Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{-8}\right) +\left(\frac{-8}{-4}\right) +\left(\frac{4}{-2}\right)\\= \frac{-5}{8}+ \frac{8}{4}-\frac{4}{2}\\=\frac{-5}{8}+\frac{2}{1}-\frac{2}{1}\\=\frac{-5+2-2}{8}\\=\frac{-5}{8}\)
2. \(+\left(\frac{3}{2}\right) +\left(\frac{4}{5}\right) -\left(\frac{-10}{-11}\right)\\= \frac{3}{2}+ \frac{4}{5}-\frac{10}{11}\\=\frac{165}{110}+\frac{88}{110}-\frac{100}{110}\\=\frac{165+88-100}{110}\\=\frac{153}{110}\)
3. \(+\left(\frac{10}{7}\right) +\left(\frac{7}{8}\right) +\left(\frac{7}{-4}\right)\\= \frac{10}{7}+ \frac{7}{8}-\frac{7}{4}\\=\frac{80}{56}+\frac{49}{56}-\frac{98}{56}\\=\frac{80+49-98}{56}\\=\frac{31}{56}\)
4. \(-\left(\frac{-10}{7}\right) -\left(\frac{-7}{9}\right) +\left(\frac{-11}{-10}\right)\\= \frac{10}{7}+ \frac{7}{9}+\frac{11}{10}\\=\frac{900}{630}+\frac{490}{630}+\frac{693}{630}\\=\frac{900+490+693}{630}\\=\frac{2083}{630}\)
5. \(-\left(\frac{-8}{9}\right) +\left(\frac{3}{4}\right) +\left(\frac{9}{3}\right)\\= \frac{8}{9}+ \frac{3}{4}+\frac{9}{3}\\=\frac{8}{9}+\frac{3}{4}+\frac{3}{1}\\=\frac{32}{36}+\frac{27}{36}+\frac{108}{36}\\=\frac{32+27+108}{36}\\=\frac{167}{36}\)
6. \(-\left(\frac{7}{-8}\right) +\left(\frac{-2}{2}\right) +\left(\frac{-4}{7}\right)\\= \frac{7}{8}- \frac{2}{2}-\frac{4}{7}\\=\frac{7}{8}-\frac{1}{1}-\frac{4}{7}\\=\frac{49}{56}-\frac{56}{56}-\frac{32}{56}\\=\frac{49-56-32}{56}\\=\frac{-39}{56}\)
7. \(-\left(\frac{10}{9}\right) -\left(\frac{4}{-9}\right) -\left(\frac{-11}{7}\right)\\= \frac{-10}{9}+ \frac{4}{9}+\frac{11}{7}\\=\frac{-70}{63}+\frac{28}{63}+\frac{99}{63}\\=\frac{-70+28+99}{63}\\=\frac{57}{63}\\=\frac{19}{21}\)
8. \(-\left(\frac{-6}{5}\right) -\left(\frac{3}{-7}\right) -\left(\frac{9}{-4}\right)\\= \frac{6}{5}+ \frac{3}{7}+\frac{9}{4}\\=\frac{168}{140}+\frac{60}{140}+\frac{315}{140}\\=\frac{168+60+315}{140}\\=\frac{543}{140}\)
9. \(+\left(\frac{-7}{-3}\right) -\left(\frac{7}{-6}\right) +\left(\frac{8}{4}\right)\\= \frac{7}{3}+ \frac{7}{6}+\frac{8}{4}\\=\frac{7}{3}+\frac{7}{6}+\frac{2}{1}\\=\frac{14}{6}+\frac{7}{6}+\frac{12}{6}\\=\frac{14+7+12}{6}\\=\frac{33}{6}\\=\frac{11}{2}\)
10. \(-\left(\frac{-7}{6}\right) +\left(\frac{6}{7}\right) +\left(\frac{-4}{-6}\right)\\= \frac{7}{6}+ \frac{6}{7}+\frac{4}{6}\\=\frac{7}{6}+\frac{6}{7}+\frac{2}{3}\\=\frac{49}{42}+\frac{36}{42}+\frac{28}{42}\\=\frac{49+36+28}{42}\\=\frac{113}{42}\)
11. \(-\left(\frac{8}{-7}\right) -\left(\frac{-3}{8}\right) +\left(\frac{2}{-10}\right)\\= \frac{8}{7}+ \frac{3}{8}-\frac{2}{10}\\=\frac{8}{7}+\frac{3}{8}-\frac{1}{5}\\=\frac{320}{280}+\frac{105}{280}-\frac{56}{280}\\=\frac{320+105-56}{280}\\=\frac{369}{280}\)
12. \(+\left(\frac{-5}{2}\right) +\left(\frac{6}{6}\right) -\left(\frac{-10}{-10}\right)\\= \frac{-5}{2}+ \frac{6}{6}-\frac{10}{10}\\=\frac{-5}{2}+\frac{1}{1}-\frac{1}{1}\\=\frac{-5+1-1}{2}\\=\frac{-5}{2}\)