Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{7}\right) -\left(\frac{-5}{-5}\right) +\left(\frac{5}{3}\right)\\= \frac{-8}{7}- \frac{5}{5}+\frac{5}{3}\\=\frac{-8}{7}-\frac{1}{1}+\frac{5}{3}\\=\frac{-24}{21}-\frac{21}{21}+\frac{35}{21}\\=\frac{-24-21+35}{21}\\=\frac{-10}{21}\)
2. \(-\left(\frac{-4}{3}\right) +\left(\frac{10}{-3}\right) +\left(\frac{-8}{8}\right)\\= \frac{4}{3}- \frac{10}{3}-\frac{8}{8}\\=\frac{4}{3}-\frac{10}{3}-\frac{1}{1}\\=\frac{4-10-1}{3}\\=\frac{-7}{3}\)
3. \(-\left(\frac{-3}{2}\right) -\left(\frac{2}{2}\right) -\left(\frac{10}{-11}\right)\\= \frac{3}{2}- \frac{2}{2}+\frac{10}{11}\\=\frac{3}{2}-\frac{1}{1}+\frac{10}{11}\\=\frac{33}{22}-\frac{22}{22}+\frac{20}{22}\\=\frac{33-22+20}{22}\\=\frac{31}{22}\)
4. \(+\left(\frac{8}{-3}\right) -\left(\frac{10}{6}\right) -\left(\frac{-12}{-6}\right)\\= \frac{-8}{3}- \frac{10}{6}-\frac{12}{6}\\=\frac{-8}{3}-\frac{5}{3}-\frac{2}{1}\\=\frac{-8-5-2}{3}\\=\frac{-15}{3}\\=\frac{-5}{1}\)
5. \(+\left(\frac{-6}{-7}\right) -\left(\frac{9}{-5}\right) +\left(\frac{5}{3}\right)\\= \frac{6}{7}+ \frac{9}{5}+\frac{5}{3}\\=\frac{90}{105}+\frac{189}{105}+\frac{175}{105}\\=\frac{90+189+175}{105}\\=\frac{454}{105}\)
6. \(+\left(\frac{4}{-9}\right) -\left(\frac{-10}{2}\right) +\left(\frac{12}{-10}\right)\\= \frac{-4}{9}+ \frac{10}{2}-\frac{12}{10}\\=\frac{-4}{9}+\frac{5}{1}-\frac{6}{5}\\=\frac{-20}{45}+\frac{225}{45}-\frac{54}{45}\\=\frac{-20+225-54}{45}\\=\frac{151}{45}\)
7. \(-\left(\frac{-5}{6}\right) +\left(\frac{-7}{-6}\right) -\left(\frac{-12}{8}\right)\\= \frac{5}{6}+ \frac{7}{6}+\frac{12}{8}\\=\frac{5}{6}+\frac{7}{6}+\frac{3}{2}\\=\frac{5+7+3}{6}\\=\frac{15}{6}\\=\frac{5}{2}\)
8. \(-\left(\frac{-3}{8}\right) -\left(\frac{8}{10}\right) +\left(\frac{4}{-9}\right)\\= \frac{3}{8}- \frac{8}{10}-\frac{4}{9}\\=\frac{3}{8}-\frac{4}{5}-\frac{4}{9}\\=\frac{135}{360}-\frac{288}{360}-\frac{160}{360}\\=\frac{135-288-160}{360}\\=\frac{-313}{360}\)
9. \(-\left(\frac{-5}{2}\right) -\left(\frac{2}{7}\right) +\left(\frac{-12}{12}\right)\\= \frac{5}{2}- \frac{2}{7}-\frac{12}{12}\\=\frac{5}{2}-\frac{2}{7}-\frac{1}{1}\\=\frac{35}{14}-\frac{4}{14}-\frac{14}{14}\\=\frac{35-4-14}{14}\\=\frac{17}{14}\)
10. \(-\left(\frac{-10}{-3}\right) +\left(\frac{-5}{-5}\right) +\left(\frac{10}{-9}\right)\\= \frac{-10}{3}+ \frac{5}{5}-\frac{10}{9}\\=\frac{-10}{3}+\frac{1}{1}-\frac{10}{9}\\=\frac{-30}{9}+\frac{9}{9}-\frac{10}{9}\\=\frac{-30+9-10}{9}\\=\frac{-31}{9}\)
11. \(+\left(\frac{8}{7}\right) -\left(\frac{7}{10}\right) +\left(\frac{8}{-11}\right)\\= \frac{8}{7}- \frac{7}{10}-\frac{8}{11}\\=\frac{880}{770}-\frac{539}{770}-\frac{560}{770}\\=\frac{880-539-560}{770}\\=\frac{-219}{770}\)
12. \(-\left(\frac{-2}{-3}\right) +\left(\frac{8}{5}\right) +\left(\frac{-7}{12}\right)\\= \frac{-2}{3}+ \frac{8}{5}-\frac{7}{12}\\=\frac{-40}{60}+\frac{96}{60}-\frac{35}{60}\\=\frac{-40+96-35}{60}\\=\frac{21}{60}\\=\frac{7}{20}\)