Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{-3}\right) +\left(\frac{-9}{-8}\right) +\left(\frac{-4}{-8}\right)\\= \frac{-10}{3}+ \frac{9}{8}+\frac{4}{8}\\=\frac{-10}{3}+\frac{9}{8}+\frac{1}{2}\\=\frac{-80}{24}+\frac{27}{24}+\frac{12}{24}\\=\frac{-80+27+12}{24}\\=\frac{-41}{24}\)
2. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-10}{5}\right) +\left(\frac{2}{-6}\right)\\= \frac{6}{5}+ \frac{10}{5}-\frac{2}{6}\\=\frac{6}{5}+\frac{2}{1}-\frac{1}{3}\\=\frac{18}{15}+\frac{30}{15}-\frac{5}{15}\\=\frac{18+30-5}{15}\\=\frac{43}{15}\)
3. \(-\left(\frac{-3}{-2}\right) -\left(\frac{-7}{2}\right) +\left(\frac{-4}{-8}\right)\\= \frac{-3}{2}+ \frac{7}{2}+\frac{4}{8}\\=\frac{-3}{2}+\frac{7}{2}+\frac{1}{2}\\=\frac{-3+7+1}{2}\\=\frac{5}{2}\)
4. \(-\left(\frac{-2}{-5}\right) -\left(\frac{-9}{-3}\right) -\left(\frac{4}{9}\right)\\= \frac{-2}{5}- \frac{9}{3}-\frac{4}{9}\\=\frac{-2}{5}-\frac{3}{1}-\frac{4}{9}\\=\frac{-18}{45}-\frac{135}{45}-\frac{20}{45}\\=\frac{-18-135-20}{45}\\=\frac{-173}{45}\)
5. \(-\left(\frac{5}{2}\right) +\left(\frac{-6}{-6}\right) +\left(\frac{7}{5}\right)\\= \frac{-5}{2}+ \frac{6}{6}+\frac{7}{5}\\=\frac{-5}{2}+\frac{1}{1}+\frac{7}{5}\\=\frac{-25}{10}+\frac{10}{10}+\frac{14}{10}\\=\frac{-25+10+14}{10}\\=\frac{-1}{10}\)
6. \(-\left(\frac{10}{-7}\right) +\left(\frac{-4}{-10}\right) -\left(\frac{9}{6}\right)\\= \frac{10}{7}+ \frac{4}{10}-\frac{9}{6}\\=\frac{10}{7}+\frac{2}{5}-\frac{3}{2}\\=\frac{100}{70}+\frac{28}{70}-\frac{105}{70}\\=\frac{100+28-105}{70}\\=\frac{23}{70}\)
7. \(-\left(\frac{-7}{-5}\right) +\left(\frac{2}{-9}\right) -\left(\frac{-11}{11}\right)\\= \frac{-7}{5}- \frac{2}{9}+\frac{11}{11}\\=\frac{-7}{5}-\frac{2}{9}+\frac{1}{1}\\=\frac{-63}{45}-\frac{10}{45}+\frac{45}{45}\\=\frac{-63-10+45}{45}\\=\frac{-28}{45}\)
8. \(-\left(\frac{-7}{-2}\right) -\left(\frac{-3}{-4}\right) -\left(\frac{2}{-8}\right)\\= \frac{-7}{2}- \frac{3}{4}+\frac{2}{8}\\=\frac{-7}{2}-\frac{3}{4}+\frac{1}{4}\\=\frac{-14}{4}-\frac{3}{4}+\frac{1}{4}\\=\frac{-14-3+1}{4}\\=\frac{-16}{4}\\=\frac{-4}{1}\)
9. \(-\left(\frac{-3}{-8}\right) +\left(\frac{6}{-4}\right) +\left(\frac{8}{-12}\right)\\= \frac{-3}{8}- \frac{6}{4}-\frac{8}{12}\\=\frac{-3}{8}-\frac{3}{2}-\frac{2}{3}\\=\frac{-9}{24}-\frac{36}{24}-\frac{16}{24}\\=\frac{-9-36-16}{24}\\=\frac{-61}{24}\)
10. \(-\left(\frac{-7}{-6}\right) -\left(\frac{-3}{3}\right) -\left(\frac{-2}{-11}\right)\\= \frac{-7}{6}+ \frac{3}{3}-\frac{2}{11}\\=\frac{-7}{6}+\frac{1}{1}-\frac{2}{11}\\=\frac{-77}{66}+\frac{66}{66}-\frac{12}{66}\\=\frac{-77+66-12}{66}\\=\frac{-23}{66}\)
11. \(-\left(\frac{3}{-4}\right) -\left(\frac{4}{-9}\right) -\left(\frac{-11}{-10}\right)\\= \frac{3}{4}+ \frac{4}{9}-\frac{11}{10}\\=\frac{135}{180}+\frac{80}{180}-\frac{198}{180}\\=\frac{135+80-198}{180}\\=\frac{17}{180}\)
12. \(-\left(\frac{-9}{-5}\right) +\left(\frac{-7}{5}\right) -\left(\frac{-9}{10}\right)\\= \frac{-9}{5}- \frac{7}{5}+\frac{9}{10}\\=\frac{-18}{10}-\frac{14}{10}+\frac{9}{10}\\=\frac{-18-14+9}{10}\\=\frac{-23}{10}\)