Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{7}\right) +\left(\frac{7}{8}\right) -\left(\frac{-7}{-4}\right)\\= \frac{-6}{7}+ \frac{7}{8}-\frac{7}{4}\\=\frac{-48}{56}+\frac{49}{56}-\frac{98}{56}\\=\frac{-48+49-98}{56}\\=\frac{-97}{56}\)
2. \(-\left(\frac{-2}{7}\right) +\left(\frac{9}{4}\right) -\left(\frac{7}{11}\right)\\= \frac{2}{7}+ \frac{9}{4}-\frac{7}{11}\\=\frac{88}{308}+\frac{693}{308}-\frac{196}{308}\\=\frac{88+693-196}{308}\\=\frac{585}{308}\)
3. \(+\left(\frac{-4}{-9}\right) -\left(\frac{-2}{-9}\right) -\left(\frac{-2}{-7}\right)\\= \frac{4}{9}- \frac{2}{9}-\frac{2}{7}\\=\frac{28}{63}-\frac{14}{63}-\frac{18}{63}\\=\frac{28-14-18}{63}\\=\frac{-4}{63}\)
4. \(+\left(\frac{-9}{-2}\right) +\left(\frac{5}{-8}\right) -\left(\frac{2}{6}\right)\\= \frac{9}{2}- \frac{5}{8}-\frac{2}{6}\\=\frac{9}{2}-\frac{5}{8}-\frac{1}{3}\\=\frac{108}{24}-\frac{15}{24}-\frac{8}{24}\\=\frac{108-15-8}{24}\\=\frac{85}{24}\)
5. \(+\left(\frac{10}{-9}\right) -\left(\frac{-4}{-2}\right) -\left(\frac{9}{-8}\right)\\= \frac{-10}{9}- \frac{4}{2}+\frac{9}{8}\\=\frac{-10}{9}-\frac{2}{1}+\frac{9}{8}\\=\frac{-80}{72}-\frac{144}{72}+\frac{81}{72}\\=\frac{-80-144+81}{72}\\=\frac{-143}{72}\)
6. \(-\left(\frac{9}{-4}\right) +\left(\frac{-7}{-4}\right) -\left(\frac{-10}{2}\right)\\= \frac{9}{4}+ \frac{7}{4}+\frac{10}{2}\\=\frac{9}{4}+\frac{7}{4}+\frac{5}{1}\\=\frac{9+7+5}{4}\\=\frac{21}{4}\)
7. \(+\left(\frac{7}{-8}\right) +\left(\frac{7}{-5}\right) -\left(\frac{-6}{-10}\right)\\= \frac{-7}{8}- \frac{7}{5}-\frac{6}{10}\\=\frac{-7}{8}-\frac{7}{5}-\frac{3}{5}\\=\frac{-35}{40}-\frac{56}{40}-\frac{24}{40}\\=\frac{-35-56-24}{40}\\=\frac{-115}{40}\\=\frac{-23}{8}\)
8. \(+\left(\frac{-4}{-3}\right) +\left(\frac{9}{-9}\right) -\left(\frac{12}{-9}\right)\\= \frac{4}{3}- \frac{9}{9}+\frac{12}{9}\\=\frac{4}{3}-\frac{1}{1}+\frac{4}{3}\\=\frac{4-1+4}{3}\\=\frac{7}{3}\)
9. \(+\left(\frac{6}{-5}\right) -\left(\frac{5}{-8}\right) +\left(\frac{-8}{-4}\right)\\= \frac{-6}{5}+ \frac{5}{8}+\frac{8}{4}\\=\frac{-6}{5}+\frac{5}{8}+\frac{2}{1}\\=\frac{-48}{40}+\frac{25}{40}+\frac{80}{40}\\=\frac{-48+25+80}{40}\\=\frac{57}{40}\)
10. \(+\left(\frac{-8}{-3}\right) +\left(\frac{-5}{6}\right) -\left(\frac{10}{-5}\right)\\= \frac{8}{3}- \frac{5}{6}+\frac{10}{5}\\=\frac{8}{3}-\frac{5}{6}+\frac{2}{1}\\=\frac{16}{6}-\frac{5}{6}+\frac{12}{6}\\=\frac{16-5+12}{6}\\=\frac{23}{6}\)
11. \(+\left(\frac{-5}{-7}\right) -\left(\frac{-5}{-6}\right) +\left(\frac{-2}{-3}\right)\\= \frac{5}{7}- \frac{5}{6}+\frac{2}{3}\\=\frac{30}{42}-\frac{35}{42}+\frac{28}{42}\\=\frac{30-35+28}{42}\\=\frac{23}{42}\)
12. \(-\left(\frac{-8}{-5}\right) +\left(\frac{-3}{-9}\right) -\left(\frac{-9}{-3}\right)\\= \frac{-8}{5}+ \frac{3}{9}-\frac{9}{3}\\=\frac{-8}{5}+\frac{1}{3}-\frac{3}{1}\\=\frac{-24}{15}+\frac{5}{15}-\frac{45}{15}\\=\frac{-24+5-45}{15}\\=\frac{-64}{15}\)