Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{2}\right) +\left(\frac{-8}{-10}\right) +\left(\frac{-4}{9}\right)\\= \frac{9}{2}+ \frac{8}{10}-\frac{4}{9}\\=\frac{9}{2}+\frac{4}{5}-\frac{4}{9}\\=\frac{405}{90}+\frac{72}{90}-\frac{40}{90}\\=\frac{405+72-40}{90}\\=\frac{437}{90}\)
2. \(+\left(\frac{7}{-8}\right) -\left(\frac{-10}{-5}\right) +\left(\frac{9}{-9}\right)\\= \frac{-7}{8}- \frac{10}{5}-\frac{9}{9}\\=\frac{-7}{8}-\frac{2}{1}-\frac{1}{1}\\=\frac{-7-2-1}{8}\\=\frac{-10}{8}\\=\frac{-5}{4}\)
3. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-2}{-6}\right) -\left(\frac{-5}{11}\right)\\= \frac{6}{5}- \frac{2}{6}+\frac{5}{11}\\=\frac{6}{5}-\frac{1}{3}+\frac{5}{11}\\=\frac{198}{165}-\frac{55}{165}+\frac{75}{165}\\=\frac{198-55+75}{165}\\=\frac{218}{165}\)
4. \(-\left(\frac{-3}{-7}\right) -\left(\frac{-2}{10}\right) +\left(\frac{-9}{-7}\right)\\= \frac{-3}{7}+ \frac{2}{10}+\frac{9}{7}\\=\frac{-3}{7}+\frac{1}{5}+\frac{9}{7}\\=\frac{-15}{35}+\frac{7}{35}+\frac{45}{35}\\=\frac{-15+7+45}{35}\\=\frac{37}{35}\)
5. \(-\left(\frac{-8}{-9}\right) -\left(\frac{-3}{3}\right) +\left(\frac{8}{3}\right)\\= \frac{-8}{9}+ \frac{3}{3}+\frac{8}{3}\\=\frac{-8}{9}+\frac{1}{1}+\frac{8}{3}\\=\frac{-8+1+8}{9}\\=\frac{1}{9}\)
6. \(-\left(\frac{6}{7}\right) -\left(\frac{-2}{-8}\right) +\left(\frac{9}{7}\right)\\= \frac{-6}{7}- \frac{2}{8}+\frac{9}{7}\\=\frac{-6}{7}-\frac{1}{4}+\frac{9}{7}\\=\frac{-24}{28}-\frac{7}{28}+\frac{36}{28}\\=\frac{-24-7+36}{28}\\=\frac{5}{28}\)
7. \(-\left(\frac{-9}{-4}\right) +\left(\frac{-5}{8}\right) -\left(\frac{-11}{11}\right)\\= \frac{-9}{4}- \frac{5}{8}+\frac{11}{11}\\=\frac{-9}{4}-\frac{5}{8}+\frac{1}{1}\\=\frac{-18}{8}-\frac{5}{8}+\frac{8}{8}\\=\frac{-18-5+8}{8}\\=\frac{-15}{8}\)
8. \(-\left(\frac{3}{-7}\right) +\left(\frac{4}{-10}\right) +\left(\frac{-9}{12}\right)\\= \frac{3}{7}- \frac{4}{10}-\frac{9}{12}\\=\frac{3}{7}-\frac{2}{5}-\frac{3}{4}\\=\frac{60}{140}-\frac{56}{140}-\frac{105}{140}\\=\frac{60-56-105}{140}\\=\frac{-101}{140}\)
9. \(-\left(\frac{-10}{-3}\right) -\left(\frac{6}{5}\right) +\left(\frac{4}{-9}\right)\\= \frac{-10}{3}- \frac{6}{5}-\frac{4}{9}\\=\frac{-150}{45}-\frac{54}{45}-\frac{20}{45}\\=\frac{-150-54-20}{45}\\=\frac{-224}{45}\)
10. \(+\left(\frac{-10}{-7}\right) -\left(\frac{-2}{7}\right) -\left(\frac{-3}{12}\right)\\= \frac{10}{7}+ \frac{2}{7}+\frac{3}{12}\\=\frac{10}{7}+\frac{2}{7}+\frac{1}{4}\\=\frac{40}{28}+\frac{8}{28}+\frac{7}{28}\\=\frac{40+8+7}{28}\\=\frac{55}{28}\)
11. \(-\left(\frac{2}{7}\right) +\left(\frac{4}{7}\right) -\left(\frac{-10}{-12}\right)\\= \frac{-2}{7}+ \frac{4}{7}-\frac{10}{12}\\=\frac{-2}{7}+\frac{4}{7}-\frac{5}{6}\\=\frac{-12}{42}+\frac{24}{42}-\frac{35}{42}\\=\frac{-12+24-35}{42}\\=\frac{-23}{42}\)
12. \(-\left(\frac{-4}{-7}\right) -\left(\frac{8}{2}\right) -\left(\frac{12}{4}\right)\\= \frac{-4}{7}- \frac{8}{2}-\frac{12}{4}\\=\frac{-4}{7}-\frac{4}{1}-\frac{3}{1}\\=\frac{-4-4-3}{7}\\=\frac{-11}{7}\)