Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{3}\right) -\left(\frac{-9}{2}\right) +\left(\frac{-10}{8}\right)\\= \frac{-8}{3}+ \frac{9}{2}-\frac{10}{8}\\=\frac{-8}{3}+\frac{9}{2}-\frac{5}{4}\\=\frac{-32}{12}+\frac{54}{12}-\frac{15}{12}\\=\frac{-32+54-15}{12}\\=\frac{7}{12}\)
2. \(+\left(\frac{4}{-3}\right) +\left(\frac{-6}{-3}\right) +\left(\frac{7}{-12}\right)\\= \frac{-4}{3}+ \frac{6}{3}-\frac{7}{12}\\=\frac{-4}{3}+\frac{2}{1}-\frac{7}{12}\\=\frac{-16}{12}+\frac{24}{12}-\frac{7}{12}\\=\frac{-16+24-7}{12}\\=\frac{1}{12}\)
3. \(+\left(\frac{-7}{2}\right) +\left(\frac{5}{2}\right) +\left(\frac{-3}{4}\right)\\= \frac{-7}{2}+ \frac{5}{2}-\frac{3}{4}\\=\frac{-14}{4}+\frac{10}{4}-\frac{3}{4}\\=\frac{-14+10-3}{4}\\=\frac{-7}{4}\)
4. \(+\left(\frac{-5}{-6}\right) +\left(\frac{-5}{-10}\right) -\left(\frac{-7}{-9}\right)\\= \frac{5}{6}+ \frac{5}{10}-\frac{7}{9}\\=\frac{5}{6}+\frac{1}{2}-\frac{7}{9}\\=\frac{15}{18}+\frac{9}{18}-\frac{14}{18}\\=\frac{15+9-14}{18}\\=\frac{10}{18}\\=\frac{5}{9}\)
5. \(-\left(\frac{-4}{-9}\right) -\left(\frac{10}{-8}\right) -\left(\frac{-5}{10}\right)\\= \frac{-4}{9}+ \frac{10}{8}+\frac{5}{10}\\=\frac{-4}{9}+\frac{5}{4}+\frac{1}{2}\\=\frac{-16}{36}+\frac{45}{36}+\frac{18}{36}\\=\frac{-16+45+18}{36}\\=\frac{47}{36}\)
6. \(-\left(\frac{5}{2}\right) -\left(\frac{-4}{-4}\right) -\left(\frac{-7}{-8}\right)\\= \frac{-5}{2}- \frac{4}{4}-\frac{7}{8}\\=\frac{-5}{2}-\frac{1}{1}-\frac{7}{8}\\=\frac{-20}{8}-\frac{8}{8}-\frac{7}{8}\\=\frac{-20-8-7}{8}\\=\frac{-35}{8}\)
7. \(-\left(\frac{8}{-5}\right) +\left(\frac{-4}{-2}\right) +\left(\frac{-6}{-5}\right)\\= \frac{8}{5}+ \frac{4}{2}+\frac{6}{5}\\=\frac{8}{5}+\frac{2}{1}+\frac{6}{5}\\=\frac{8+2+6}{5}\\=\frac{16}{5}\)
8. \(+\left(\frac{-4}{-3}\right) +\left(\frac{8}{-2}\right) +\left(\frac{-4}{-6}\right)\\= \frac{4}{3}- \frac{8}{2}+\frac{4}{6}\\=\frac{4}{3}-\frac{4}{1}+\frac{2}{3}\\=\frac{4-4+2}{3}\\=\frac{2}{3}\)
9. \(+\left(\frac{6}{-5}\right) +\left(\frac{-9}{7}\right) -\left(\frac{-7}{-12}\right)\\= \frac{-6}{5}- \frac{9}{7}-\frac{7}{12}\\=\frac{-504}{420}-\frac{540}{420}-\frac{245}{420}\\=\frac{-504-540-245}{420}\\=\frac{-1289}{420}\)
10. \(-\left(\frac{8}{5}\right) +\left(\frac{-10}{-9}\right) +\left(\frac{9}{-3}\right)\\= \frac{-8}{5}+ \frac{10}{9}-\frac{9}{3}\\=\frac{-8}{5}+\frac{10}{9}-\frac{3}{1}\\=\frac{-72}{45}+\frac{50}{45}-\frac{135}{45}\\=\frac{-72+50-135}{45}\\=\frac{-157}{45}\)
11. \(-\left(\frac{-5}{-8}\right) +\left(\frac{-7}{-4}\right) -\left(\frac{-3}{2}\right)\\= \frac{-5}{8}+ \frac{7}{4}+\frac{3}{2}\\=\frac{-5+7+3}{8}\\=\frac{5}{8}\)
12. \(-\left(\frac{-3}{4}\right) +\left(\frac{4}{9}\right) +\left(\frac{-9}{11}\right)\\= \frac{3}{4}+ \frac{4}{9}-\frac{9}{11}\\=\frac{297}{396}+\frac{176}{396}-\frac{324}{396}\\=\frac{297+176-324}{396}\\=\frac{149}{396}\)