Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{7}{3}\right) +\left(\frac{8}{9}\right) +\left(\frac{2}{10}\right)\\= \frac{-7}{3}+ \frac{8}{9}+\frac{2}{10}\\=\frac{-7}{3}+\frac{8}{9}+\frac{1}{5}\\=\frac{-105}{45}+\frac{40}{45}+\frac{9}{45}\\=\frac{-105+40+9}{45}\\=\frac{-56}{45}\)
2. \(-\left(\frac{3}{-4}\right) -\left(\frac{-7}{7}\right) +\left(\frac{7}{12}\right)\\= \frac{3}{4}+ \frac{7}{7}+\frac{7}{12}\\=\frac{3}{4}+\frac{1}{1}+\frac{7}{12}\\=\frac{9}{12}+\frac{12}{12}+\frac{7}{12}\\=\frac{9+12+7}{12}\\=\frac{28}{12}\\=\frac{7}{3}\)
3. \(+\left(\frac{-4}{7}\right) +\left(\frac{8}{6}\right) +\left(\frac{-10}{-9}\right)\\= \frac{-4}{7}+ \frac{8}{6}+\frac{10}{9}\\=\frac{-4}{7}+\frac{4}{3}+\frac{10}{9}\\=\frac{-36}{63}+\frac{84}{63}+\frac{70}{63}\\=\frac{-36+84+70}{63}\\=\frac{118}{63}\)
4. \(-\left(\frac{3}{7}\right) +\left(\frac{2}{9}\right) -\left(\frac{-6}{-4}\right)\\= \frac{-3}{7}+ \frac{2}{9}-\frac{6}{4}\\=\frac{-3}{7}+\frac{2}{9}-\frac{3}{2}\\=\frac{-54}{126}+\frac{28}{126}-\frac{189}{126}\\=\frac{-54+28-189}{126}\\=\frac{-215}{126}\)
5. \(-\left(\frac{7}{4}\right) +\left(\frac{10}{-4}\right) -\left(\frac{8}{9}\right)\\= \frac{-7}{4}- \frac{10}{4}-\frac{8}{9}\\=\frac{-7}{4}-\frac{5}{2}-\frac{8}{9}\\=\frac{-63}{36}-\frac{90}{36}-\frac{32}{36}\\=\frac{-63-90-32}{36}\\=\frac{-185}{36}\)
6. \(-\left(\frac{5}{8}\right) +\left(\frac{3}{5}\right) +\left(\frac{12}{4}\right)\\= \frac{-5}{8}+ \frac{3}{5}+\frac{12}{4}\\=\frac{-5}{8}+\frac{3}{5}+\frac{3}{1}\\=\frac{-25}{40}+\frac{24}{40}+\frac{120}{40}\\=\frac{-25+24+120}{40}\\=\frac{119}{40}\)
7. \(-\left(\frac{2}{3}\right) +\left(\frac{7}{8}\right) +\left(\frac{-6}{-4}\right)\\= \frac{-2}{3}+ \frac{7}{8}+\frac{6}{4}\\=\frac{-2}{3}+\frac{7}{8}+\frac{3}{2}\\=\frac{-16}{24}+\frac{21}{24}+\frac{36}{24}\\=\frac{-16+21+36}{24}\\=\frac{41}{24}\)
8. \(-\left(\frac{4}{3}\right) +\left(\frac{9}{-3}\right) +\left(\frac{5}{-9}\right)\\= \frac{-4}{3}- \frac{9}{3}-\frac{5}{9}\\=\frac{-4}{3}-\frac{3}{1}-\frac{5}{9}\\=\frac{-12}{9}-\frac{27}{9}-\frac{5}{9}\\=\frac{-12-27-5}{9}\\=\frac{-44}{9}\)
9. \(-\left(\frac{9}{-7}\right) +\left(\frac{3}{-10}\right) +\left(\frac{-6}{11}\right)\\= \frac{9}{7}- \frac{3}{10}-\frac{6}{11}\\=\frac{990}{770}-\frac{231}{770}-\frac{420}{770}\\=\frac{990-231-420}{770}\\=\frac{339}{770}\)
10. \(-\left(\frac{-8}{3}\right) -\left(\frac{-6}{6}\right) -\left(\frac{-2}{3}\right)\\= \frac{8}{3}+ \frac{6}{6}+\frac{2}{3}\\=\frac{8}{3}+\frac{1}{1}+\frac{2}{3}\\=\frac{8+1+2}{3}\\=\frac{11}{3}\)
11. \(+\left(\frac{-7}{-5}\right) +\left(\frac{5}{9}\right) +\left(\frac{-7}{7}\right)\\= \frac{7}{5}+ \frac{5}{9}-\frac{7}{7}\\=\frac{7}{5}+\frac{5}{9}-\frac{1}{1}\\=\frac{63}{45}+\frac{25}{45}-\frac{45}{45}\\=\frac{63+25-45}{45}\\=\frac{43}{45}\)
12. \(-\left(\frac{-5}{2}\right) +\left(\frac{-6}{-2}\right) -\left(\frac{6}{-4}\right)\\= \frac{5}{2}+ \frac{6}{2}+\frac{6}{4}\\=\frac{5}{2}+\frac{3}{1}+\frac{3}{2}\\=\frac{5+3+3}{2}\\=\frac{11}{2}\)