Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{-8}\right) +\left(\frac{-9}{-5}\right) -\left(\frac{7}{5}\right)\\= \frac{5}{8}+ \frac{9}{5}-\frac{7}{5}\\=\frac{25}{40}+\frac{72}{40}-\frac{56}{40}\\=\frac{25+72-56}{40}\\=\frac{41}{40}\)
2. \(-\left(\frac{-10}{-7}\right) +\left(\frac{5}{-10}\right) -\left(\frac{-4}{6}\right)\\= \frac{-10}{7}- \frac{5}{10}+\frac{4}{6}\\=\frac{-10}{7}-\frac{1}{2}+\frac{2}{3}\\=\frac{-60}{42}-\frac{21}{42}+\frac{28}{42}\\=\frac{-60-21+28}{42}\\=\frac{-53}{42}\)
3. \(-\left(\frac{2}{9}\right) -\left(\frac{2}{-3}\right) +\left(\frac{-3}{-7}\right)\\= \frac{-2}{9}+ \frac{2}{3}+\frac{3}{7}\\=\frac{-14}{63}+\frac{42}{63}+\frac{27}{63}\\=\frac{-14+42+27}{63}\\=\frac{55}{63}\)
4. \(-\left(\frac{4}{9}\right) +\left(\frac{6}{10}\right) -\left(\frac{2}{-5}\right)\\= \frac{-4}{9}+ \frac{6}{10}+\frac{2}{5}\\=\frac{-4}{9}+\frac{3}{5}+\frac{2}{5}\\=\frac{-20}{45}+\frac{27}{45}+\frac{18}{45}\\=\frac{-20+27+18}{45}\\=\frac{25}{45}\\=\frac{5}{9}\)
5. \(-\left(\frac{7}{6}\right) +\left(\frac{5}{6}\right) -\left(\frac{11}{-4}\right)\\= \frac{-7}{6}+ \frac{5}{6}+\frac{11}{4}\\=\frac{-14}{12}+\frac{10}{12}+\frac{33}{12}\\=\frac{-14+10+33}{12}\\=\frac{29}{12}\)
6. \(+\left(\frac{-5}{-4}\right) -\left(\frac{-2}{-5}\right) +\left(\frac{-5}{-10}\right)\\= \frac{5}{4}- \frac{2}{5}+\frac{5}{10}\\=\frac{5}{4}-\frac{2}{5}+\frac{1}{2}\\=\frac{25}{20}-\frac{8}{20}+\frac{10}{20}\\=\frac{25-8+10}{20}\\=\frac{27}{20}\)
7. \(+\left(\frac{-5}{-4}\right) +\left(\frac{7}{10}\right) +\left(\frac{6}{-11}\right)\\= \frac{5}{4}+ \frac{7}{10}-\frac{6}{11}\\=\frac{275}{220}+\frac{154}{220}-\frac{120}{220}\\=\frac{275+154-120}{220}\\=\frac{309}{220}\)
8. \(-\left(\frac{-8}{5}\right) -\left(\frac{2}{-2}\right) -\left(\frac{-12}{-2}\right)\\= \frac{8}{5}+ \frac{2}{2}-\frac{12}{2}\\=\frac{8}{5}+\frac{1}{1}-\frac{6}{1}\\=\frac{8+1-6}{5}\\=\frac{3}{5}\)
9. \(-\left(\frac{9}{2}\right) -\left(\frac{-7}{-6}\right) +\left(\frac{6}{8}\right)\\= \frac{-9}{2}- \frac{7}{6}+\frac{6}{8}\\=\frac{-9}{2}-\frac{7}{6}+\frac{3}{4}\\=\frac{-54}{12}-\frac{14}{12}+\frac{9}{12}\\=\frac{-54-14+9}{12}\\=\frac{-59}{12}\)
10. \(-\left(\frac{-4}{3}\right) -\left(\frac{-3}{7}\right) +\left(\frac{-5}{5}\right)\\= \frac{4}{3}+ \frac{3}{7}-\frac{5}{5}\\=\frac{4}{3}+\frac{3}{7}-\frac{1}{1}\\=\frac{28}{21}+\frac{9}{21}-\frac{21}{21}\\=\frac{28+9-21}{21}\\=\frac{16}{21}\)
11. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-10}{8}\right) +\left(\frac{-12}{-10}\right)\\= \frac{-6}{5}- \frac{10}{8}+\frac{12}{10}\\=\frac{-6}{5}-\frac{5}{4}+\frac{6}{5}\\=\frac{-24}{20}-\frac{25}{20}+\frac{24}{20}\\=\frac{-24-25+24}{20}\\=\frac{-25}{20}\\=\frac{-5}{4}\)
12. \(+\left(\frac{4}{9}\right) +\left(\frac{-5}{-6}\right) +\left(\frac{-7}{2}\right)\\= \frac{4}{9}+ \frac{5}{6}-\frac{7}{2}\\=\frac{8}{18}+\frac{15}{18}-\frac{63}{18}\\=\frac{8+15-63}{18}\\=\frac{-40}{18}\\=\frac{-20}{9}\)