Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{2}\right) -\left(\frac{-7}{-2}\right) +\left(\frac{-10}{-12}\right)\\= \frac{-5}{2}- \frac{7}{2}+\frac{10}{12}\\=\frac{-5}{2}-\frac{7}{2}+\frac{5}{6}\\=\frac{-15}{6}-\frac{21}{6}+\frac{5}{6}\\=\frac{-15-21+5}{6}\\=\frac{-31}{6}\)
2. \(+\left(\frac{5}{-7}\right) -\left(\frac{5}{-2}\right) -\left(\frac{12}{-11}\right)\\= \frac{-5}{7}+ \frac{5}{2}+\frac{12}{11}\\=\frac{-110}{154}+\frac{385}{154}+\frac{168}{154}\\=\frac{-110+385+168}{154}\\=\frac{443}{154}\)
3. \(-\left(\frac{-8}{-3}\right) +\left(\frac{-10}{9}\right) +\left(\frac{6}{9}\right)\\= \frac{-8}{3}- \frac{10}{9}+\frac{6}{9}\\=\frac{-8}{3}-\frac{10}{9}+\frac{2}{3}\\=\frac{-24}{9}-\frac{10}{9}+\frac{6}{9}\\=\frac{-24-10+6}{9}\\=\frac{-28}{9}\)
4. \(+\left(\frac{4}{3}\right) +\left(\frac{10}{-5}\right) +\left(\frac{-12}{9}\right)\\= \frac{4}{3}- \frac{10}{5}-\frac{12}{9}\\=\frac{4}{3}-\frac{2}{1}-\frac{4}{3}\\=\frac{4-2-4}{3}\\=\frac{-2}{3}\)
5. \(+\left(\frac{10}{3}\right) +\left(\frac{6}{5}\right) -\left(\frac{-3}{-3}\right)\\= \frac{10}{3}+ \frac{6}{5}-\frac{3}{3}\\=\frac{10}{3}+\frac{6}{5}-\frac{1}{1}\\=\frac{50}{15}+\frac{18}{15}-\frac{15}{15}\\=\frac{50+18-15}{15}\\=\frac{53}{15}\)
6. \(+\left(\frac{10}{3}\right) -\left(\frac{-5}{4}\right) +\left(\frac{-11}{-3}\right)\\= \frac{10}{3}+ \frac{5}{4}+\frac{11}{3}\\=\frac{40}{12}+\frac{15}{12}+\frac{44}{12}\\=\frac{40+15+44}{12}\\=\frac{99}{12}\\=\frac{33}{4}\)
7. \(+\left(\frac{8}{9}\right) -\left(\frac{5}{-2}\right) +\left(\frac{6}{-9}\right)\\= \frac{8}{9}+ \frac{5}{2}-\frac{6}{9}\\=\frac{8}{9}+\frac{5}{2}-\frac{2}{3}\\=\frac{16}{18}+\frac{45}{18}-\frac{12}{18}\\=\frac{16+45-12}{18}\\=\frac{49}{18}\)
8. \(+\left(\frac{8}{-3}\right) +\left(\frac{10}{-4}\right) +\left(\frac{7}{-5}\right)\\= \frac{-8}{3}- \frac{10}{4}-\frac{7}{5}\\=\frac{-8}{3}-\frac{5}{2}-\frac{7}{5}\\=\frac{-80}{30}-\frac{75}{30}-\frac{42}{30}\\=\frac{-80-75-42}{30}\\=\frac{-197}{30}\)
9. \(+\left(\frac{-9}{-2}\right) +\left(\frac{3}{-9}\right) -\left(\frac{10}{12}\right)\\= \frac{9}{2}- \frac{3}{9}-\frac{10}{12}\\=\frac{9}{2}-\frac{1}{3}-\frac{5}{6}\\=\frac{27}{6}-\frac{2}{6}-\frac{5}{6}\\=\frac{27-2-5}{6}\\=\frac{20}{6}\\=\frac{10}{3}\)
10. \(+\left(\frac{-4}{-7}\right) -\left(\frac{10}{-7}\right) +\left(\frac{6}{12}\right)\\= \frac{4}{7}+ \frac{10}{7}+\frac{6}{12}\\=\frac{4}{7}+\frac{10}{7}+\frac{1}{2}\\=\frac{8}{14}+\frac{20}{14}+\frac{7}{14}\\=\frac{8+20+7}{14}\\=\frac{35}{14}\\=\frac{5}{2}\)
11. \(+\left(\frac{-7}{2}\right) -\left(\frac{3}{-10}\right) +\left(\frac{5}{-7}\right)\\= \frac{-7}{2}+ \frac{3}{10}-\frac{5}{7}\\=\frac{-245}{70}+\frac{21}{70}-\frac{50}{70}\\=\frac{-245+21-50}{70}\\=\frac{-274}{70}\\=\frac{-137}{35}\)
12. \(+\left(\frac{-8}{5}\right) -\left(\frac{-3}{-5}\right) +\left(\frac{-12}{-3}\right)\\= \frac{-8}{5}- \frac{3}{5}+\frac{12}{3}\\=\frac{-8}{5}-\frac{3}{5}+\frac{4}{1}\\=\frac{-8-3+4}{5}\\=\frac{-7}{5}\)