Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{7}\right) -\left(\frac{4}{4}\right) -\left(\frac{4}{12}\right)\\= \frac{4}{7}- \frac{4}{4}-\frac{4}{12}\\=\frac{4}{7}-\frac{1}{1}-\frac{1}{3}\\=\frac{12}{21}-\frac{21}{21}-\frac{7}{21}\\=\frac{12-21-7}{21}\\=\frac{-16}{21}\)
2. \(+\left(\frac{-4}{7}\right) +\left(\frac{-5}{-2}\right) +\left(\frac{-9}{-10}\right)\\= \frac{-4}{7}+ \frac{5}{2}+\frac{9}{10}\\=\frac{-40}{70}+\frac{175}{70}+\frac{63}{70}\\=\frac{-40+175+63}{70}\\=\frac{198}{70}\\=\frac{99}{35}\)
3. \(+\left(\frac{2}{-3}\right) -\left(\frac{5}{-9}\right) -\left(\frac{2}{4}\right)\\= \frac{-2}{3}+ \frac{5}{9}-\frac{2}{4}\\=\frac{-2}{3}+\frac{5}{9}-\frac{1}{2}\\=\frac{-12}{18}+\frac{10}{18}-\frac{9}{18}\\=\frac{-12+10-9}{18}\\=\frac{-11}{18}\)
4. \(-\left(\frac{8}{7}\right) -\left(\frac{4}{2}\right) -\left(\frac{-2}{-7}\right)\\= \frac{-8}{7}- \frac{4}{2}-\frac{2}{7}\\=\frac{-8}{7}-\frac{2}{1}-\frac{2}{7}\\=\frac{-8-2-2}{7}\\=\frac{-12}{7}\)
5. \(+\left(\frac{-3}{2}\right) -\left(\frac{9}{-10}\right) +\left(\frac{-5}{-2}\right)\\= \frac{-3}{2}+ \frac{9}{10}+\frac{5}{2}\\=\frac{-15}{10}+\frac{9}{10}+\frac{25}{10}\\=\frac{-15+9+25}{10}\\=\frac{19}{10}\)
6. \(+\left(\frac{-5}{2}\right) +\left(\frac{6}{10}\right) +\left(\frac{9}{-10}\right)\\= \frac{-5}{2}+ \frac{6}{10}-\frac{9}{10}\\=\frac{-5}{2}+\frac{3}{5}-\frac{9}{10}\\=\frac{-25}{10}+\frac{6}{10}-\frac{9}{10}\\=\frac{-25+6-9}{10}\\=\frac{-28}{10}\\=\frac{-14}{5}\)
7. \(-\left(\frac{5}{-6}\right) -\left(\frac{-5}{6}\right) +\left(\frac{10}{-7}\right)\\= \frac{5}{6}+ \frac{5}{6}-\frac{10}{7}\\=\frac{35}{42}+\frac{35}{42}-\frac{60}{42}\\=\frac{35+35-60}{42}\\=\frac{10}{42}\\=\frac{5}{21}\)
8. \(+\left(\frac{5}{-2}\right) +\left(\frac{-6}{9}\right) -\left(\frac{-5}{10}\right)\\= \frac{-5}{2}- \frac{6}{9}+\frac{5}{10}\\=\frac{-5}{2}-\frac{2}{3}+\frac{1}{2}\\=\frac{-15}{6}-\frac{4}{6}+\frac{3}{6}\\=\frac{-15-4+3}{6}\\=\frac{-16}{6}\\=\frac{-8}{3}\)
9. \(+\left(\frac{9}{4}\right) +\left(\frac{-6}{-8}\right) +\left(\frac{-11}{-2}\right)\\= \frac{9}{4}+ \frac{6}{8}+\frac{11}{2}\\=\frac{9}{4}+\frac{3}{4}+\frac{11}{2}\\=\frac{9+3+11}{4}\\=\frac{23}{4}\)
10. \(+\left(\frac{-10}{7}\right) -\left(\frac{4}{9}\right) -\left(\frac{-9}{-12}\right)\\= \frac{-10}{7}- \frac{4}{9}-\frac{9}{12}\\=\frac{-10}{7}-\frac{4}{9}-\frac{3}{4}\\=\frac{-360}{252}-\frac{112}{252}-\frac{189}{252}\\=\frac{-360-112-189}{252}\\=\frac{-661}{252}\)
11. \(+\left(\frac{4}{5}\right) -\left(\frac{-7}{5}\right) +\left(\frac{10}{12}\right)\\= \frac{4}{5}+ \frac{7}{5}+\frac{10}{12}\\=\frac{4}{5}+\frac{7}{5}+\frac{5}{6}\\=\frac{24}{30}+\frac{42}{30}+\frac{25}{30}\\=\frac{24+42+25}{30}\\=\frac{91}{30}\)
12. \(+\left(\frac{-10}{-3}\right) +\left(\frac{-3}{6}\right) +\left(\frac{-5}{-3}\right)\\= \frac{10}{3}- \frac{3}{6}+\frac{5}{3}\\=\frac{10}{3}-\frac{1}{2}+\frac{5}{3}\\=\frac{20}{6}-\frac{3}{6}+\frac{10}{6}\\=\frac{20-3+10}{6}\\=\frac{27}{6}\\=\frac{9}{2}\)