Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{-7}\right) +\left(\frac{9}{2}\right) -\left(\frac{-2}{11}\right)\\= \frac{2}{7}+ \frac{9}{2}+\frac{2}{11}\\=\frac{44}{154}+\frac{693}{154}+\frac{28}{154}\\=\frac{44+693+28}{154}\\=\frac{765}{154}\)
2. \(+\left(\frac{9}{5}\right) +\left(\frac{2}{5}\right) -\left(\frac{7}{-2}\right)\\= \frac{9}{5}+ \frac{2}{5}+\frac{7}{2}\\=\frac{18}{10}+\frac{4}{10}+\frac{35}{10}\\=\frac{18+4+35}{10}\\=\frac{57}{10}\)
3. \(+\left(\frac{-8}{3}\right) -\left(\frac{6}{-2}\right) -\left(\frac{-6}{-6}\right)\\= \frac{-8}{3}+ \frac{6}{2}-\frac{6}{6}\\=\frac{-8}{3}+\frac{3}{1}-\frac{1}{1}\\=\frac{-8+3-1}{3}\\=\frac{-6}{3}\\=\frac{-2}{1}\)
4. \(+\left(\frac{-8}{3}\right) +\left(\frac{-6}{-4}\right) -\left(\frac{-7}{-4}\right)\\= \frac{-8}{3}+ \frac{6}{4}-\frac{7}{4}\\=\frac{-8}{3}+\frac{3}{2}-\frac{7}{4}\\=\frac{-32}{12}+\frac{18}{12}-\frac{21}{12}\\=\frac{-32+18-21}{12}\\=\frac{-35}{12}\)
5. \(+\left(\frac{-7}{9}\right) +\left(\frac{-8}{6}\right) +\left(\frac{6}{-8}\right)\\= \frac{-7}{9}- \frac{8}{6}-\frac{6}{8}\\=\frac{-7}{9}-\frac{4}{3}-\frac{3}{4}\\=\frac{-28}{36}-\frac{48}{36}-\frac{27}{36}\\=\frac{-28-48-27}{36}\\=\frac{-103}{36}\)
6. \(+\left(\frac{-9}{7}\right) -\left(\frac{-4}{-2}\right) +\left(\frac{6}{-7}\right)\\= \frac{-9}{7}- \frac{4}{2}-\frac{6}{7}\\=\frac{-9}{7}-\frac{2}{1}-\frac{6}{7}\\=\frac{-9-2-6}{7}\\=\frac{-17}{7}\)
7. \(+\left(\frac{9}{-7}\right) +\left(\frac{6}{9}\right) -\left(\frac{-12}{12}\right)\\= \frac{-9}{7}+ \frac{6}{9}+\frac{12}{12}\\=\frac{-9}{7}+\frac{2}{3}+\frac{1}{1}\\=\frac{-27}{21}+\frac{14}{21}+\frac{21}{21}\\=\frac{-27+14+21}{21}\\=\frac{8}{21}\)
8. \(-\left(\frac{-5}{2}\right) +\left(\frac{7}{7}\right) +\left(\frac{-4}{5}\right)\\= \frac{5}{2}+ \frac{7}{7}-\frac{4}{5}\\=\frac{5}{2}+\frac{1}{1}-\frac{4}{5}\\=\frac{25}{10}+\frac{10}{10}-\frac{8}{10}\\=\frac{25+10-8}{10}\\=\frac{27}{10}\)
9. \(+\left(\frac{7}{9}\right) -\left(\frac{-2}{3}\right) +\left(\frac{-3}{4}\right)\\= \frac{7}{9}+ \frac{2}{3}-\frac{3}{4}\\=\frac{28}{36}+\frac{24}{36}-\frac{27}{36}\\=\frac{28+24-27}{36}\\=\frac{25}{36}\)
10. \(-\left(\frac{7}{4}\right) -\left(\frac{10}{-2}\right) +\left(\frac{8}{4}\right)\\= \frac{-7}{4}+ \frac{10}{2}+\frac{8}{4}\\=\frac{-7}{4}+\frac{5}{1}+\frac{2}{1}\\=\frac{-7+5+2}{4}\\=\frac{0}{4}\\=\frac{0}{1}\)
11. \(+\left(\frac{7}{9}\right) +\left(\frac{-3}{-8}\right) +\left(\frac{-8}{7}\right)\\= \frac{7}{9}+ \frac{3}{8}-\frac{8}{7}\\=\frac{392}{504}+\frac{189}{504}-\frac{576}{504}\\=\frac{392+189-576}{504}\\=\frac{5}{504}\)
12. \(+\left(\frac{-6}{-5}\right) -\left(\frac{5}{9}\right) -\left(\frac{-3}{-11}\right)\\= \frac{6}{5}- \frac{5}{9}-\frac{3}{11}\\=\frac{594}{495}-\frac{275}{495}-\frac{135}{495}\\=\frac{594-275-135}{495}\\=\frac{184}{495}\)