Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(+\left(\frac{3}{-4}\right) +\left(\frac{-6}{-9}\right) -\left(\frac{8}{5}\right)\\= \frac{-3}{4}+ \frac{6}{9}-\frac{8}{5}\\=\frac{-3}{4}+\frac{2}{3}-\frac{8}{5}\\=\frac{-45}{60}+\frac{40}{60}-\frac{96}{60}\\=\frac{-45+40-96}{60}\\=\frac{-101}{60}\)
2. \(+\left(\frac{10}{9}\right) -\left(\frac{-3}{7}\right) -\left(\frac{-3}{-7}\right)\\= \frac{10}{9}+ \frac{3}{7}-\frac{3}{7}\\=\frac{70}{63}+\frac{27}{63}-\frac{27}{63}\\=\frac{70+27-27}{63}\\=\frac{70}{63}\\=\frac{10}{9}\)
3. \(+\left(\frac{-2}{-9}\right) +\left(\frac{8}{-4}\right) -\left(\frac{-11}{3}\right)\\= \frac{2}{9}- \frac{8}{4}+\frac{11}{3}\\=\frac{2}{9}-\frac{2}{1}+\frac{11}{3}\\=\frac{2-2+11}{9}\\=\frac{11}{9}\)
4. \(-\left(\frac{5}{-4}\right) -\left(\frac{8}{-8}\right) +\left(\frac{-4}{8}\right)\\= \frac{5}{4}+ \frac{8}{8}-\frac{4}{8}\\=\frac{5}{4}+\frac{1}{1}-\frac{1}{2}\\=\frac{5+1-1}{4}\\=\frac{5}{4}\)
5. \(-\left(\frac{-5}{6}\right) +\left(\frac{-9}{-3}\right) +\left(\frac{-7}{2}\right)\\= \frac{5}{6}+ \frac{9}{3}-\frac{7}{2}\\=\frac{5}{6}+\frac{3}{1}-\frac{7}{2}\\=\frac{5+3-7}{6}\\=\frac{1}{6}\)
6. \(-\left(\frac{-10}{-7}\right) +\left(\frac{8}{10}\right) -\left(\frac{4}{9}\right)\\= \frac{-10}{7}+ \frac{8}{10}-\frac{4}{9}\\=\frac{-10}{7}+\frac{4}{5}-\frac{4}{9}\\=\frac{-450}{315}+\frac{252}{315}-\frac{140}{315}\\=\frac{-450+252-140}{315}\\=\frac{-338}{315}\)
7. \(+\left(\frac{-8}{9}\right) +\left(\frac{-8}{6}\right) -\left(\frac{3}{-12}\right)\\= \frac{-8}{9}- \frac{8}{6}+\frac{3}{12}\\=\frac{-8}{9}-\frac{4}{3}+\frac{1}{4}\\=\frac{-32}{36}-\frac{48}{36}+\frac{9}{36}\\=\frac{-32-48+9}{36}\\=\frac{-71}{36}\)
8. \(-\left(\frac{-5}{-7}\right) +\left(\frac{-8}{6}\right) +\left(\frac{7}{-2}\right)\\= \frac{-5}{7}- \frac{8}{6}-\frac{7}{2}\\=\frac{-5}{7}-\frac{4}{3}-\frac{7}{2}\\=\frac{-30}{42}-\frac{56}{42}-\frac{147}{42}\\=\frac{-30-56-147}{42}\\=\frac{-233}{42}\)
9. \(-\left(\frac{-4}{-3}\right) +\left(\frac{-7}{-8}\right) +\left(\frac{-6}{-2}\right)\\= \frac{-4}{3}+ \frac{7}{8}+\frac{6}{2}\\=\frac{-4}{3}+\frac{7}{8}+\frac{3}{1}\\=\frac{-32}{24}+\frac{21}{24}+\frac{72}{24}\\=\frac{-32+21+72}{24}\\=\frac{61}{24}\)
10. \(+\left(\frac{-2}{9}\right) +\left(\frac{5}{-6}\right) -\left(\frac{-10}{-8}\right)\\= \frac{-2}{9}- \frac{5}{6}-\frac{10}{8}\\=\frac{-2}{9}-\frac{5}{6}-\frac{5}{4}\\=\frac{-8}{36}-\frac{30}{36}-\frac{45}{36}\\=\frac{-8-30-45}{36}\\=\frac{-83}{36}\)
11. \(+\left(\frac{8}{3}\right) -\left(\frac{-7}{10}\right) +\left(\frac{-2}{-12}\right)\\= \frac{8}{3}+ \frac{7}{10}+\frac{2}{12}\\=\frac{8}{3}+\frac{7}{10}+\frac{1}{6}\\=\frac{80}{30}+\frac{21}{30}+\frac{5}{30}\\=\frac{80+21+5}{30}\\=\frac{106}{30}\\=\frac{53}{15}\)
12. \(+\left(\frac{2}{-7}\right) +\left(\frac{7}{-8}\right) -\left(\frac{12}{10}\right)\\= \frac{-2}{7}- \frac{7}{8}-\frac{12}{10}\\=\frac{-2}{7}-\frac{7}{8}-\frac{6}{5}\\=\frac{-80}{280}-\frac{245}{280}-\frac{336}{280}\\=\frac{-80-245-336}{280}\\=\frac{-661}{280}\)