Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{2}\right) +\left(\frac{2}{-10}\right) -\left(\frac{4}{-3}\right)\\= \frac{5}{2}- \frac{2}{10}+\frac{4}{3}\\=\frac{5}{2}-\frac{1}{5}+\frac{4}{3}\\=\frac{75}{30}-\frac{6}{30}+\frac{40}{30}\\=\frac{75-6+40}{30}\\=\frac{109}{30}\)
2. \(+\left(\frac{3}{-8}\right) +\left(\frac{-8}{-7}\right) +\left(\frac{3}{-2}\right)\\= \frac{-3}{8}+ \frac{8}{7}-\frac{3}{2}\\=\frac{-21}{56}+\frac{64}{56}-\frac{84}{56}\\=\frac{-21+64-84}{56}\\=\frac{-41}{56}\)
3. \(-\left(\frac{-10}{7}\right) +\left(\frac{-8}{-6}\right) -\left(\frac{5}{-6}\right)\\= \frac{10}{7}+ \frac{8}{6}+\frac{5}{6}\\=\frac{10}{7}+\frac{4}{3}+\frac{5}{6}\\=\frac{60}{42}+\frac{56}{42}+\frac{35}{42}\\=\frac{60+56+35}{42}\\=\frac{151}{42}\)
4. \(+\left(\frac{7}{-6}\right) -\left(\frac{7}{5}\right) +\left(\frac{-6}{3}\right)\\= \frac{-7}{6}- \frac{7}{5}-\frac{6}{3}\\=\frac{-7}{6}-\frac{7}{5}-\frac{2}{1}\\=\frac{-35}{30}-\frac{42}{30}-\frac{60}{30}\\=\frac{-35-42-60}{30}\\=\frac{-137}{30}\)
5. \(-\left(\frac{2}{-5}\right) +\left(\frac{-3}{-10}\right) +\left(\frac{11}{-11}\right)\\= \frac{2}{5}+ \frac{3}{10}-\frac{11}{11}\\=\frac{2}{5}+\frac{3}{10}-\frac{1}{1}\\=\frac{4}{10}+\frac{3}{10}-\frac{10}{10}\\=\frac{4+3-10}{10}\\=\frac{-3}{10}\)
6. \(+\left(\frac{2}{7}\right) +\left(\frac{10}{-8}\right) +\left(\frac{8}{5}\right)\\= \frac{2}{7}- \frac{10}{8}+\frac{8}{5}\\=\frac{2}{7}-\frac{5}{4}+\frac{8}{5}\\=\frac{40}{140}-\frac{175}{140}+\frac{224}{140}\\=\frac{40-175+224}{140}\\=\frac{89}{140}\)
7. \(+\left(\frac{5}{-6}\right) -\left(\frac{4}{-8}\right) +\left(\frac{-4}{-9}\right)\\= \frac{-5}{6}+ \frac{4}{8}+\frac{4}{9}\\=\frac{-5}{6}+\frac{1}{2}+\frac{4}{9}\\=\frac{-15}{18}+\frac{9}{18}+\frac{8}{18}\\=\frac{-15+9+8}{18}\\=\frac{2}{18}\\=\frac{1}{9}\)
8. \(+\left(\frac{2}{-9}\right) +\left(\frac{10}{-2}\right) +\left(\frac{-10}{4}\right)\\= \frac{-2}{9}- \frac{10}{2}-\frac{10}{4}\\=\frac{-2}{9}-\frac{5}{1}-\frac{5}{2}\\=\frac{-4}{18}-\frac{90}{18}-\frac{45}{18}\\=\frac{-4-90-45}{18}\\=\frac{-139}{18}\)
9. \(-\left(\frac{-5}{-9}\right) -\left(\frac{-3}{-10}\right) +\left(\frac{10}{-2}\right)\\= \frac{-5}{9}- \frac{3}{10}-\frac{10}{2}\\=\frac{-5}{9}-\frac{3}{10}-\frac{5}{1}\\=\frac{-50}{90}-\frac{27}{90}-\frac{450}{90}\\=\frac{-50-27-450}{90}\\=\frac{-527}{90}\)
10. \(+\left(\frac{4}{-3}\right) +\left(\frac{6}{-5}\right) -\left(\frac{-9}{6}\right)\\= \frac{-4}{3}- \frac{6}{5}+\frac{9}{6}\\=\frac{-4}{3}-\frac{6}{5}+\frac{3}{2}\\=\frac{-40}{30}-\frac{36}{30}+\frac{45}{30}\\=\frac{-40-36+45}{30}\\=\frac{-31}{30}\)
11. \(+\left(\frac{2}{-7}\right) +\left(\frac{8}{-8}\right) -\left(\frac{11}{-2}\right)\\= \frac{-2}{7}- \frac{8}{8}+\frac{11}{2}\\=\frac{-2}{7}-\frac{1}{1}+\frac{11}{2}\\=\frac{-4}{14}-\frac{14}{14}+\frac{77}{14}\\=\frac{-4-14+77}{14}\\=\frac{59}{14}\)
12. \(+\left(\frac{-4}{-5}\right) +\left(\frac{-7}{-4}\right) -\left(\frac{-7}{11}\right)\\= \frac{4}{5}+ \frac{7}{4}+\frac{7}{11}\\=\frac{176}{220}+\frac{385}{220}+\frac{140}{220}\\=\frac{176+385+140}{220}\\=\frac{701}{220}\)