Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{8}{3}\right) -\left(\frac{8}{8}\right) +\left(\frac{-6}{-3}\right)\\= \frac{8}{3}- \frac{8}{8}+\frac{6}{3}\\=\frac{8}{3}-\frac{1}{1}+\frac{2}{1}\\=\frac{8-1+2}{3}\\=\frac{9}{3}\\=\frac{3}{1}\)
2. \(+\left(\frac{-4}{5}\right) -\left(\frac{-3}{-3}\right) -\left(\frac{-7}{9}\right)\\= \frac{-4}{5}- \frac{3}{3}+\frac{7}{9}\\=\frac{-4}{5}-\frac{1}{1}+\frac{7}{9}\\=\frac{-36}{45}-\frac{45}{45}+\frac{35}{45}\\=\frac{-36-45+35}{45}\\=\frac{-46}{45}\)
3. \(-\left(\frac{4}{9}\right) +\left(\frac{8}{6}\right) +\left(\frac{4}{-10}\right)\\= \frac{-4}{9}+ \frac{8}{6}-\frac{4}{10}\\=\frac{-4}{9}+\frac{4}{3}-\frac{2}{5}\\=\frac{-20}{45}+\frac{60}{45}-\frac{18}{45}\\=\frac{-20+60-18}{45}\\=\frac{22}{45}\)
4. \(+\left(\frac{-3}{4}\right) +\left(\frac{2}{4}\right) -\left(\frac{11}{-4}\right)\\= \frac{-3}{4}+ \frac{2}{4}+\frac{11}{4}\\=\frac{-3}{4}+\frac{1}{2}+\frac{11}{4}\\=\frac{-3+1+11}{4}\\=\frac{9}{4}\)
5. \(+\left(\frac{-4}{-7}\right) -\left(\frac{8}{8}\right) +\left(\frac{5}{-6}\right)\\= \frac{4}{7}- \frac{8}{8}-\frac{5}{6}\\=\frac{4}{7}-\frac{1}{1}-\frac{5}{6}\\=\frac{24}{42}-\frac{42}{42}-\frac{35}{42}\\=\frac{24-42-35}{42}\\=\frac{-53}{42}\)
6. \(+\left(\frac{3}{-8}\right) +\left(\frac{2}{-8}\right) -\left(\frac{-12}{-4}\right)\\= \frac{-3}{8}- \frac{2}{8}-\frac{12}{4}\\=\frac{-3}{8}-\frac{1}{4}-\frac{3}{1}\\=\frac{-3-1-3}{8}\\=\frac{-7}{8}\)
7. \(-\left(\frac{-8}{-9}\right) +\left(\frac{-5}{-9}\right) +\left(\frac{-5}{2}\right)\\= \frac{-8}{9}+ \frac{5}{9}-\frac{5}{2}\\=\frac{-16}{18}+\frac{10}{18}-\frac{45}{18}\\=\frac{-16+10-45}{18}\\=\frac{-51}{18}\\=\frac{-17}{6}\)
8. \(-\left(\frac{7}{8}\right) +\left(\frac{5}{-4}\right) -\left(\frac{-3}{10}\right)\\= \frac{-7}{8}- \frac{5}{4}+\frac{3}{10}\\=\frac{-35}{40}-\frac{50}{40}+\frac{12}{40}\\=\frac{-35-50+12}{40}\\=\frac{-73}{40}\)
9. \(-\left(\frac{-3}{4}\right) +\left(\frac{3}{8}\right) +\left(\frac{3}{8}\right)\\= \frac{3}{4}+ \frac{3}{8}+\frac{3}{8}\\=\frac{6}{8}+\frac{3}{8}+\frac{3}{8}\\=\frac{6+3+3}{8}\\=\frac{12}{8}\\=\frac{3}{2}\)
10. \(-\left(\frac{-7}{-3}\right) +\left(\frac{4}{-8}\right) +\left(\frac{11}{7}\right)\\= \frac{-7}{3}- \frac{4}{8}+\frac{11}{7}\\=\frac{-7}{3}-\frac{1}{2}+\frac{11}{7}\\=\frac{-98}{42}-\frac{21}{42}+\frac{66}{42}\\=\frac{-98-21+66}{42}\\=\frac{-53}{42}\)
11. \(-\left(\frac{5}{-8}\right) +\left(\frac{-10}{-5}\right) -\left(\frac{5}{-12}\right)\\= \frac{5}{8}+ \frac{10}{5}+\frac{5}{12}\\=\frac{5}{8}+\frac{2}{1}+\frac{5}{12}\\=\frac{15}{24}+\frac{48}{24}+\frac{10}{24}\\=\frac{15+48+10}{24}\\=\frac{73}{24}\)
12. \(+\left(\frac{-8}{5}\right) -\left(\frac{-9}{-7}\right) -\left(\frac{4}{2}\right)\\= \frac{-8}{5}- \frac{9}{7}-\frac{4}{2}\\=\frac{-8}{5}-\frac{9}{7}-\frac{2}{1}\\=\frac{-56}{35}-\frac{45}{35}-\frac{70}{35}\\=\frac{-56-45-70}{35}\\=\frac{-171}{35}\)