Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{9}\right) -\left(\frac{10}{3}\right) +\left(\frac{12}{8}\right)\\= \frac{10}{9}- \frac{10}{3}+\frac{12}{8}\\=\frac{10}{9}-\frac{10}{3}+\frac{3}{2}\\=\frac{20}{18}-\frac{60}{18}+\frac{27}{18}\\=\frac{20-60+27}{18}\\=\frac{-13}{18}\)
2. \(+\left(\frac{9}{-2}\right) +\left(\frac{-9}{-4}\right) -\left(\frac{-10}{-2}\right)\\= \frac{-9}{2}+ \frac{9}{4}-\frac{10}{2}\\=\frac{-9}{2}+\frac{9}{4}-\frac{5}{1}\\=\frac{-18}{4}+\frac{9}{4}-\frac{20}{4}\\=\frac{-18+9-20}{4}\\=\frac{-29}{4}\)
3. \(+\left(\frac{6}{-5}\right) -\left(\frac{-2}{-5}\right) -\left(\frac{6}{7}\right)\\= \frac{-6}{5}- \frac{2}{5}-\frac{6}{7}\\=\frac{-42}{35}-\frac{14}{35}-\frac{30}{35}\\=\frac{-42-14-30}{35}\\=\frac{-86}{35}\)
4. \(-\left(\frac{6}{5}\right) +\left(\frac{-3}{-3}\right) -\left(\frac{6}{8}\right)\\= \frac{-6}{5}+ \frac{3}{3}-\frac{6}{8}\\=\frac{-6}{5}+\frac{1}{1}-\frac{3}{4}\\=\frac{-24}{20}+\frac{20}{20}-\frac{15}{20}\\=\frac{-24+20-15}{20}\\=\frac{-19}{20}\)
5. \(-\left(\frac{-7}{3}\right) +\left(\frac{9}{5}\right) -\left(\frac{12}{10}\right)\\= \frac{7}{3}+ \frac{9}{5}-\frac{12}{10}\\=\frac{7}{3}+\frac{9}{5}-\frac{6}{5}\\=\frac{35}{15}+\frac{27}{15}-\frac{18}{15}\\=\frac{35+27-18}{15}\\=\frac{44}{15}\)
6. \(-\left(\frac{-5}{6}\right) -\left(\frac{3}{5}\right) -\left(\frac{-2}{10}\right)\\= \frac{5}{6}- \frac{3}{5}+\frac{2}{10}\\=\frac{5}{6}-\frac{3}{5}+\frac{1}{5}\\=\frac{25}{30}-\frac{18}{30}+\frac{6}{30}\\=\frac{25-18+6}{30}\\=\frac{13}{30}\)
7. \(-\left(\frac{4}{9}\right) -\left(\frac{6}{6}\right) +\left(\frac{12}{5}\right)\\= \frac{-4}{9}- \frac{6}{6}+\frac{12}{5}\\=\frac{-4}{9}-\frac{1}{1}+\frac{12}{5}\\=\frac{-20}{45}-\frac{45}{45}+\frac{108}{45}\\=\frac{-20-45+108}{45}\\=\frac{43}{45}\)
8. \(+\left(\frac{5}{2}\right) +\left(\frac{-8}{9}\right) +\left(\frac{7}{-11}\right)\\= \frac{5}{2}- \frac{8}{9}-\frac{7}{11}\\=\frac{495}{198}-\frac{176}{198}-\frac{126}{198}\\=\frac{495-176-126}{198}\\=\frac{193}{198}\)
9. \(-\left(\frac{-9}{-4}\right) -\left(\frac{-9}{3}\right) +\left(\frac{7}{2}\right)\\= \frac{-9}{4}+ \frac{9}{3}+\frac{7}{2}\\=\frac{-9}{4}+\frac{3}{1}+\frac{7}{2}\\=\frac{-9+3+7}{4}\\=\frac{1}{4}\)
10. \(-\left(\frac{6}{-7}\right) +\left(\frac{3}{4}\right) +\left(\frac{-10}{8}\right)\\= \frac{6}{7}+ \frac{3}{4}-\frac{10}{8}\\=\frac{6}{7}+\frac{3}{4}-\frac{5}{4}\\=\frac{24}{28}+\frac{21}{28}-\frac{35}{28}\\=\frac{24+21-35}{28}\\=\frac{10}{28}\\=\frac{5}{14}\)
11. \(-\left(\frac{9}{7}\right) +\left(\frac{-6}{5}\right) +\left(\frac{-9}{-8}\right)\\= \frac{-9}{7}- \frac{6}{5}+\frac{9}{8}\\=\frac{-360}{280}-\frac{336}{280}+\frac{315}{280}\\=\frac{-360-336+315}{280}\\=\frac{-381}{280}\)
12. \(+\left(\frac{8}{3}\right) +\left(\frac{-2}{-7}\right) +\left(\frac{-12}{6}\right)\\= \frac{8}{3}+ \frac{2}{7}-\frac{12}{6}\\=\frac{8}{3}+\frac{2}{7}-\frac{2}{1}\\=\frac{56}{21}+\frac{6}{21}-\frac{42}{21}\\=\frac{56+6-42}{21}\\=\frac{20}{21}\)