Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{2}{-3}\right) -\left(\frac{7}{9}\right) -\left(\frac{-9}{10}\right)\\= \frac{2}{3}- \frac{7}{9}+\frac{9}{10}\\=\frac{60}{90}-\frac{70}{90}+\frac{81}{90}\\=\frac{60-70+81}{90}\\=\frac{71}{90}\)
2. \(-\left(\frac{-4}{-3}\right) -\left(\frac{8}{-8}\right) +\left(\frac{11}{-11}\right)\\= \frac{-4}{3}+ \frac{8}{8}-\frac{11}{11}\\=\frac{-4}{3}+\frac{1}{1}-\frac{1}{1}\\=\frac{-4+1-1}{3}\\=\frac{-4}{3}\)
3. \(-\left(\frac{6}{7}\right) -\left(\frac{4}{-9}\right) +\left(\frac{-4}{4}\right)\\= \frac{-6}{7}+ \frac{4}{9}-\frac{4}{4}\\=\frac{-6}{7}+\frac{4}{9}-\frac{1}{1}\\=\frac{-54}{63}+\frac{28}{63}-\frac{63}{63}\\=\frac{-54+28-63}{63}\\=\frac{-89}{63}\)
4. \(-\left(\frac{9}{-5}\right) -\left(\frac{7}{9}\right) +\left(\frac{-2}{-5}\right)\\= \frac{9}{5}- \frac{7}{9}+\frac{2}{5}\\=\frac{81}{45}-\frac{35}{45}+\frac{18}{45}\\=\frac{81-35+18}{45}\\=\frac{64}{45}\)
5. \(-\left(\frac{8}{7}\right) +\left(\frac{-10}{6}\right) -\left(\frac{8}{-8}\right)\\= \frac{-8}{7}- \frac{10}{6}+\frac{8}{8}\\=\frac{-8}{7}-\frac{5}{3}+\frac{1}{1}\\=\frac{-24}{21}-\frac{35}{21}+\frac{21}{21}\\=\frac{-24-35+21}{21}\\=\frac{-38}{21}\)
6. \(+\left(\frac{4}{5}\right) -\left(\frac{10}{4}\right) +\left(\frac{-12}{-6}\right)\\= \frac{4}{5}- \frac{10}{4}+\frac{12}{6}\\=\frac{4}{5}-\frac{5}{2}+\frac{2}{1}\\=\frac{8}{10}-\frac{25}{10}+\frac{20}{10}\\=\frac{8-25+20}{10}\\=\frac{3}{10}\)
7. \(-\left(\frac{3}{2}\right) -\left(\frac{6}{-10}\right) -\left(\frac{6}{-3}\right)\\= \frac{-3}{2}+ \frac{6}{10}+\frac{6}{3}\\=\frac{-3}{2}+\frac{3}{5}+\frac{2}{1}\\=\frac{-15}{10}+\frac{6}{10}+\frac{20}{10}\\=\frac{-15+6+20}{10}\\=\frac{11}{10}\)
8. \(+\left(\frac{10}{7}\right) -\left(\frac{-3}{5}\right) -\left(\frac{10}{-6}\right)\\= \frac{10}{7}+ \frac{3}{5}+\frac{10}{6}\\=\frac{10}{7}+\frac{3}{5}+\frac{5}{3}\\=\frac{150}{105}+\frac{63}{105}+\frac{175}{105}\\=\frac{150+63+175}{105}\\=\frac{388}{105}\)
9. \(-\left(\frac{2}{3}\right) +\left(\frac{-8}{4}\right) +\left(\frac{12}{4}\right)\\= \frac{-2}{3}- \frac{8}{4}+\frac{12}{4}\\=\frac{-2}{3}-\frac{2}{1}+\frac{3}{1}\\=\frac{-2-2+3}{3}\\=\frac{-1}{3}\)
10. \(+\left(\frac{-3}{-7}\right) +\left(\frac{-9}{-2}\right) -\left(\frac{-4}{-11}\right)\\= \frac{3}{7}+ \frac{9}{2}-\frac{4}{11}\\=\frac{66}{154}+\frac{693}{154}-\frac{56}{154}\\=\frac{66+693-56}{154}\\=\frac{703}{154}\)
11. \(-\left(\frac{9}{-7}\right) +\left(\frac{-3}{2}\right) -\left(\frac{-2}{9}\right)\\= \frac{9}{7}- \frac{3}{2}+\frac{2}{9}\\=\frac{162}{126}-\frac{189}{126}+\frac{28}{126}\\=\frac{162-189+28}{126}\\=\frac{1}{126}\)
12. \(-\left(\frac{2}{5}\right) +\left(\frac{-5}{-9}\right) +\left(\frac{3}{4}\right)\\= \frac{-2}{5}+ \frac{5}{9}+\frac{3}{4}\\=\frac{-72}{180}+\frac{100}{180}+\frac{135}{180}\\=\frac{-72+100+135}{180}\\=\frac{163}{180}\)