Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

---

Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{2}\right) -\left(\frac{10}{-3}\right) +\left(\frac{6}{12}\right)\\= \frac{3}{2}+ \frac{10}{3}+\frac{6}{12}\\=\frac{3}{2}+\frac{10}{3}+\frac{1}{2}\\=\frac{9}{6}+\frac{20}{6}+\frac{3}{6}\\=\frac{9+20+3}{6}\\=\frac{32}{6}\\=\frac{16}{3}\)
2. \(+\left(\frac{3}{5}\right) +\left(\frac{-3}{-9}\right) -\left(\frac{2}{2}\right)\\= \frac{3}{5}+ \frac{3}{9}-\frac{2}{2}\\=\frac{3}{5}+\frac{1}{3}-\frac{1}{1}\\=\frac{9}{15}+\frac{5}{15}-\frac{15}{15}\\=\frac{9+5-15}{15}\\=\frac{-1}{15}\)
3. \(+\left(\frac{6}{5}\right) -\left(\frac{-10}{-2}\right) +\left(\frac{-8}{11}\right)\\= \frac{6}{5}- \frac{10}{2}-\frac{8}{11}\\=\frac{6}{5}-\frac{5}{1}-\frac{8}{11}\\=\frac{66}{55}-\frac{275}{55}-\frac{40}{55}\\=\frac{66-275-40}{55}\\=\frac{-249}{55}\)
4. \(+\left(\frac{-4}{-3}\right) +\left(\frac{-5}{4}\right) -\left(\frac{12}{12}\right)\\= \frac{4}{3}- \frac{5}{4}-\frac{12}{12}\\=\frac{4}{3}-\frac{5}{4}-\frac{1}{1}\\=\frac{16}{12}-\frac{15}{12}-\frac{12}{12}\\=\frac{16-15-12}{12}\\=\frac{-11}{12}\)
5. \(+\left(\frac{10}{-3}\right) +\left(\frac{-4}{-7}\right) +\left(\frac{2}{8}\right)\\= \frac{-10}{3}+ \frac{4}{7}+\frac{2}{8}\\=\frac{-10}{3}+\frac{4}{7}+\frac{1}{4}\\=\frac{-280}{84}+\frac{48}{84}+\frac{21}{84}\\=\frac{-280+48+21}{84}\\=\frac{-211}{84}\)
6. \(+\left(\frac{5}{-2}\right) +\left(\frac{6}{-4}\right) -\left(\frac{-2}{7}\right)\\= \frac{-5}{2}- \frac{6}{4}+\frac{2}{7}\\=\frac{-5}{2}-\frac{3}{2}+\frac{2}{7}\\=\frac{-35}{14}-\frac{21}{14}+\frac{4}{14}\\=\frac{-35-21+4}{14}\\=\frac{-52}{14}\\=\frac{-26}{7}\)
7. \(-\left(\frac{7}{-8}\right) -\left(\frac{10}{4}\right) +\left(\frac{-3}{-2}\right)\\= \frac{7}{8}- \frac{10}{4}+\frac{3}{2}\\=\frac{7}{8}-\frac{5}{2}+\frac{3}{2}\\=\frac{7-5+3}{8}\\=\frac{5}{8}\)
8. \(-\left(\frac{4}{9}\right) -\left(\frac{6}{8}\right) +\left(\frac{2}{5}\right)\\= \frac{-4}{9}- \frac{6}{8}+\frac{2}{5}\\=\frac{-4}{9}-\frac{3}{4}+\frac{2}{5}\\=\frac{-80}{180}-\frac{135}{180}+\frac{72}{180}\\=\frac{-80-135+72}{180}\\=\frac{-143}{180}\)
9. \(+\left(\frac{-7}{-2}\right) +\left(\frac{9}{-7}\right) +\left(\frac{-7}{-7}\right)\\= \frac{7}{2}- \frac{9}{7}+\frac{7}{7}\\=\frac{7}{2}-\frac{9}{7}+\frac{1}{1}\\=\frac{49}{14}-\frac{18}{14}+\frac{14}{14}\\=\frac{49-18+14}{14}\\=\frac{45}{14}\)
10. \(+\left(\frac{-7}{-2}\right) +\left(\frac{-7}{-6}\right) -\left(\frac{3}{-11}\right)\\= \frac{7}{2}+ \frac{7}{6}+\frac{3}{11}\\=\frac{231}{66}+\frac{77}{66}+\frac{18}{66}\\=\frac{231+77+18}{66}\\=\frac{326}{66}\\=\frac{163}{33}\)
11. \(+\left(\frac{7}{-3}\right) -\left(\frac{-10}{-8}\right) +\left(\frac{-11}{9}\right)\\= \frac{-7}{3}- \frac{10}{8}-\frac{11}{9}\\=\frac{-7}{3}-\frac{5}{4}-\frac{11}{9}\\=\frac{-84}{36}-\frac{45}{36}-\frac{44}{36}\\=\frac{-84-45-44}{36}\\=\frac{-173}{36}\)
12. \(-\left(\frac{7}{3}\right) +\left(\frac{4}{-10}\right) -\left(\frac{-2}{-3}\right)\\= \frac{-7}{3}- \frac{4}{10}-\frac{2}{3}\\=\frac{-7}{3}-\frac{2}{5}-\frac{2}{3}\\=\frac{-35}{15}-\frac{6}{15}-\frac{10}{15}\\=\frac{-35-6-10}{15}\\=\frac{-51}{15}\\=\frac{-17}{5}\)