Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{-2}\right) +\left(\frac{-3}{-10}\right) +\left(\frac{7}{5}\right)\\= \frac{-3}{2}+ \frac{3}{10}+\frac{7}{5}\\=\frac{-15}{10}+\frac{3}{10}+\frac{14}{10}\\=\frac{-15+3+14}{10}\\=\frac{2}{10}\\=\frac{1}{5}\)
2. \(+\left(\frac{-2}{-9}\right) -\left(\frac{9}{-10}\right) +\left(\frac{9}{6}\right)\\= \frac{2}{9}+ \frac{9}{10}+\frac{9}{6}\\=\frac{2}{9}+\frac{9}{10}+\frac{3}{2}\\=\frac{20}{90}+\frac{81}{90}+\frac{135}{90}\\=\frac{20+81+135}{90}\\=\frac{236}{90}\\=\frac{118}{45}\)
3. \(-\left(\frac{2}{3}\right) -\left(\frac{-6}{5}\right) -\left(\frac{-4}{12}\right)\\= \frac{-2}{3}+ \frac{6}{5}+\frac{4}{12}\\=\frac{-2}{3}+\frac{6}{5}+\frac{1}{3}\\=\frac{-10}{15}+\frac{18}{15}+\frac{5}{15}\\=\frac{-10+18+5}{15}\\=\frac{13}{15}\)
4. \(-\left(\frac{3}{2}\right) -\left(\frac{6}{4}\right) +\left(\frac{6}{11}\right)\\= \frac{-3}{2}- \frac{6}{4}+\frac{6}{11}\\=\frac{-3}{2}-\frac{3}{2}+\frac{6}{11}\\=\frac{-33}{22}-\frac{33}{22}+\frac{12}{22}\\=\frac{-33-33+12}{22}\\=\frac{-54}{22}\\=\frac{-27}{11}\)
5. \(-\left(\frac{-5}{8}\right) +\left(\frac{4}{-9}\right) -\left(\frac{8}{-4}\right)\\= \frac{5}{8}- \frac{4}{9}+\frac{8}{4}\\=\frac{5}{8}-\frac{4}{9}+\frac{2}{1}\\=\frac{45}{72}-\frac{32}{72}+\frac{144}{72}\\=\frac{45-32+144}{72}\\=\frac{157}{72}\)
6. \(-\left(\frac{-9}{-2}\right) +\left(\frac{2}{10}\right) +\left(\frac{-3}{-4}\right)\\= \frac{-9}{2}+ \frac{2}{10}+\frac{3}{4}\\=\frac{-9}{2}+\frac{1}{5}+\frac{3}{4}\\=\frac{-90}{20}+\frac{4}{20}+\frac{15}{20}\\=\frac{-90+4+15}{20}\\=\frac{-71}{20}\)
7. \(+\left(\frac{-10}{3}\right) +\left(\frac{3}{-8}\right) -\left(\frac{4}{-8}\right)\\= \frac{-10}{3}- \frac{3}{8}+\frac{4}{8}\\=\frac{-10}{3}-\frac{3}{8}+\frac{1}{2}\\=\frac{-80}{24}-\frac{9}{24}+\frac{12}{24}\\=\frac{-80-9+12}{24}\\=\frac{-77}{24}\)
8. \(-\left(\frac{-10}{-3}\right) +\left(\frac{3}{-9}\right) +\left(\frac{7}{-6}\right)\\= \frac{-10}{3}- \frac{3}{9}-\frac{7}{6}\\=\frac{-10}{3}-\frac{1}{3}-\frac{7}{6}\\=\frac{-20}{6}-\frac{2}{6}-\frac{7}{6}\\=\frac{-20-2-7}{6}\\=\frac{-29}{6}\)
9. \(-\left(\frac{7}{2}\right) +\left(\frac{-5}{-6}\right) -\left(\frac{5}{-12}\right)\\= \frac{-7}{2}+ \frac{5}{6}+\frac{5}{12}\\=\frac{-42}{12}+\frac{10}{12}+\frac{5}{12}\\=\frac{-42+10+5}{12}\\=\frac{-27}{12}\\=\frac{-9}{4}\)
10. \(+\left(\frac{-6}{-7}\right) +\left(\frac{2}{-3}\right) +\left(\frac{3}{-9}\right)\\= \frac{6}{7}- \frac{2}{3}-\frac{3}{9}\\=\frac{6}{7}-\frac{2}{3}-\frac{1}{3}\\=\frac{18}{21}-\frac{14}{21}-\frac{7}{21}\\=\frac{18-14-7}{21}\\=\frac{-3}{21}\\=\frac{-1}{7}\)
11. \(+\left(\frac{4}{-3}\right) +\left(\frac{-2}{-9}\right) +\left(\frac{4}{9}\right)\\= \frac{-4}{3}+ \frac{2}{9}+\frac{4}{9}\\=\frac{-12}{9}+\frac{2}{9}+\frac{4}{9}\\=\frac{-12+2+4}{9}\\=\frac{-6}{9}\\=\frac{-2}{3}\)
12. \(-\left(\frac{3}{-2}\right) +\left(\frac{6}{-6}\right) +\left(\frac{9}{-6}\right)\\= \frac{3}{2}- \frac{6}{6}-\frac{9}{6}\\=\frac{3}{2}-\frac{1}{1}-\frac{3}{2}\\=\frac{3-1-3}{2}\\=\frac{-1}{2}\)