Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{3}{2}\right) -\left(\frac{-4}{-10}\right) +\left(\frac{2}{-4}\right)\\= \frac{3}{2}- \frac{4}{10}-\frac{2}{4}\\=\frac{3}{2}-\frac{2}{5}-\frac{1}{2}\\=\frac{15}{10}-\frac{4}{10}-\frac{5}{10}\\=\frac{15-4-5}{10}\\=\frac{6}{10}\\=\frac{3}{5}\)
2. \(+\left(\frac{6}{5}\right) +\left(\frac{6}{-9}\right) +\left(\frac{10}{-4}\right)\\= \frac{6}{5}- \frac{6}{9}-\frac{10}{4}\\=\frac{6}{5}-\frac{2}{3}-\frac{5}{2}\\=\frac{36}{30}-\frac{20}{30}-\frac{75}{30}\\=\frac{36-20-75}{30}\\=\frac{-59}{30}\)
3. \(-\left(\frac{-3}{2}\right) +\left(\frac{-5}{5}\right) +\left(\frac{6}{-3}\right)\\= \frac{3}{2}- \frac{5}{5}-\frac{6}{3}\\=\frac{3}{2}-\frac{1}{1}-\frac{2}{1}\\=\frac{3-1-2}{2}\\=\frac{0}{2}\\=\frac{0}{1}\)
4. \(-\left(\frac{7}{-2}\right) +\left(\frac{3}{8}\right) +\left(\frac{-7}{-12}\right)\\= \frac{7}{2}+ \frac{3}{8}+\frac{7}{12}\\=\frac{84}{24}+\frac{9}{24}+\frac{14}{24}\\=\frac{84+9+14}{24}\\=\frac{107}{24}\)
5. \(+\left(\frac{7}{-9}\right) -\left(\frac{-5}{4}\right) -\left(\frac{-9}{7}\right)\\= \frac{-7}{9}+ \frac{5}{4}+\frac{9}{7}\\=\frac{-196}{252}+\frac{315}{252}+\frac{324}{252}\\=\frac{-196+315+324}{252}\\=\frac{443}{252}\)
6. \(+\left(\frac{8}{9}\right) +\left(\frac{-8}{-9}\right) -\left(\frac{6}{10}\right)\\= \frac{8}{9}+ \frac{8}{9}-\frac{6}{10}\\=\frac{8}{9}+\frac{8}{9}-\frac{3}{5}\\=\frac{40}{45}+\frac{40}{45}-\frac{27}{45}\\=\frac{40+40-27}{45}\\=\frac{53}{45}\)
7. \(-\left(\frac{-10}{9}\right) +\left(\frac{8}{5}\right) +\left(\frac{-3}{-2}\right)\\= \frac{10}{9}+ \frac{8}{5}+\frac{3}{2}\\=\frac{100}{90}+\frac{144}{90}+\frac{135}{90}\\=\frac{100+144+135}{90}\\=\frac{379}{90}\)
8. \(-\left(\frac{3}{2}\right) +\left(\frac{-2}{3}\right) +\left(\frac{2}{-8}\right)\\= \frac{-3}{2}- \frac{2}{3}-\frac{2}{8}\\=\frac{-3}{2}-\frac{2}{3}-\frac{1}{4}\\=\frac{-18}{12}-\frac{8}{12}-\frac{3}{12}\\=\frac{-18-8-3}{12}\\=\frac{-29}{12}\)
9. \(+\left(\frac{-9}{4}\right) +\left(\frac{-4}{-3}\right) +\left(\frac{3}{-2}\right)\\= \frac{-9}{4}+ \frac{4}{3}-\frac{3}{2}\\=\frac{-27}{12}+\frac{16}{12}-\frac{18}{12}\\=\frac{-27+16-18}{12}\\=\frac{-29}{12}\)
10. \(+\left(\frac{-4}{-7}\right) +\left(\frac{2}{4}\right) +\left(\frac{-11}{-5}\right)\\= \frac{4}{7}+ \frac{2}{4}+\frac{11}{5}\\=\frac{4}{7}+\frac{1}{2}+\frac{11}{5}\\=\frac{40}{70}+\frac{35}{70}+\frac{154}{70}\\=\frac{40+35+154}{70}\\=\frac{229}{70}\)
11. \(-\left(\frac{7}{-2}\right) -\left(\frac{3}{7}\right) -\left(\frac{10}{4}\right)\\= \frac{7}{2}- \frac{3}{7}-\frac{10}{4}\\=\frac{7}{2}-\frac{3}{7}-\frac{5}{2}\\=\frac{49}{14}-\frac{6}{14}-\frac{35}{14}\\=\frac{49-6-35}{14}\\=\frac{8}{14}\\=\frac{4}{7}\)
12. \(+\left(\frac{-7}{-3}\right) +\left(\frac{7}{8}\right) -\left(\frac{11}{9}\right)\\= \frac{7}{3}+ \frac{7}{8}-\frac{11}{9}\\=\frac{168}{72}+\frac{63}{72}-\frac{88}{72}\\=\frac{168+63-88}{72}\\=\frac{143}{72}\)