Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{2}\right) +\left(\frac{-6}{-3}\right) +\left(\frac{9}{6}\right)\\= \frac{5}{2}+ \frac{6}{3}+\frac{9}{6}\\=\frac{5}{2}+\frac{2}{1}+\frac{3}{2}\\=\frac{5+2+3}{2}\\=\frac{10}{2}\\=\frac{5}{1}\)
2. \(+\left(\frac{5}{-9}\right) -\left(\frac{7}{3}\right) -\left(\frac{3}{-8}\right)\\= \frac{-5}{9}- \frac{7}{3}+\frac{3}{8}\\=\frac{-40}{72}-\frac{168}{72}+\frac{27}{72}\\=\frac{-40-168+27}{72}\\=\frac{-181}{72}\)
3. \(-\left(\frac{2}{3}\right) +\left(\frac{4}{-7}\right) -\left(\frac{10}{8}\right)\\= \frac{-2}{3}- \frac{4}{7}-\frac{10}{8}\\=\frac{-2}{3}-\frac{4}{7}-\frac{5}{4}\\=\frac{-56}{84}-\frac{48}{84}-\frac{105}{84}\\=\frac{-56-48-105}{84}\\=\frac{-209}{84}\)
4. \(-\left(\frac{8}{-7}\right) +\left(\frac{-8}{-3}\right) -\left(\frac{-4}{5}\right)\\= \frac{8}{7}+ \frac{8}{3}+\frac{4}{5}\\=\frac{120}{105}+\frac{280}{105}+\frac{84}{105}\\=\frac{120+280+84}{105}\\=\frac{484}{105}\)
5. \(-\left(\frac{-6}{5}\right) -\left(\frac{-9}{-4}\right) -\left(\frac{6}{11}\right)\\= \frac{6}{5}- \frac{9}{4}-\frac{6}{11}\\=\frac{264}{220}-\frac{495}{220}-\frac{120}{220}\\=\frac{264-495-120}{220}\\=\frac{-351}{220}\)
6. \(+\left(\frac{2}{3}\right) -\left(\frac{3}{2}\right) -\left(\frac{2}{11}\right)\\= \frac{2}{3}- \frac{3}{2}-\frac{2}{11}\\=\frac{44}{66}-\frac{99}{66}-\frac{12}{66}\\=\frac{44-99-12}{66}\\=\frac{-67}{66}\)
7. \(+\left(\frac{-7}{-6}\right) -\left(\frac{5}{9}\right) -\left(\frac{11}{2}\right)\\= \frac{7}{6}- \frac{5}{9}-\frac{11}{2}\\=\frac{21}{18}-\frac{10}{18}-\frac{99}{18}\\=\frac{21-10-99}{18}\\=\frac{-88}{18}\\=\frac{-44}{9}\)
8. \(-\left(\frac{3}{-8}\right) -\left(\frac{-9}{4}\right) -\left(\frac{7}{-8}\right)\\= \frac{3}{8}+ \frac{9}{4}+\frac{7}{8}\\=\frac{3+9+7}{8}\\=\frac{19}{8}\)
9. \(-\left(\frac{-8}{-3}\right) +\left(\frac{-3}{7}\right) +\left(\frac{-3}{-5}\right)\\= \frac{-8}{3}- \frac{3}{7}+\frac{3}{5}\\=\frac{-280}{105}-\frac{45}{105}+\frac{63}{105}\\=\frac{-280-45+63}{105}\\=\frac{-262}{105}\)
10. \(+\left(\frac{-10}{7}\right) -\left(\frac{7}{-4}\right) -\left(\frac{-5}{-12}\right)\\= \frac{-10}{7}+ \frac{7}{4}-\frac{5}{12}\\=\frac{-120}{84}+\frac{147}{84}-\frac{35}{84}\\=\frac{-120+147-35}{84}\\=\frac{-8}{84}\\=\frac{-2}{21}\)
11. \(-\left(\frac{4}{3}\right) -\left(\frac{7}{-9}\right) -\left(\frac{12}{-4}\right)\\= \frac{-4}{3}+ \frac{7}{9}+\frac{12}{4}\\=\frac{-4}{3}+\frac{7}{9}+\frac{3}{1}\\=\frac{-12}{9}+\frac{7}{9}+\frac{27}{9}\\=\frac{-12+7+27}{9}\\=\frac{22}{9}\)
12. \(+\left(\frac{-4}{3}\right) -\left(\frac{6}{-10}\right) -\left(\frac{-10}{5}\right)\\= \frac{-4}{3}+ \frac{6}{10}+\frac{10}{5}\\=\frac{-4}{3}+\frac{3}{5}+\frac{2}{1}\\=\frac{-20}{15}+\frac{9}{15}+\frac{30}{15}\\=\frac{-20+9+30}{15}\\=\frac{19}{15}\)