Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{-2}\right) -\left(\frac{6}{5}\right) +\left(\frac{12}{8}\right)\\= \frac{-3}{2}- \frac{6}{5}+\frac{12}{8}\\=\frac{-3}{2}-\frac{6}{5}+\frac{3}{2}\\=\frac{-15}{10}-\frac{12}{10}+\frac{15}{10}\\=\frac{-15-12+15}{10}\\=\frac{-12}{10}\\=\frac{-6}{5}\)
2. \(-\left(\frac{-3}{2}\right) +\left(\frac{7}{-9}\right) +\left(\frac{2}{6}\right)\\= \frac{3}{2}- \frac{7}{9}+\frac{2}{6}\\=\frac{3}{2}-\frac{7}{9}+\frac{1}{3}\\=\frac{27}{18}-\frac{14}{18}+\frac{6}{18}\\=\frac{27-14+6}{18}\\=\frac{19}{18}\)
3. \(-\left(\frac{6}{-7}\right) +\left(\frac{-5}{-4}\right) +\left(\frac{-11}{-6}\right)\\= \frac{6}{7}+ \frac{5}{4}+\frac{11}{6}\\=\frac{72}{84}+\frac{105}{84}+\frac{154}{84}\\=\frac{72+105+154}{84}\\=\frac{331}{84}\)
4. \(+\left(\frac{-2}{-9}\right) -\left(\frac{-5}{-7}\right) -\left(\frac{-12}{-4}\right)\\= \frac{2}{9}- \frac{5}{7}-\frac{12}{4}\\=\frac{2}{9}-\frac{5}{7}-\frac{3}{1}\\=\frac{14}{63}-\frac{45}{63}-\frac{189}{63}\\=\frac{14-45-189}{63}\\=\frac{-220}{63}\)
5. \(-\left(\frac{-6}{5}\right) -\left(\frac{-9}{5}\right) -\left(\frac{10}{-7}\right)\\= \frac{6}{5}+ \frac{9}{5}+\frac{10}{7}\\=\frac{42}{35}+\frac{63}{35}+\frac{50}{35}\\=\frac{42+63+50}{35}\\=\frac{155}{35}\\=\frac{31}{7}\)
6. \(+\left(\frac{-3}{-2}\right) +\left(\frac{4}{2}\right) +\left(\frac{-6}{-10}\right)\\= \frac{3}{2}+ \frac{4}{2}+\frac{6}{10}\\=\frac{3}{2}+\frac{2}{1}+\frac{3}{5}\\=\frac{15}{10}+\frac{20}{10}+\frac{6}{10}\\=\frac{15+20+6}{10}\\=\frac{41}{10}\)
7. \(+\left(\frac{8}{-3}\right) -\left(\frac{3}{2}\right) -\left(\frac{3}{-12}\right)\\= \frac{-8}{3}- \frac{3}{2}+\frac{3}{12}\\=\frac{-8}{3}-\frac{3}{2}+\frac{1}{4}\\=\frac{-32}{12}-\frac{18}{12}+\frac{3}{12}\\=\frac{-32-18+3}{12}\\=\frac{-47}{12}\)
8. \(-\left(\frac{-7}{-6}\right) -\left(\frac{-8}{-10}\right) +\left(\frac{-4}{11}\right)\\= \frac{-7}{6}- \frac{8}{10}-\frac{4}{11}\\=\frac{-7}{6}-\frac{4}{5}-\frac{4}{11}\\=\frac{-385}{330}-\frac{264}{330}-\frac{120}{330}\\=\frac{-385-264-120}{330}\\=\frac{-769}{330}\)
9. \(+\left(\frac{-2}{-3}\right) -\left(\frac{-3}{-7}\right) -\left(\frac{2}{10}\right)\\= \frac{2}{3}- \frac{3}{7}-\frac{2}{10}\\=\frac{2}{3}-\frac{3}{7}-\frac{1}{5}\\=\frac{70}{105}-\frac{45}{105}-\frac{21}{105}\\=\frac{70-45-21}{105}\\=\frac{4}{105}\)
10. \(-\left(\frac{6}{-5}\right) -\left(\frac{-4}{7}\right) +\left(\frac{-10}{-12}\right)\\= \frac{6}{5}+ \frac{4}{7}+\frac{10}{12}\\=\frac{6}{5}+\frac{4}{7}+\frac{5}{6}\\=\frac{252}{210}+\frac{120}{210}+\frac{175}{210}\\=\frac{252+120+175}{210}\\=\frac{547}{210}\)
11. \(+\left(\frac{3}{-2}\right) +\left(\frac{-5}{7}\right) +\left(\frac{-2}{9}\right)\\= \frac{-3}{2}- \frac{5}{7}-\frac{2}{9}\\=\frac{-189}{126}-\frac{90}{126}-\frac{28}{126}\\=\frac{-189-90-28}{126}\\=\frac{-307}{126}\)
12. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-4}{-5}\right) +\left(\frac{4}{-5}\right)\\= \frac{-6}{5}+ \frac{4}{5}-\frac{4}{5}\\=\frac{-6+4-4}{5}\\=\frac{-6}{5}\)