Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-7}\right) -\left(\frac{-4}{2}\right) +\left(\frac{-9}{9}\right)\\= \frac{10}{7}+ \frac{4}{2}-\frac{9}{9}\\=\frac{10}{7}+\frac{2}{1}-\frac{1}{1}\\=\frac{10+2-1}{7}\\=\frac{11}{7}\)
2. \(+\left(\frac{-2}{7}\right) +\left(\frac{9}{-8}\right) -\left(\frac{-8}{7}\right)\\= \frac{-2}{7}- \frac{9}{8}+\frac{8}{7}\\=\frac{-16}{56}-\frac{63}{56}+\frac{64}{56}\\=\frac{-16-63+64}{56}\\=\frac{-15}{56}\)
3. \(-\left(\frac{-3}{-7}\right) -\left(\frac{-9}{-10}\right) +\left(\frac{12}{8}\right)\\= \frac{-3}{7}- \frac{9}{10}+\frac{12}{8}\\=\frac{-3}{7}-\frac{9}{10}+\frac{3}{2}\\=\frac{-30}{70}-\frac{63}{70}+\frac{105}{70}\\=\frac{-30-63+105}{70}\\=\frac{12}{70}\\=\frac{6}{35}\)
4. \(+\left(\frac{-10}{-7}\right) -\left(\frac{9}{-2}\right) -\left(\frac{8}{-6}\right)\\= \frac{10}{7}+ \frac{9}{2}+\frac{8}{6}\\=\frac{10}{7}+\frac{9}{2}+\frac{4}{3}\\=\frac{60}{42}+\frac{189}{42}+\frac{56}{42}\\=\frac{60+189+56}{42}\\=\frac{305}{42}\)
5. \(-\left(\frac{8}{5}\right) -\left(\frac{-9}{8}\right) +\left(\frac{-8}{3}\right)\\= \frac{-8}{5}+ \frac{9}{8}-\frac{8}{3}\\=\frac{-192}{120}+\frac{135}{120}-\frac{320}{120}\\=\frac{-192+135-320}{120}\\=\frac{-377}{120}\)
6. \(-\left(\frac{-6}{-7}\right) -\left(\frac{-2}{-5}\right) +\left(\frac{5}{11}\right)\\= \frac{-6}{7}- \frac{2}{5}+\frac{5}{11}\\=\frac{-330}{385}-\frac{154}{385}+\frac{175}{385}\\=\frac{-330-154+175}{385}\\=\frac{-309}{385}\)
7. \(+\left(\frac{9}{-4}\right) +\left(\frac{9}{-6}\right) -\left(\frac{2}{6}\right)\\= \frac{-9}{4}- \frac{9}{6}-\frac{2}{6}\\=\frac{-9}{4}-\frac{3}{2}-\frac{1}{3}\\=\frac{-27}{12}-\frac{18}{12}-\frac{4}{12}\\=\frac{-27-18-4}{12}\\=\frac{-49}{12}\)
8. \(+\left(\frac{-9}{-10}\right) +\left(\frac{-4}{5}\right) +\left(\frac{-8}{-10}\right)\\= \frac{9}{10}- \frac{4}{5}+\frac{8}{10}\\=\frac{9}{10}-\frac{4}{5}+\frac{4}{5}\\=\frac{9-4+4}{10}\\=\frac{9}{10}\)
9. \(-\left(\frac{5}{8}\right) -\left(\frac{3}{10}\right) +\left(\frac{6}{6}\right)\\= \frac{-5}{8}- \frac{3}{10}+\frac{6}{6}\\=\frac{-5}{8}-\frac{3}{10}+\frac{1}{1}\\=\frac{-25}{40}-\frac{12}{40}+\frac{40}{40}\\=\frac{-25-12+40}{40}\\=\frac{3}{40}\)
10. \(+\left(\frac{4}{-3}\right) -\left(\frac{-10}{6}\right) +\left(\frac{8}{12}\right)\\= \frac{-4}{3}+ \frac{10}{6}+\frac{8}{12}\\=\frac{-4}{3}+\frac{5}{3}+\frac{2}{3}\\=\frac{-4+5+2}{3}\\=\frac{3}{3}\\=\frac{1}{1}\)
11. \(+\left(\frac{10}{7}\right) -\left(\frac{10}{2}\right) +\left(\frac{-2}{11}\right)\\= \frac{10}{7}- \frac{10}{2}-\frac{2}{11}\\=\frac{10}{7}-\frac{5}{1}-\frac{2}{11}\\=\frac{110}{77}-\frac{385}{77}-\frac{14}{77}\\=\frac{110-385-14}{77}\\=\frac{-289}{77}\)
12. \(+\left(\frac{5}{3}\right) +\left(\frac{6}{-4}\right) -\left(\frac{-6}{-6}\right)\\= \frac{5}{3}- \frac{6}{4}-\frac{6}{6}\\=\frac{5}{3}-\frac{3}{2}-\frac{1}{1}\\=\frac{10}{6}-\frac{9}{6}-\frac{6}{6}\\=\frac{10-9-6}{6}\\=\frac{-5}{6}\)