Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{2}\right) -\left(\frac{7}{6}\right) +\left(\frac{-5}{-3}\right)\\= \frac{-7}{2}- \frac{7}{6}+\frac{5}{3}\\=\frac{-21}{6}-\frac{7}{6}+\frac{10}{6}\\=\frac{-21-7+10}{6}\\=\frac{-18}{6}\\=\frac{-3}{1}\)
2. \(+\left(\frac{-2}{-9}\right) -\left(\frac{7}{-4}\right) -\left(\frac{10}{-3}\right)\\= \frac{2}{9}+ \frac{7}{4}+\frac{10}{3}\\=\frac{8}{36}+\frac{63}{36}+\frac{120}{36}\\=\frac{8+63+120}{36}\\=\frac{191}{36}\)
3. \(+\left(\frac{-5}{-6}\right) -\left(\frac{9}{-2}\right) -\left(\frac{-8}{12}\right)\\= \frac{5}{6}+ \frac{9}{2}+\frac{8}{12}\\=\frac{5}{6}+\frac{9}{2}+\frac{2}{3}\\=\frac{5+9+2}{6}\\=\frac{16}{6}\\=\frac{8}{3}\)
4. \(-\left(\frac{5}{-2}\right) +\left(\frac{4}{-9}\right) -\left(\frac{10}{-10}\right)\\= \frac{5}{2}- \frac{4}{9}+\frac{10}{10}\\=\frac{5}{2}-\frac{4}{9}+\frac{1}{1}\\=\frac{45}{18}-\frac{8}{18}+\frac{18}{18}\\=\frac{45-8+18}{18}\\=\frac{55}{18}\)
5. \(-\left(\frac{-5}{6}\right) -\left(\frac{9}{-6}\right) -\left(\frac{6}{-10}\right)\\= \frac{5}{6}+ \frac{9}{6}+\frac{6}{10}\\=\frac{5}{6}+\frac{3}{2}+\frac{3}{5}\\=\frac{25}{30}+\frac{45}{30}+\frac{18}{30}\\=\frac{25+45+18}{30}\\=\frac{88}{30}\\=\frac{44}{15}\)
6. \(+\left(\frac{7}{6}\right) +\left(\frac{2}{8}\right) +\left(\frac{-7}{4}\right)\\= \frac{7}{6}+ \frac{2}{8}-\frac{7}{4}\\=\frac{7}{6}+\frac{1}{4}-\frac{7}{4}\\=\frac{14}{12}+\frac{3}{12}-\frac{21}{12}\\=\frac{14+3-21}{12}\\=\frac{-4}{12}\\=\frac{-1}{3}\)
7. \(+\left(\frac{-2}{-3}\right) +\left(\frac{-2}{7}\right) +\left(\frac{11}{6}\right)\\= \frac{2}{3}- \frac{2}{7}+\frac{11}{6}\\=\frac{28}{42}-\frac{12}{42}+\frac{77}{42}\\=\frac{28-12+77}{42}\\=\frac{93}{42}\\=\frac{31}{14}\)
8. \(-\left(\frac{-9}{5}\right) +\left(\frac{10}{2}\right) +\left(\frac{-11}{9}\right)\\= \frac{9}{5}+ \frac{10}{2}-\frac{11}{9}\\=\frac{9}{5}+\frac{5}{1}-\frac{11}{9}\\=\frac{81}{45}+\frac{225}{45}-\frac{55}{45}\\=\frac{81+225-55}{45}\\=\frac{251}{45}\)
9. \(-\left(\frac{-6}{-7}\right) -\left(\frac{-4}{-3}\right) -\left(\frac{-10}{5}\right)\\= \frac{-6}{7}- \frac{4}{3}+\frac{10}{5}\\=\frac{-6}{7}-\frac{4}{3}+\frac{2}{1}\\=\frac{-18}{21}-\frac{28}{21}+\frac{42}{21}\\=\frac{-18-28+42}{21}\\=\frac{-4}{21}\)
10. \(+\left(\frac{10}{-7}\right) -\left(\frac{6}{-5}\right) +\left(\frac{5}{10}\right)\\= \frac{-10}{7}+ \frac{6}{5}+\frac{5}{10}\\=\frac{-10}{7}+\frac{6}{5}+\frac{1}{2}\\=\frac{-100}{70}+\frac{84}{70}+\frac{35}{70}\\=\frac{-100+84+35}{70}\\=\frac{19}{70}\)
11. \(-\left(\frac{-10}{3}\right) -\left(\frac{-3}{10}\right) +\left(\frac{4}{-2}\right)\\= \frac{10}{3}+ \frac{3}{10}-\frac{4}{2}\\=\frac{10}{3}+\frac{3}{10}-\frac{2}{1}\\=\frac{100}{30}+\frac{9}{30}-\frac{60}{30}\\=\frac{100+9-60}{30}\\=\frac{49}{30}\)
12. \(-\left(\frac{2}{-9}\right) -\left(\frac{5}{-9}\right) +\left(\frac{10}{9}\right)\\= \frac{2}{9}+ \frac{5}{9}+\frac{10}{9}\\=\frac{2+5+10}{9}\\=\frac{17}{9}\)