Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{6}{5}\right) -\left(\frac{-5}{-7}\right) -\left(\frac{7}{-4}\right)\\= \frac{6}{5}- \frac{5}{7}+\frac{7}{4}\\=\frac{168}{140}-\frac{100}{140}+\frac{245}{140}\\=\frac{168-100+245}{140}\\=\frac{313}{140}\)
2. \(-\left(\frac{6}{-5}\right) +\left(\frac{-8}{-8}\right) +\left(\frac{-3}{-2}\right)\\= \frac{6}{5}+ \frac{8}{8}+\frac{3}{2}\\=\frac{6}{5}+\frac{1}{1}+\frac{3}{2}\\=\frac{12}{10}+\frac{10}{10}+\frac{15}{10}\\=\frac{12+10+15}{10}\\=\frac{37}{10}\)
3. \(-\left(\frac{-3}{-2}\right) +\left(\frac{3}{-5}\right) -\left(\frac{-9}{-6}\right)\\= \frac{-3}{2}- \frac{3}{5}-\frac{9}{6}\\=\frac{-3}{2}-\frac{3}{5}-\frac{3}{2}\\=\frac{-15}{10}-\frac{6}{10}-\frac{15}{10}\\=\frac{-15-6-15}{10}\\=\frac{-36}{10}\\=\frac{-18}{5}\)
4. \(+\left(\frac{5}{-4}\right) -\left(\frac{10}{5}\right) +\left(\frac{11}{4}\right)\\= \frac{-5}{4}- \frac{10}{5}+\frac{11}{4}\\=\frac{-5}{4}-\frac{2}{1}+\frac{11}{4}\\=\frac{-5-2+11}{4}\\=\frac{4}{4}\\=\frac{1}{1}\)
5. \(-\left(\frac{3}{-4}\right) +\left(\frac{-9}{-4}\right) +\left(\frac{8}{6}\right)\\= \frac{3}{4}+ \frac{9}{4}+\frac{8}{6}\\=\frac{3}{4}+\frac{9}{4}+\frac{4}{3}\\=\frac{9}{12}+\frac{27}{12}+\frac{16}{12}\\=\frac{9+27+16}{12}\\=\frac{52}{12}\\=\frac{13}{3}\)
6. \(-\left(\frac{-3}{5}\right) -\left(\frac{5}{-9}\right) -\left(\frac{-2}{6}\right)\\= \frac{3}{5}+ \frac{5}{9}+\frac{2}{6}\\=\frac{3}{5}+\frac{5}{9}+\frac{1}{3}\\=\frac{27}{45}+\frac{25}{45}+\frac{15}{45}\\=\frac{27+25+15}{45}\\=\frac{67}{45}\)
7. \(-\left(\frac{-10}{-3}\right) +\left(\frac{7}{-7}\right) +\left(\frac{-5}{10}\right)\\= \frac{-10}{3}- \frac{7}{7}-\frac{5}{10}\\=\frac{-10}{3}-\frac{1}{1}-\frac{1}{2}\\=\frac{-20}{6}-\frac{6}{6}-\frac{3}{6}\\=\frac{-20-6-3}{6}\\=\frac{-29}{6}\)
8. \(-\left(\frac{-3}{7}\right) +\left(\frac{10}{-6}\right) -\left(\frac{3}{7}\right)\\= \frac{3}{7}- \frac{10}{6}-\frac{3}{7}\\=\frac{3}{7}-\frac{5}{3}-\frac{3}{7}\\=\frac{9}{21}-\frac{35}{21}-\frac{9}{21}\\=\frac{9-35-9}{21}\\=\frac{-35}{21}\\=\frac{-5}{3}\)
9. \(+\left(\frac{-9}{7}\right) -\left(\frac{3}{10}\right) -\left(\frac{9}{-6}\right)\\= \frac{-9}{7}- \frac{3}{10}+\frac{9}{6}\\=\frac{-9}{7}-\frac{3}{10}+\frac{3}{2}\\=\frac{-90}{70}-\frac{21}{70}+\frac{105}{70}\\=\frac{-90-21+105}{70}\\=\frac{-6}{70}\\=\frac{-3}{35}\)
10. \(+\left(\frac{3}{-5}\right) -\left(\frac{6}{6}\right) +\left(\frac{-6}{-3}\right)\\= \frac{-3}{5}- \frac{6}{6}+\frac{6}{3}\\=\frac{-3}{5}-\frac{1}{1}+\frac{2}{1}\\=\frac{-3-1+2}{5}\\=\frac{-2}{5}\)
11. \(-\left(\frac{2}{-9}\right) -\left(\frac{-6}{7}\right) -\left(\frac{9}{12}\right)\\= \frac{2}{9}+ \frac{6}{7}-\frac{9}{12}\\=\frac{2}{9}+\frac{6}{7}-\frac{3}{4}\\=\frac{56}{252}+\frac{216}{252}-\frac{189}{252}\\=\frac{56+216-189}{252}\\=\frac{83}{252}\)
12. \(+\left(\frac{-3}{2}\right) +\left(\frac{3}{-6}\right) +\left(\frac{-11}{3}\right)\\= \frac{-3}{2}- \frac{3}{6}-\frac{11}{3}\\=\frac{-3}{2}-\frac{1}{2}-\frac{11}{3}\\=\frac{-9}{6}-\frac{3}{6}-\frac{22}{6}\\=\frac{-9-3-22}{6}\\=\frac{-34}{6}\\=\frac{-17}{3}\)