Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{-9}\right) -\left(\frac{10}{-2}\right) -\left(\frac{7}{4}\right)\\= \frac{-2}{9}+ \frac{10}{2}-\frac{7}{4}\\=\frac{-2}{9}+\frac{5}{1}-\frac{7}{4}\\=\frac{-8}{36}+\frac{180}{36}-\frac{63}{36}\\=\frac{-8+180-63}{36}\\=\frac{109}{36}\)
2. \(+\left(\frac{5}{-8}\right) -\left(\frac{-8}{8}\right) -\left(\frac{10}{-2}\right)\\= \frac{-5}{8}+ \frac{8}{8}+\frac{10}{2}\\=\frac{-5}{8}+\frac{1}{1}+\frac{5}{1}\\=\frac{-5+1+5}{8}\\=\frac{1}{8}\)
3. \(-\left(\frac{8}{-9}\right) -\left(\frac{-5}{-5}\right) -\left(\frac{9}{-7}\right)\\= \frac{8}{9}- \frac{5}{5}+\frac{9}{7}\\=\frac{8}{9}-\frac{1}{1}+\frac{9}{7}\\=\frac{56}{63}-\frac{63}{63}+\frac{81}{63}\\=\frac{56-63+81}{63}\\=\frac{74}{63}\)
4. \(+\left(\frac{-3}{7}\right) +\left(\frac{-5}{-2}\right) +\left(\frac{-10}{-8}\right)\\= \frac{-3}{7}+ \frac{5}{2}+\frac{10}{8}\\=\frac{-3}{7}+\frac{5}{2}+\frac{5}{4}\\=\frac{-12}{28}+\frac{70}{28}+\frac{35}{28}\\=\frac{-12+70+35}{28}\\=\frac{93}{28}\)
5. \(+\left(\frac{-2}{-5}\right) -\left(\frac{4}{9}\right) -\left(\frac{-4}{7}\right)\\= \frac{2}{5}- \frac{4}{9}+\frac{4}{7}\\=\frac{126}{315}-\frac{140}{315}+\frac{180}{315}\\=\frac{126-140+180}{315}\\=\frac{166}{315}\)
6. \(-\left(\frac{3}{2}\right) -\left(\frac{10}{-9}\right) -\left(\frac{5}{5}\right)\\= \frac{-3}{2}+ \frac{10}{9}-\frac{5}{5}\\=\frac{-3}{2}+\frac{10}{9}-\frac{1}{1}\\=\frac{-27}{18}+\frac{20}{18}-\frac{18}{18}\\=\frac{-27+20-18}{18}\\=\frac{-25}{18}\)
7. \(-\left(\frac{6}{5}\right) -\left(\frac{8}{5}\right) +\left(\frac{4}{2}\right)\\= \frac{-6}{5}- \frac{8}{5}+\frac{4}{2}\\=\frac{-6}{5}-\frac{8}{5}+\frac{2}{1}\\=\frac{-6-8+2}{5}\\=\frac{-12}{5}\)
8. \(-\left(\frac{9}{2}\right) -\left(\frac{-4}{-3}\right) -\left(\frac{5}{-2}\right)\\= \frac{-9}{2}- \frac{4}{3}+\frac{5}{2}\\=\frac{-27}{6}-\frac{8}{6}+\frac{15}{6}\\=\frac{-27-8+15}{6}\\=\frac{-20}{6}\\=\frac{-10}{3}\)
9. \(+\left(\frac{-8}{3}\right) -\left(\frac{5}{3}\right) -\left(\frac{11}{-3}\right)\\= \frac{-8}{3}- \frac{5}{3}+\frac{11}{3}\\=\frac{-8-5+11}{3}\\=\frac{-2}{3}\)
10. \(-\left(\frac{-5}{-6}\right) +\left(\frac{-8}{5}\right) -\left(\frac{12}{6}\right)\\= \frac{-5}{6}- \frac{8}{5}-\frac{12}{6}\\=\frac{-5}{6}-\frac{8}{5}-\frac{2}{1}\\=\frac{-25}{30}-\frac{48}{30}-\frac{60}{30}\\=\frac{-25-48-60}{30}\\=\frac{-133}{30}\)
11. \(-\left(\frac{-6}{-7}\right) -\left(\frac{-3}{9}\right) -\left(\frac{3}{8}\right)\\= \frac{-6}{7}+ \frac{3}{9}-\frac{3}{8}\\=\frac{-6}{7}+\frac{1}{3}-\frac{3}{8}\\=\frac{-144}{168}+\frac{56}{168}-\frac{63}{168}\\=\frac{-144+56-63}{168}\\=\frac{-151}{168}\)
12. \(+\left(\frac{3}{-4}\right) +\left(\frac{4}{3}\right) +\left(\frac{8}{-4}\right)\\= \frac{-3}{4}+ \frac{4}{3}-\frac{8}{4}\\=\frac{-3}{4}+\frac{4}{3}-\frac{2}{1}\\=\frac{-9}{12}+\frac{16}{12}-\frac{24}{12}\\=\frac{-9+16-24}{12}\\=\frac{-17}{12}\)