Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{-4}\right) -\left(\frac{5}{2}\right) +\left(\frac{11}{12}\right)\\= \frac{7}{4}- \frac{5}{2}+\frac{11}{12}\\=\frac{21}{12}-\frac{30}{12}+\frac{11}{12}\\=\frac{21-30+11}{12}\\=\frac{2}{12}\\=\frac{1}{6}\)
2. \(+\left(\frac{-4}{3}\right) +\left(\frac{-10}{-6}\right) +\left(\frac{3}{12}\right)\\= \frac{-4}{3}+ \frac{10}{6}+\frac{3}{12}\\=\frac{-4}{3}+\frac{5}{3}+\frac{1}{4}\\=\frac{-16}{12}+\frac{20}{12}+\frac{3}{12}\\=\frac{-16+20+3}{12}\\=\frac{7}{12}\)
3. \(+\left(\frac{-4}{-7}\right) -\left(\frac{-2}{9}\right) -\left(\frac{-3}{12}\right)\\= \frac{4}{7}+ \frac{2}{9}+\frac{3}{12}\\=\frac{4}{7}+\frac{2}{9}+\frac{1}{4}\\=\frac{144}{252}+\frac{56}{252}+\frac{63}{252}\\=\frac{144+56+63}{252}\\=\frac{263}{252}\)
4. \(-\left(\frac{-4}{-3}\right) +\left(\frac{2}{-6}\right) +\left(\frac{-3}{2}\right)\\= \frac{-4}{3}- \frac{2}{6}-\frac{3}{2}\\=\frac{-4}{3}-\frac{1}{3}-\frac{3}{2}\\=\frac{-8}{6}-\frac{2}{6}-\frac{9}{6}\\=\frac{-8-2-9}{6}\\=\frac{-19}{6}\)
5. \(+\left(\frac{-3}{8}\right) +\left(\frac{-10}{-4}\right) +\left(\frac{-3}{-6}\right)\\= \frac{-3}{8}+ \frac{10}{4}+\frac{3}{6}\\=\frac{-3}{8}+\frac{5}{2}+\frac{1}{2}\\=\frac{-3+5+1}{8}\\=\frac{3}{8}\)
6. \(-\left(\frac{-9}{4}\right) -\left(\frac{-9}{-4}\right) -\left(\frac{2}{-12}\right)\\= \frac{9}{4}- \frac{9}{4}+\frac{2}{12}\\=\frac{9}{4}-\frac{9}{4}+\frac{1}{6}\\=\frac{27}{12}-\frac{27}{12}+\frac{2}{12}\\=\frac{27-27+2}{12}\\=\frac{2}{12}\\=\frac{1}{6}\)
7. \(-\left(\frac{-4}{3}\right) +\left(\frac{5}{5}\right) -\left(\frac{3}{6}\right)\\= \frac{4}{3}+ \frac{5}{5}-\frac{3}{6}\\=\frac{4}{3}+\frac{1}{1}-\frac{1}{2}\\=\frac{8}{6}+\frac{6}{6}-\frac{3}{6}\\=\frac{8+6-3}{6}\\=\frac{11}{6}\)
8. \(-\left(\frac{8}{7}\right) +\left(\frac{-7}{9}\right) -\left(\frac{9}{4}\right)\\= \frac{-8}{7}- \frac{7}{9}-\frac{9}{4}\\=\frac{-288}{252}-\frac{196}{252}-\frac{567}{252}\\=\frac{-288-196-567}{252}\\=\frac{-1051}{252}\)
9. \(-\left(\frac{7}{-2}\right) -\left(\frac{-10}{-10}\right) +\left(\frac{7}{-4}\right)\\= \frac{7}{2}- \frac{10}{10}-\frac{7}{4}\\=\frac{7}{2}-\frac{1}{1}-\frac{7}{4}\\=\frac{14}{4}-\frac{4}{4}-\frac{7}{4}\\=\frac{14-4-7}{4}\\=\frac{3}{4}\)
10. \(-\left(\frac{-8}{5}\right) -\left(\frac{10}{3}\right) -\left(\frac{-11}{-9}\right)\\= \frac{8}{5}- \frac{10}{3}-\frac{11}{9}\\=\frac{72}{45}-\frac{150}{45}-\frac{55}{45}\\=\frac{72-150-55}{45}\\=\frac{-133}{45}\)
11. \(+\left(\frac{6}{-5}\right) +\left(\frac{5}{8}\right) -\left(\frac{-7}{3}\right)\\= \frac{-6}{5}+ \frac{5}{8}+\frac{7}{3}\\=\frac{-144}{120}+\frac{75}{120}+\frac{280}{120}\\=\frac{-144+75+280}{120}\\=\frac{211}{120}\)
12. \(+\left(\frac{6}{-5}\right) +\left(\frac{-7}{2}\right) +\left(\frac{-11}{-7}\right)\\= \frac{-6}{5}- \frac{7}{2}+\frac{11}{7}\\=\frac{-84}{70}-\frac{245}{70}+\frac{110}{70}\\=\frac{-84-245+110}{70}\\=\frac{-219}{70}\)