Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{6}{-5}\right) -\left(\frac{6}{10}\right) -\left(\frac{10}{7}\right)\\= \frac{6}{5}- \frac{6}{10}-\frac{10}{7}\\=\frac{6}{5}-\frac{3}{5}-\frac{10}{7}\\=\frac{42}{35}-\frac{21}{35}-\frac{50}{35}\\=\frac{42-21-50}{35}\\=\frac{-29}{35}\)
2. \(+\left(\frac{-8}{-9}\right) +\left(\frac{10}{4}\right) -\left(\frac{7}{-9}\right)\\= \frac{8}{9}+ \frac{10}{4}+\frac{7}{9}\\=\frac{8}{9}+\frac{5}{2}+\frac{7}{9}\\=\frac{16}{18}+\frac{45}{18}+\frac{14}{18}\\=\frac{16+45+14}{18}\\=\frac{75}{18}\\=\frac{25}{6}\)
3. \(+\left(\frac{5}{4}\right) -\left(\frac{-3}{6}\right) +\left(\frac{3}{9}\right)\\= \frac{5}{4}+ \frac{3}{6}+\frac{3}{9}\\=\frac{5}{4}+\frac{1}{2}+\frac{1}{3}\\=\frac{15}{12}+\frac{6}{12}+\frac{4}{12}\\=\frac{15+6+4}{12}\\=\frac{25}{12}\)
4. \(+\left(\frac{7}{-4}\right) -\left(\frac{9}{7}\right) +\left(\frac{4}{-10}\right)\\= \frac{-7}{4}- \frac{9}{7}-\frac{4}{10}\\=\frac{-7}{4}-\frac{9}{7}-\frac{2}{5}\\=\frac{-245}{140}-\frac{180}{140}-\frac{56}{140}\\=\frac{-245-180-56}{140}\\=\frac{-481}{140}\)
5. \(+\left(\frac{-4}{3}\right) -\left(\frac{-6}{6}\right) -\left(\frac{-6}{-6}\right)\\= \frac{-4}{3}+ \frac{6}{6}-\frac{6}{6}\\=\frac{-4}{3}+\frac{1}{1}-\frac{1}{1}\\=\frac{-4+1-1}{3}\\=\frac{-4}{3}\)
6. \(-\left(\frac{2}{-3}\right) -\left(\frac{10}{-6}\right) -\left(\frac{4}{3}\right)\\= \frac{2}{3}+ \frac{10}{6}-\frac{4}{3}\\=\frac{2}{3}+\frac{5}{3}-\frac{4}{3}\\=\frac{2+5-4}{3}\\=\frac{3}{3}\\=\frac{1}{1}\)
7. \(+\left(\frac{8}{7}\right) +\left(\frac{-8}{-10}\right) +\left(\frac{6}{-7}\right)\\= \frac{8}{7}+ \frac{8}{10}-\frac{6}{7}\\=\frac{8}{7}+\frac{4}{5}-\frac{6}{7}\\=\frac{40}{35}+\frac{28}{35}-\frac{30}{35}\\=\frac{40+28-30}{35}\\=\frac{38}{35}\)
8. \(+\left(\frac{-2}{-9}\right) -\left(\frac{-3}{7}\right) +\left(\frac{-12}{12}\right)\\= \frac{2}{9}+ \frac{3}{7}-\frac{12}{12}\\=\frac{2}{9}+\frac{3}{7}-\frac{1}{1}\\=\frac{14}{63}+\frac{27}{63}-\frac{63}{63}\\=\frac{14+27-63}{63}\\=\frac{-22}{63}\)
9. \(-\left(\frac{10}{3}\right) -\left(\frac{-6}{-6}\right) -\left(\frac{-11}{6}\right)\\= \frac{-10}{3}- \frac{6}{6}+\frac{11}{6}\\=\frac{-10}{3}-\frac{1}{1}+\frac{11}{6}\\=\frac{-20}{6}-\frac{6}{6}+\frac{11}{6}\\=\frac{-20-6+11}{6}\\=\frac{-15}{6}\\=\frac{-5}{2}\)
10. \(+\left(\frac{6}{5}\right) -\left(\frac{4}{-7}\right) +\left(\frac{5}{6}\right)\\= \frac{6}{5}+ \frac{4}{7}+\frac{5}{6}\\=\frac{252}{210}+\frac{120}{210}+\frac{175}{210}\\=\frac{252+120+175}{210}\\=\frac{547}{210}\)
11. \(+\left(\frac{-10}{-7}\right) +\left(\frac{-7}{6}\right) +\left(\frac{-6}{5}\right)\\= \frac{10}{7}- \frac{7}{6}-\frac{6}{5}\\=\frac{300}{210}-\frac{245}{210}-\frac{252}{210}\\=\frac{300-245-252}{210}\\=\frac{-197}{210}\)
12. \(-\left(\frac{9}{7}\right) +\left(\frac{-10}{-5}\right) +\left(\frac{2}{7}\right)\\= \frac{-9}{7}+ \frac{10}{5}+\frac{2}{7}\\=\frac{-9}{7}+\frac{2}{1}+\frac{2}{7}\\=\frac{-9+2+2}{7}\\=\frac{-5}{7}\)