Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{-9}\right) -\left(\frac{-2}{-6}\right) +\left(\frac{8}{7}\right)\\= \frac{-10}{9}- \frac{2}{6}+\frac{8}{7}\\=\frac{-10}{9}-\frac{1}{3}+\frac{8}{7}\\=\frac{-70}{63}-\frac{21}{63}+\frac{72}{63}\\=\frac{-70-21+72}{63}\\=\frac{-19}{63}\)
2. \(-\left(\frac{8}{3}\right) +\left(\frac{8}{6}\right) +\left(\frac{4}{-12}\right)\\= \frac{-8}{3}+ \frac{8}{6}-\frac{4}{12}\\=\frac{-8}{3}+\frac{4}{3}-\frac{1}{3}\\=\frac{-8+4-1}{3}\\=\frac{-5}{3}\)
3. \(+\left(\frac{-10}{7}\right) +\left(\frac{4}{5}\right) -\left(\frac{-6}{-8}\right)\\= \frac{-10}{7}+ \frac{4}{5}-\frac{6}{8}\\=\frac{-10}{7}+\frac{4}{5}-\frac{3}{4}\\=\frac{-200}{140}+\frac{112}{140}-\frac{105}{140}\\=\frac{-200+112-105}{140}\\=\frac{-193}{140}\)
4. \(+\left(\frac{2}{-3}\right) +\left(\frac{7}{4}\right) +\left(\frac{-8}{-10}\right)\\= \frac{-2}{3}+ \frac{7}{4}+\frac{8}{10}\\=\frac{-2}{3}+\frac{7}{4}+\frac{4}{5}\\=\frac{-40}{60}+\frac{105}{60}+\frac{48}{60}\\=\frac{-40+105+48}{60}\\=\frac{113}{60}\)
5. \(-\left(\frac{-3}{-2}\right) +\left(\frac{-9}{-2}\right) +\left(\frac{10}{8}\right)\\= \frac{-3}{2}+ \frac{9}{2}+\frac{10}{8}\\=\frac{-3}{2}+\frac{9}{2}+\frac{5}{4}\\=\frac{-6}{4}+\frac{18}{4}+\frac{5}{4}\\=\frac{-6+18+5}{4}\\=\frac{17}{4}\)
6. \(+\left(\frac{-3}{7}\right) +\left(\frac{5}{10}\right) -\left(\frac{-11}{4}\right)\\= \frac{-3}{7}+ \frac{5}{10}+\frac{11}{4}\\=\frac{-3}{7}+\frac{1}{2}+\frac{11}{4}\\=\frac{-12}{28}+\frac{14}{28}+\frac{77}{28}\\=\frac{-12+14+77}{28}\\=\frac{79}{28}\)
7. \(-\left(\frac{9}{-8}\right) +\left(\frac{-9}{2}\right) -\left(\frac{-3}{-11}\right)\\= \frac{9}{8}- \frac{9}{2}-\frac{3}{11}\\=\frac{99}{88}-\frac{396}{88}-\frac{24}{88}\\=\frac{99-396-24}{88}\\=\frac{-321}{88}\)
8. \(-\left(\frac{-4}{9}\right) +\left(\frac{6}{8}\right) +\left(\frac{5}{12}\right)\\= \frac{4}{9}+ \frac{6}{8}+\frac{5}{12}\\=\frac{4}{9}+\frac{3}{4}+\frac{5}{12}\\=\frac{16}{36}+\frac{27}{36}+\frac{15}{36}\\=\frac{16+27+15}{36}\\=\frac{58}{36}\\=\frac{29}{18}\)
9. \(-\left(\frac{-7}{-2}\right) -\left(\frac{6}{5}\right) -\left(\frac{6}{-8}\right)\\= \frac{-7}{2}- \frac{6}{5}+\frac{6}{8}\\=\frac{-7}{2}-\frac{6}{5}+\frac{3}{4}\\=\frac{-70}{20}-\frac{24}{20}+\frac{15}{20}\\=\frac{-70-24+15}{20}\\=\frac{-79}{20}\)
10. \(+\left(\frac{2}{3}\right) -\left(\frac{6}{-2}\right) +\left(\frac{2}{-4}\right)\\= \frac{2}{3}+ \frac{6}{2}-\frac{2}{4}\\=\frac{2}{3}+\frac{3}{1}-\frac{1}{2}\\=\frac{4}{6}+\frac{18}{6}-\frac{3}{6}\\=\frac{4+18-3}{6}\\=\frac{19}{6}\)
11. \(+\left(\frac{-5}{-2}\right) -\left(\frac{-3}{-6}\right) +\left(\frac{2}{8}\right)\\= \frac{5}{2}- \frac{3}{6}+\frac{2}{8}\\=\frac{5}{2}-\frac{1}{2}+\frac{1}{4}\\=\frac{10}{4}-\frac{2}{4}+\frac{1}{4}\\=\frac{10-2+1}{4}\\=\frac{9}{4}\)
12. \(-\left(\frac{6}{5}\right) -\left(\frac{-8}{7}\right) -\left(\frac{-5}{-12}\right)\\= \frac{-6}{5}+ \frac{8}{7}-\frac{5}{12}\\=\frac{-504}{420}+\frac{480}{420}-\frac{175}{420}\\=\frac{-504+480-175}{420}\\=\frac{-199}{420}\)