Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{5}\right) -\left(\frac{-6}{-3}\right) +\left(\frac{-4}{-11}\right)\\= \frac{-7}{5}- \frac{6}{3}+\frac{4}{11}\\=\frac{-7}{5}-\frac{2}{1}+\frac{4}{11}\\=\frac{-77}{55}-\frac{110}{55}+\frac{20}{55}\\=\frac{-77-110+20}{55}\\=\frac{-167}{55}\)
2. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-5}{6}\right) +\left(\frac{-11}{-8}\right)\\= \frac{-6}{5}+ \frac{5}{6}+\frac{11}{8}\\=\frac{-144}{120}+\frac{100}{120}+\frac{165}{120}\\=\frac{-144+100+165}{120}\\=\frac{121}{120}\)
3. \(+\left(\frac{4}{7}\right) +\left(\frac{-8}{9}\right) +\left(\frac{8}{-11}\right)\\= \frac{4}{7}- \frac{8}{9}-\frac{8}{11}\\=\frac{396}{693}-\frac{616}{693}-\frac{504}{693}\\=\frac{396-616-504}{693}\\=\frac{-724}{693}\)
4. \(+\left(\frac{-6}{-5}\right) +\left(\frac{2}{8}\right) -\left(\frac{-3}{-10}\right)\\= \frac{6}{5}+ \frac{2}{8}-\frac{3}{10}\\=\frac{6}{5}+\frac{1}{4}-\frac{3}{10}\\=\frac{24}{20}+\frac{5}{20}-\frac{6}{20}\\=\frac{24+5-6}{20}\\=\frac{23}{20}\)
5. \(+\left(\frac{3}{-2}\right) -\left(\frac{-5}{-5}\right) -\left(\frac{8}{12}\right)\\= \frac{-3}{2}- \frac{5}{5}-\frac{8}{12}\\=\frac{-3}{2}-\frac{1}{1}-\frac{2}{3}\\=\frac{-9}{6}-\frac{6}{6}-\frac{4}{6}\\=\frac{-9-6-4}{6}\\=\frac{-19}{6}\)
6. \(+\left(\frac{-8}{3}\right) +\left(\frac{-8}{-9}\right) +\left(\frac{-9}{-2}\right)\\= \frac{-8}{3}+ \frac{8}{9}+\frac{9}{2}\\=\frac{-48}{18}+\frac{16}{18}+\frac{81}{18}\\=\frac{-48+16+81}{18}\\=\frac{49}{18}\)
7. \(-\left(\frac{4}{5}\right) +\left(\frac{-7}{-7}\right) +\left(\frac{8}{6}\right)\\= \frac{-4}{5}+ \frac{7}{7}+\frac{8}{6}\\=\frac{-4}{5}+\frac{1}{1}+\frac{4}{3}\\=\frac{-12}{15}+\frac{15}{15}+\frac{20}{15}\\=\frac{-12+15+20}{15}\\=\frac{23}{15}\)
8. \(+\left(\frac{-8}{7}\right) -\left(\frac{-2}{-7}\right) +\left(\frac{2}{6}\right)\\= \frac{-8}{7}- \frac{2}{7}+\frac{2}{6}\\=\frac{-8}{7}-\frac{2}{7}+\frac{1}{3}\\=\frac{-24}{21}-\frac{6}{21}+\frac{7}{21}\\=\frac{-24-6+7}{21}\\=\frac{-23}{21}\)
9. \(+\left(\frac{-8}{3}\right) -\left(\frac{6}{8}\right) -\left(\frac{-10}{-9}\right)\\= \frac{-8}{3}- \frac{6}{8}-\frac{10}{9}\\=\frac{-8}{3}-\frac{3}{4}-\frac{10}{9}\\=\frac{-96}{36}-\frac{27}{36}-\frac{40}{36}\\=\frac{-96-27-40}{36}\\=\frac{-163}{36}\)
10. \(+\left(\frac{-7}{-3}\right) -\left(\frac{10}{-2}\right) +\left(\frac{3}{12}\right)\\= \frac{7}{3}+ \frac{10}{2}+\frac{3}{12}\\=\frac{7}{3}+\frac{5}{1}+\frac{1}{4}\\=\frac{28}{12}+\frac{60}{12}+\frac{3}{12}\\=\frac{28+60+3}{12}\\=\frac{91}{12}\)
11. \(-\left(\frac{-9}{-7}\right) -\left(\frac{-3}{-5}\right) -\left(\frac{-3}{8}\right)\\= \frac{-9}{7}- \frac{3}{5}+\frac{3}{8}\\=\frac{-360}{280}-\frac{168}{280}+\frac{105}{280}\\=\frac{-360-168+105}{280}\\=\frac{-423}{280}\)
12. \(-\left(\frac{4}{3}\right) -\left(\frac{-10}{3}\right) +\left(\frac{-11}{3}\right)\\= \frac{-4}{3}+ \frac{10}{3}-\frac{11}{3}\\=\frac{-4+10-11}{3}\\=\frac{-5}{3}\)