}{9}\right) +\left(\frac{2}{-2}\right) -\left(\frac{11}{-12}\right)\\= \frac{-5}{9}- \frac{2}{2}+\frac{11}{12}\\=\frac{-5}{9}-\frac{1}{1}+\frac{11}{12}\\=\frac{-20}{36}-\frac{36}{36}+\frac{33}{36}\\=\frac{-20-36+33}{36}\\=\frac{-23}{36}\)
5. \(+\left(\frac{5}{7}\right) -\left(\frac{-5}{-7}\right) -\left(\frac{-10}{-12}\right)\\= \frac{5}{7}- \frac{5}{7}-\frac{10}{12}\\=\frac{5}{7}-\frac{5}{7}-\frac{5}{6}\\=\frac{30}{42}-\frac{30}{42}-\frac{35}{42}\\=\frac{30-30-35}{42}\\=\frac{-35}{42}\\=\frac{-5}{6}\)
6. \(+\left(\frac{-5}{2}\right) +\left(\frac{-3}{9}\right) +\left(\frac{9}{-12}\right)\\= \frac{-5}{2}- \frac{3}{9}-\frac{9}{12}\\=\frac{-5}{2}-\frac{1}{3}-\frac{3}{4}\\=\frac{-30}{12}-\frac{4}{12}-\frac{9}{12}\\=\frac{-30-4-9}{12}\\=\frac{-43}{12}\)
7. \(-\left(\frac{6}{5}\right) +\left(\frac{-5}{-2}\right) -\left(\frac{5}{10}\right)\\= \frac{-6}{5}+ \frac{5}{2}-\frac{5}{10}\\=\frac{-6}{5}+\frac{5}{2}-\frac{1}{2}\\=\frac{-12}{10}+\frac{25}{10}-\frac{5}{10}\\=\frac{-12+25-5}{10}\\=\frac{8}{10}\\=\frac{4}{5}\)
8. \(+\left(\frac{-7}{-8}\right) -\left(\frac{3}{8}\right) +\left(\frac{3}{-6}\right)\\= \frac{7}{8}- \frac{3}{8}-\frac{3}{6}\\=\frac{7}{8}-\frac{3}{8}-\frac{1}{2}\\=\frac{7-3-1}{8}\\=\frac{3}{8}\)
9. \(-\left(\frac{-10}{-3}\right) +\left(\frac{9}{-3}\right) +\left(\frac{-3}{-3}\right)\\= \frac{-10}{3}- \frac{9}{3}+\frac{3}{3}\\=\frac{-10}{3}-\frac{3}{1}+\frac{1}{1}\\=\frac{-10-3+1}{3}\\=\frac{-12}{3}\\=\frac{-4}{1}\)
10. \(+\left(\frac{5}{6}\right) -\left(\frac{5}{9}\right) +\left(\frac{10}{-7}\right)\\= \frac{5}{6}- \frac{5}{9}-\frac{10}{7}\\=\frac{105}{126}-\frac{70}{126}-\frac{180}{126}\\=\frac{105-70-180}{126}\\=\frac{-145}{126}\)
11. \(-\left(\frac{2}{3}\right) +\left(\frac{-6}{8}\right) -\left(\frac{-12}{-6}\right)\\= \frac{-2}{3}- \frac{6}{8}-\frac{12}{6}\\=\frac{-2}{3}-\frac{3}{4}-\frac{2}{1}\\=\frac{-8}{12}-\frac{9}{12}-\frac{24}{12}\\=\frac{-8-9-24}{12}\\=\frac{-41}{12}\)
12. \(+\left(\frac{-8}{7}\right) -\left(\frac{4}{9}\right) +\left(\frac{7}{7}\right)\\= \frac{-8}{7}- \frac{4}{9}+\frac{7}{7}\\=\frac{-8}{7}-\frac{4}{9}+\frac{1}{1}\\=\frac{-72}{63}-\frac{28}{63}+\frac{63}{63}\\=\frac{-72-28+63}{63}\\=\frac{-37}{63}\)