Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{5}\right) +\left(\frac{-3}{-2}\right) -\left(\frac{-10}{-3}\right)\\= \frac{-2}{5}+ \frac{3}{2}-\frac{10}{3}\\=\frac{-12}{30}+\frac{45}{30}-\frac{100}{30}\\=\frac{-12+45-100}{30}\\=\frac{-67}{30}\)
2. \(-\left(\frac{8}{-3}\right) -\left(\frac{6}{7}\right) +\left(\frac{-6}{4}\right)\\= \frac{8}{3}- \frac{6}{7}-\frac{6}{4}\\=\frac{8}{3}-\frac{6}{7}-\frac{3}{2}\\=\frac{112}{42}-\frac{36}{42}-\frac{63}{42}\\=\frac{112-36-63}{42}\\=\frac{13}{42}\)
3. \(-\left(\frac{-10}{9}\right) +\left(\frac{-4}{-3}\right) +\left(\frac{-11}{-3}\right)\\= \frac{10}{9}+ \frac{4}{3}+\frac{11}{3}\\=\frac{10+4+11}{9}\\=\frac{25}{9}\)
4. \(-\left(\frac{-3}{-7}\right) +\left(\frac{3}{-9}\right) -\left(\frac{-12}{3}\right)\\= \frac{-3}{7}- \frac{3}{9}+\frac{12}{3}\\=\frac{-3}{7}-\frac{1}{3}+\frac{4}{1}\\=\frac{-9}{21}-\frac{7}{21}+\frac{84}{21}\\=\frac{-9-7+84}{21}\\=\frac{68}{21}\)
5. \(-\left(\frac{-4}{-9}\right) -\left(\frac{9}{2}\right) -\left(\frac{-12}{-8}\right)\\= \frac{-4}{9}- \frac{9}{2}-\frac{12}{8}\\=\frac{-4}{9}-\frac{9}{2}-\frac{3}{2}\\=\frac{-8}{18}-\frac{81}{18}-\frac{27}{18}\\=\frac{-8-81-27}{18}\\=\frac{-116}{18}\\=\frac{-58}{9}\)
6. \(+\left(\frac{8}{9}\right) -\left(\frac{-9}{2}\right) -\left(\frac{10}{3}\right)\\= \frac{8}{9}+ \frac{9}{2}-\frac{10}{3}\\=\frac{16}{18}+\frac{81}{18}-\frac{60}{18}\\=\frac{16+81-60}{18}\\=\frac{37}{18}\)
7. \(-\left(\frac{-10}{7}\right) -\left(\frac{10}{-8}\right) +\left(\frac{-9}{-2}\right)\\= \frac{10}{7}+ \frac{10}{8}+\frac{9}{2}\\=\frac{10}{7}+\frac{5}{4}+\frac{9}{2}\\=\frac{40}{28}+\frac{35}{28}+\frac{126}{28}\\=\frac{40+35+126}{28}\\=\frac{201}{28}\)
8. \(-\left(\frac{6}{-5}\right) -\left(\frac{-10}{7}\right) +\left(\frac{-3}{3}\right)\\= \frac{6}{5}+ \frac{10}{7}-\frac{3}{3}\\=\frac{6}{5}+\frac{10}{7}-\frac{1}{1}\\=\frac{42}{35}+\frac{50}{35}-\frac{35}{35}\\=\frac{42+50-35}{35}\\=\frac{57}{35}\)
9. \(-\left(\frac{-5}{-2}\right) +\left(\frac{-6}{10}\right) +\left(\frac{-2}{6}\right)\\= \frac{-5}{2}- \frac{6}{10}-\frac{2}{6}\\=\frac{-5}{2}-\frac{3}{5}-\frac{1}{3}\\=\frac{-75}{30}-\frac{18}{30}-\frac{10}{30}\\=\frac{-75-18-10}{30}\\=\frac{-103}{30}\)
10. \(+\left(\frac{-3}{5}\right) -\left(\frac{-4}{-9}\right) -\left(\frac{-11}{8}\right)\\= \frac{-3}{5}- \frac{4}{9}+\frac{11}{8}\\=\frac{-216}{360}-\frac{160}{360}+\frac{495}{360}\\=\frac{-216-160+495}{360}\\=\frac{119}{360}\)
11. \(+\left(\frac{-9}{8}\right) +\left(\frac{-10}{8}\right) -\left(\frac{10}{12}\right)\\= \frac{-9}{8}- \frac{10}{8}-\frac{10}{12}\\=\frac{-9}{8}-\frac{5}{4}-\frac{5}{6}\\=\frac{-27}{24}-\frac{30}{24}-\frac{20}{24}\\=\frac{-27-30-20}{24}\\=\frac{-77}{24}\)
12. \(-\left(\frac{5}{9}\right) +\left(\frac{-3}{9}\right) -\left(\frac{11}{-6}\right)\\= \frac{-5}{9}- \frac{3}{9}+\frac{11}{6}\\=\frac{-5}{9}-\frac{1}{3}+\frac{11}{6}\\=\frac{-10}{18}-\frac{6}{18}+\frac{33}{18}\\=\frac{-10-6+33}{18}\\=\frac{17}{18}\)