Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{-8}\right) -\left(\frac{-10}{3}\right) +\left(\frac{3}{-6}\right)\\= \frac{3}{8}+ \frac{10}{3}-\frac{3}{6}\\=\frac{3}{8}+\frac{10}{3}-\frac{1}{2}\\=\frac{9}{24}+\frac{80}{24}-\frac{12}{24}\\=\frac{9+80-12}{24}\\=\frac{77}{24}\)
2. \(-\left(\frac{-8}{-5}\right) +\left(\frac{2}{-8}\right) +\left(\frac{10}{-2}\right)\\= \frac{-8}{5}- \frac{2}{8}-\frac{10}{2}\\=\frac{-8}{5}-\frac{1}{4}-\frac{5}{1}\\=\frac{-32}{20}-\frac{5}{20}-\frac{100}{20}\\=\frac{-32-5-100}{20}\\=\frac{-137}{20}\)
3. \(+\left(\frac{-10}{-9}\right) +\left(\frac{-6}{-5}\right) -\left(\frac{-9}{-7}\right)\\= \frac{10}{9}+ \frac{6}{5}-\frac{9}{7}\\=\frac{350}{315}+\frac{378}{315}-\frac{405}{315}\\=\frac{350+378-405}{315}\\=\frac{323}{315}\)
4. \(+\left(\frac{4}{9}\right) -\left(\frac{-2}{-8}\right) -\left(\frac{8}{11}\right)\\= \frac{4}{9}- \frac{2}{8}-\frac{8}{11}\\=\frac{4}{9}-\frac{1}{4}-\frac{8}{11}\\=\frac{176}{396}-\frac{99}{396}-\frac{288}{396}\\=\frac{176-99-288}{396}\\=\frac{-211}{396}\)
5. \(+\left(\frac{-9}{-4}\right) +\left(\frac{-8}{3}\right) +\left(\frac{-10}{-3}\right)\\= \frac{9}{4}- \frac{8}{3}+\frac{10}{3}\\=\frac{27}{12}-\frac{32}{12}+\frac{40}{12}\\=\frac{27-32+40}{12}\\=\frac{35}{12}\)
6. \(-\left(\frac{10}{9}\right) -\left(\frac{3}{-8}\right) -\left(\frac{7}{5}\right)\\= \frac{-10}{9}+ \frac{3}{8}-\frac{7}{5}\\=\frac{-400}{360}+\frac{135}{360}-\frac{504}{360}\\=\frac{-400+135-504}{360}\\=\frac{-769}{360}\)
7. \(+\left(\frac{-2}{-3}\right) +\left(\frac{-10}{8}\right) +\left(\frac{4}{-8}\right)\\= \frac{2}{3}- \frac{10}{8}-\frac{4}{8}\\=\frac{2}{3}-\frac{5}{4}-\frac{1}{2}\\=\frac{8}{12}-\frac{15}{12}-\frac{6}{12}\\=\frac{8-15-6}{12}\\=\frac{-13}{12}\)
8. \(-\left(\frac{-3}{-2}\right) +\left(\frac{5}{-7}\right) +\left(\frac{9}{-12}\right)\\= \frac{-3}{2}- \frac{5}{7}-\frac{9}{12}\\=\frac{-3}{2}-\frac{5}{7}-\frac{3}{4}\\=\frac{-42}{28}-\frac{20}{28}-\frac{21}{28}\\=\frac{-42-20-21}{28}\\=\frac{-83}{28}\)
9. \(-\left(\frac{-5}{2}\right) +\left(\frac{10}{-8}\right) -\left(\frac{10}{-6}\right)\\= \frac{5}{2}- \frac{10}{8}+\frac{10}{6}\\=\frac{5}{2}-\frac{5}{4}+\frac{5}{3}\\=\frac{30}{12}-\frac{15}{12}+\frac{20}{12}\\=\frac{30-15+20}{12}\\=\frac{35}{12}\)
10. \(-\left(\frac{-9}{2}\right) +\left(\frac{-3}{7}\right) +\left(\frac{-10}{3}\right)\\= \frac{9}{2}- \frac{3}{7}-\frac{10}{3}\\=\frac{189}{42}-\frac{18}{42}-\frac{140}{42}\\=\frac{189-18-140}{42}\\=\frac{31}{42}\)
11. \(+\left(\frac{8}{3}\right) +\left(\frac{2}{-3}\right) -\left(\frac{7}{3}\right)\\= \frac{8}{3}- \frac{2}{3}-\frac{7}{3}\\=\frac{8-2-7}{3}\\=\frac{-1}{3}\)
12. \(-\left(\frac{-3}{-2}\right) -\left(\frac{5}{-4}\right) -\left(\frac{2}{11}\right)\\= \frac{-3}{2}+ \frac{5}{4}-\frac{2}{11}\\=\frac{-66}{44}+\frac{55}{44}-\frac{8}{44}\\=\frac{-66+55-8}{44}\\=\frac{-19}{44}\)