Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{-9}\right) -\left(\frac{-8}{-5}\right) +\left(\frac{-2}{7}\right)\\= \frac{7}{9}- \frac{8}{5}-\frac{2}{7}\\=\frac{245}{315}-\frac{504}{315}-\frac{90}{315}\\=\frac{245-504-90}{315}\\=\frac{-349}{315}\)
2. \(-\left(\frac{2}{-7}\right) +\left(\frac{5}{10}\right) +\left(\frac{-2}{7}\right)\\= \frac{2}{7}+ \frac{5}{10}-\frac{2}{7}\\=\frac{2}{7}+\frac{1}{2}-\frac{2}{7}\\=\frac{4}{14}+\frac{7}{14}-\frac{4}{14}\\=\frac{4+7-4}{14}\\=\frac{7}{14}\\=\frac{1}{2}\)
3. \(+\left(\frac{3}{-7}\right) +\left(\frac{3}{6}\right) -\left(\frac{-6}{-3}\right)\\= \frac{-3}{7}+ \frac{3}{6}-\frac{6}{3}\\=\frac{-3}{7}+\frac{1}{2}-\frac{2}{1}\\=\frac{-6}{14}+\frac{7}{14}-\frac{28}{14}\\=\frac{-6+7-28}{14}\\=\frac{-27}{14}\)
4. \(-\left(\frac{2}{3}\right) +\left(\frac{8}{-8}\right) -\left(\frac{-2}{10}\right)\\= \frac{-2}{3}- \frac{8}{8}+\frac{2}{10}\\=\frac{-2}{3}-\frac{1}{1}+\frac{1}{5}\\=\frac{-10}{15}-\frac{15}{15}+\frac{3}{15}\\=\frac{-10-15+3}{15}\\=\frac{-22}{15}\)
5. \(-\left(\frac{4}{7}\right) +\left(\frac{-4}{-10}\right) -\left(\frac{7}{-8}\right)\\= \frac{-4}{7}+ \frac{4}{10}+\frac{7}{8}\\=\frac{-4}{7}+\frac{2}{5}+\frac{7}{8}\\=\frac{-160}{280}+\frac{112}{280}+\frac{245}{280}\\=\frac{-160+112+245}{280}\\=\frac{197}{280}\)
6. \(-\left(\frac{10}{-7}\right) -\left(\frac{-8}{7}\right) -\left(\frac{-12}{-7}\right)\\= \frac{10}{7}+ \frac{8}{7}-\frac{12}{7}\\=\frac{10+8-12}{7}\\=\frac{6}{7}\)
7. \(-\left(\frac{9}{8}\right) -\left(\frac{-9}{6}\right) +\left(\frac{-12}{-12}\right)\\= \frac{-9}{8}+ \frac{9}{6}+\frac{12}{12}\\=\frac{-9}{8}+\frac{3}{2}+\frac{1}{1}\\=\frac{-9+3+1}{8}\\=\frac{-5}{8}\)
8. \(-\left(\frac{9}{-4}\right) -\left(\frac{5}{8}\right) +\left(\frac{-9}{-7}\right)\\= \frac{9}{4}- \frac{5}{8}+\frac{9}{7}\\=\frac{126}{56}-\frac{35}{56}+\frac{72}{56}\\=\frac{126-35+72}{56}\\=\frac{163}{56}\)
9. \(-\left(\frac{-5}{-2}\right) +\left(\frac{-5}{-4}\right) -\left(\frac{2}{5}\right)\\= \frac{-5}{2}+ \frac{5}{4}-\frac{2}{5}\\=\frac{-50}{20}+\frac{25}{20}-\frac{8}{20}\\=\frac{-50+25-8}{20}\\=\frac{-33}{20}\)
10. \(+\left(\frac{-10}{-7}\right) +\left(\frac{7}{7}\right) -\left(\frac{10}{-4}\right)\\= \frac{10}{7}+ \frac{7}{7}+\frac{10}{4}\\=\frac{10}{7}+\frac{1}{1}+\frac{5}{2}\\=\frac{20}{14}+\frac{14}{14}+\frac{35}{14}\\=\frac{20+14+35}{14}\\=\frac{69}{14}\)
11. \(+\left(\frac{6}{5}\right) -\left(\frac{4}{-4}\right) -\left(\frac{6}{8}\right)\\= \frac{6}{5}+ \frac{4}{4}-\frac{6}{8}\\=\frac{6}{5}+\frac{1}{1}-\frac{3}{4}\\=\frac{24}{20}+\frac{20}{20}-\frac{15}{20}\\=\frac{24+20-15}{20}\\=\frac{29}{20}\)
12. \(+\left(\frac{3}{-5}\right) +\left(\frac{2}{-4}\right) +\left(\frac{10}{6}\right)\\= \frac{-3}{5}- \frac{2}{4}+\frac{10}{6}\\=\frac{-3}{5}-\frac{1}{2}+\frac{5}{3}\\=\frac{-18}{30}-\frac{15}{30}+\frac{50}{30}\\=\frac{-18-15+50}{30}\\=\frac{17}{30}\)