Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{7}{6}\right) -\left(\frac{-10}{5}\right) +\left(\frac{-2}{-2}\right)\\= \frac{7}{6}+ \frac{10}{5}+\frac{2}{2}\\=\frac{7}{6}+\frac{2}{1}+\frac{1}{1}\\=\frac{7+2+1}{6}\\=\frac{10}{6}\\=\frac{5}{3}\)
2. \(+\left(\frac{4}{-9}\right) -\left(\frac{7}{2}\right) +\left(\frac{-9}{-4}\right)\\= \frac{-4}{9}- \frac{7}{2}+\frac{9}{4}\\=\frac{-16}{36}-\frac{126}{36}+\frac{81}{36}\\=\frac{-16-126+81}{36}\\=\frac{-61}{36}\)
3. \(+\left(\frac{-3}{2}\right) +\left(\frac{-5}{4}\right) +\left(\frac{7}{-8}\right)\\= \frac{-3}{2}- \frac{5}{4}-\frac{7}{8}\\=\frac{-12}{8}-\frac{10}{8}-\frac{7}{8}\\=\frac{-12-10-7}{8}\\=\frac{-29}{8}\)
4. \(+\left(\frac{-9}{-7}\right) -\left(\frac{-5}{-5}\right) +\left(\frac{2}{-6}\right)\\= \frac{9}{7}- \frac{5}{5}-\frac{2}{6}\\=\frac{9}{7}-\frac{1}{1}-\frac{1}{3}\\=\frac{27}{21}-\frac{21}{21}-\frac{7}{21}\\=\frac{27-21-7}{21}\\=\frac{-1}{21}\)
5. \(-\left(\frac{-8}{-7}\right) +\left(\frac{-7}{-2}\right) -\left(\frac{7}{8}\right)\\= \frac{-8}{7}+ \frac{7}{2}-\frac{7}{8}\\=\frac{-64}{56}+\frac{196}{56}-\frac{49}{56}\\=\frac{-64+196-49}{56}\\=\frac{83}{56}\)
6. \(-\left(\frac{9}{-4}\right) +\left(\frac{8}{-9}\right) -\left(\frac{3}{-12}\right)\\= \frac{9}{4}- \frac{8}{9}+\frac{3}{12}\\=\frac{9}{4}-\frac{8}{9}+\frac{1}{4}\\=\frac{81}{36}-\frac{32}{36}+\frac{9}{36}\\=\frac{81-32+9}{36}\\=\frac{58}{36}\\=\frac{29}{18}\)
7. \(+\left(\frac{-6}{5}\right) -\left(\frac{10}{9}\right) -\left(\frac{-11}{2}\right)\\= \frac{-6}{5}- \frac{10}{9}+\frac{11}{2}\\=\frac{-108}{90}-\frac{100}{90}+\frac{495}{90}\\=\frac{-108-100+495}{90}\\=\frac{287}{90}\)
8. \(+\left(\frac{8}{3}\right) -\left(\frac{-9}{10}\right) -\left(\frac{6}{6}\right)\\= \frac{8}{3}+ \frac{9}{10}-\frac{6}{6}\\=\frac{8}{3}+\frac{9}{10}-\frac{1}{1}\\=\frac{80}{30}+\frac{27}{30}-\frac{30}{30}\\=\frac{80+27-30}{30}\\=\frac{77}{30}\)
9. \(-\left(\frac{3}{7}\right) +\left(\frac{7}{-9}\right) -\left(\frac{-2}{-5}\right)\\= \frac{-3}{7}- \frac{7}{9}-\frac{2}{5}\\=\frac{-135}{315}-\frac{245}{315}-\frac{126}{315}\\=\frac{-135-245-126}{315}\\=\frac{-506}{315}\)
10. \(-\left(\frac{6}{7}\right) +\left(\frac{-3}{-8}\right) -\left(\frac{-9}{-3}\right)\\= \frac{-6}{7}+ \frac{3}{8}-\frac{9}{3}\\=\frac{-6}{7}+\frac{3}{8}-\frac{3}{1}\\=\frac{-48}{56}+\frac{21}{56}-\frac{168}{56}\\=\frac{-48+21-168}{56}\\=\frac{-195}{56}\)
11. \(-\left(\frac{7}{-8}\right) -\left(\frac{-7}{8}\right) +\left(\frac{4}{-6}\right)\\= \frac{7}{8}+ \frac{7}{8}-\frac{4}{6}\\=\frac{7}{8}+\frac{7}{8}-\frac{2}{3}\\=\frac{21}{24}+\frac{21}{24}-\frac{16}{24}\\=\frac{21+21-16}{24}\\=\frac{26}{24}\\=\frac{13}{12}\)
12. \(+\left(\frac{-3}{-8}\right) -\left(\frac{-5}{-5}\right) -\left(\frac{4}{11}\right)\\= \frac{3}{8}- \frac{5}{5}-\frac{4}{11}\\=\frac{3}{8}-\frac{1}{1}-\frac{4}{11}\\=\frac{33}{88}-\frac{88}{88}-\frac{32}{88}\\=\frac{33-88-32}{88}\\=\frac{-87}{88}\)