Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-7}{-2}\right) +\left(\frac{-8}{2}\right)\\= \frac{-6}{5}- \frac{7}{2}-\frac{8}{2}\\=\frac{-6}{5}-\frac{7}{2}-\frac{4}{1}\\=\frac{-12}{10}-\frac{35}{10}-\frac{40}{10}\\=\frac{-12-35-40}{10}\\=\frac{-87}{10}\)
2. \(-\left(\frac{-9}{8}\right) +\left(\frac{10}{-4}\right) -\left(\frac{-12}{-10}\right)\\= \frac{9}{8}- \frac{10}{4}-\frac{12}{10}\\=\frac{9}{8}-\frac{5}{2}-\frac{6}{5}\\=\frac{45}{40}-\frac{100}{40}-\frac{48}{40}\\=\frac{45-100-48}{40}\\=\frac{-103}{40}\)
3. \(-\left(\frac{-3}{-5}\right) +\left(\frac{7}{-7}\right) -\left(\frac{-11}{2}\right)\\= \frac{-3}{5}- \frac{7}{7}+\frac{11}{2}\\=\frac{-3}{5}-\frac{1}{1}+\frac{11}{2}\\=\frac{-6}{10}-\frac{10}{10}+\frac{55}{10}\\=\frac{-6-10+55}{10}\\=\frac{39}{10}\)
4. \(-\left(\frac{-7}{9}\right) +\left(\frac{10}{-7}\right) -\left(\frac{-3}{-5}\right)\\= \frac{7}{9}- \frac{10}{7}-\frac{3}{5}\\=\frac{245}{315}-\frac{450}{315}-\frac{189}{315}\\=\frac{245-450-189}{315}\\=\frac{-394}{315}\)
5. \(-\left(\frac{-6}{5}\right) +\left(\frac{3}{10}\right) -\left(\frac{-4}{4}\right)\\= \frac{6}{5}+ \frac{3}{10}+\frac{4}{4}\\=\frac{6}{5}+\frac{3}{10}+\frac{1}{1}\\=\frac{12}{10}+\frac{3}{10}+\frac{10}{10}\\=\frac{12+3+10}{10}\\=\frac{25}{10}\\=\frac{5}{2}\)
6. \(+\left(\frac{-5}{2}\right) +\left(\frac{-2}{8}\right) +\left(\frac{10}{4}\right)\\= \frac{-5}{2}- \frac{2}{8}+\frac{10}{4}\\=\frac{-5}{2}-\frac{1}{4}+\frac{5}{2}\\=\frac{-10}{4}-\frac{1}{4}+\frac{10}{4}\\=\frac{-10-1+10}{4}\\=\frac{-1}{4}\)
7. \(-\left(\frac{4}{-5}\right) +\left(\frac{9}{-8}\right) +\left(\frac{-7}{6}\right)\\= \frac{4}{5}- \frac{9}{8}-\frac{7}{6}\\=\frac{96}{120}-\frac{135}{120}-\frac{140}{120}\\=\frac{96-135-140}{120}\\=\frac{-179}{120}\)
8. \(+\left(\frac{7}{-8}\right) +\left(\frac{4}{8}\right) +\left(\frac{-6}{6}\right)\\= \frac{-7}{8}+ \frac{4}{8}-\frac{6}{6}\\=\frac{-7}{8}+\frac{1}{2}-\frac{1}{1}\\=\frac{-7+1-1}{8}\\=\frac{-7}{8}\)
9. \(+\left(\frac{-10}{-7}\right) +\left(\frac{-6}{-5}\right) +\left(\frac{2}{-12}\right)\\= \frac{10}{7}+ \frac{6}{5}-\frac{2}{12}\\=\frac{10}{7}+\frac{6}{5}-\frac{1}{6}\\=\frac{300}{210}+\frac{252}{210}-\frac{35}{210}\\=\frac{300+252-35}{210}\\=\frac{517}{210}\)
10. \(+\left(\frac{8}{7}\right) -\left(\frac{6}{-7}\right) -\left(\frac{4}{5}\right)\\= \frac{8}{7}+ \frac{6}{7}-\frac{4}{5}\\=\frac{40}{35}+\frac{30}{35}-\frac{28}{35}\\=\frac{40+30-28}{35}\\=\frac{42}{35}\\=\frac{6}{5}\)
11. \(+\left(\frac{-10}{7}\right) -\left(\frac{10}{2}\right) +\left(\frac{9}{5}\right)\\= \frac{-10}{7}- \frac{10}{2}+\frac{9}{5}\\=\frac{-10}{7}-\frac{5}{1}+\frac{9}{5}\\=\frac{-50}{35}-\frac{175}{35}+\frac{63}{35}\\=\frac{-50-175+63}{35}\\=\frac{-162}{35}\)
12. \(-\left(\frac{9}{-2}\right) -\left(\frac{-2}{7}\right) -\left(\frac{-12}{10}\right)\\= \frac{9}{2}+ \frac{2}{7}+\frac{12}{10}\\=\frac{9}{2}+\frac{2}{7}+\frac{6}{5}\\=\frac{315}{70}+\frac{20}{70}+\frac{84}{70}\\=\frac{315+20+84}{70}\\=\frac{419}{70}\)