Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-9}\right) +\left(\frac{-8}{-6}\right) -\left(\frac{-11}{5}\right)\\= \frac{10}{9}+ \frac{8}{6}+\frac{11}{5}\\=\frac{10}{9}+\frac{4}{3}+\frac{11}{5}\\=\frac{50}{45}+\frac{60}{45}+\frac{99}{45}\\=\frac{50+60+99}{45}\\=\frac{209}{45}\)
2. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-10}{7}\right) -\left(\frac{-3}{-3}\right)\\= \frac{6}{5}+ \frac{10}{7}-\frac{3}{3}\\=\frac{6}{5}+\frac{10}{7}-\frac{1}{1}\\=\frac{42}{35}+\frac{50}{35}-\frac{35}{35}\\=\frac{42+50-35}{35}\\=\frac{57}{35}\)
3. \(-\left(\frac{2}{5}\right) +\left(\frac{3}{-10}\right) -\left(\frac{8}{4}\right)\\= \frac{-2}{5}- \frac{3}{10}-\frac{8}{4}\\=\frac{-2}{5}-\frac{3}{10}-\frac{2}{1}\\=\frac{-4}{10}-\frac{3}{10}-\frac{20}{10}\\=\frac{-4-3-20}{10}\\=\frac{-27}{10}\)
4. \(-\left(\frac{5}{6}\right) +\left(\frac{10}{-6}\right) -\left(\frac{4}{-2}\right)\\= \frac{-5}{6}- \frac{10}{6}+\frac{4}{2}\\=\frac{-5}{6}-\frac{5}{3}+\frac{2}{1}\\=\frac{-5-5+2}{6}\\=\frac{-8}{6}\\=\frac{-4}{3}\)
5. \(-\left(\frac{6}{-5}\right) -\left(\frac{-7}{5}\right) -\left(\frac{-5}{3}\right)\\= \frac{6}{5}+ \frac{7}{5}+\frac{5}{3}\\=\frac{18}{15}+\frac{21}{15}+\frac{25}{15}\\=\frac{18+21+25}{15}\\=\frac{64}{15}\)
6. \(-\left(\frac{4}{9}\right) -\left(\frac{-9}{9}\right) +\left(\frac{-2}{-5}\right)\\= \frac{-4}{9}+ \frac{9}{9}+\frac{2}{5}\\=\frac{-4}{9}+\frac{1}{1}+\frac{2}{5}\\=\frac{-20}{45}+\frac{45}{45}+\frac{18}{45}\\=\frac{-20+45+18}{45}\\=\frac{43}{45}\)
7. \(+\left(\frac{-8}{-7}\right) -\left(\frac{-8}{-9}\right) -\left(\frac{10}{-4}\right)\\= \frac{8}{7}- \frac{8}{9}+\frac{10}{4}\\=\frac{8}{7}-\frac{8}{9}+\frac{5}{2}\\=\frac{144}{126}-\frac{112}{126}+\frac{315}{126}\\=\frac{144-112+315}{126}\\=\frac{347}{126}\)
8. \(-\left(\frac{6}{5}\right) -\left(\frac{-3}{5}\right) -\left(\frac{11}{8}\right)\\= \frac{-6}{5}+ \frac{3}{5}-\frac{11}{8}\\=\frac{-48}{40}+\frac{24}{40}-\frac{55}{40}\\=\frac{-48+24-55}{40}\\=\frac{-79}{40}\)
9. \(+\left(\frac{4}{9}\right) -\left(\frac{-7}{-5}\right) +\left(\frac{-6}{-4}\right)\\= \frac{4}{9}- \frac{7}{5}+\frac{6}{4}\\=\frac{4}{9}-\frac{7}{5}+\frac{3}{2}\\=\frac{40}{90}-\frac{126}{90}+\frac{135}{90}\\=\frac{40-126+135}{90}\\=\frac{49}{90}\)
10. \(-\left(\frac{-6}{-5}\right) +\left(\frac{4}{6}\right) -\left(\frac{-4}{-6}\right)\\= \frac{-6}{5}+ \frac{4}{6}-\frac{4}{6}\\=\frac{-6}{5}+\frac{2}{3}-\frac{2}{3}\\=\frac{-18}{15}+\frac{10}{15}-\frac{10}{15}\\=\frac{-18+10-10}{15}\\=\frac{-18}{15}\\=\frac{-6}{5}\)
11. \(-\left(\frac{-5}{-9}\right) -\left(\frac{-2}{8}\right) +\left(\frac{-7}{-7}\right)\\= \frac{-5}{9}+ \frac{2}{8}+\frac{7}{7}\\=\frac{-5}{9}+\frac{1}{4}+\frac{1}{1}\\=\frac{-20}{36}+\frac{9}{36}+\frac{36}{36}\\=\frac{-20+9+36}{36}\\=\frac{25}{36}\)
12. \(+\left(\frac{-6}{-7}\right) -\left(\frac{-5}{-2}\right) -\left(\frac{4}{11}\right)\\= \frac{6}{7}- \frac{5}{2}-\frac{4}{11}\\=\frac{132}{154}-\frac{385}{154}-\frac{56}{154}\\=\frac{132-385-56}{154}\\=\frac{-309}{154}\)