Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{-7}\right) -\left(\frac{7}{7}\right) -\left(\frac{-9}{-11}\right)\\= \frac{4}{7}- \frac{7}{7}-\frac{9}{11}\\=\frac{4}{7}-\frac{1}{1}-\frac{9}{11}\\=\frac{44}{77}-\frac{77}{77}-\frac{63}{77}\\=\frac{44-77-63}{77}\\=\frac{-96}{77}\)
2. \(+\left(\frac{5}{6}\right) -\left(\frac{-10}{-10}\right) +\left(\frac{5}{-9}\right)\\= \frac{5}{6}- \frac{10}{10}-\frac{5}{9}\\=\frac{5}{6}-\frac{1}{1}-\frac{5}{9}\\=\frac{15}{18}-\frac{18}{18}-\frac{10}{18}\\=\frac{15-18-10}{18}\\=\frac{-13}{18}\)
3. \(+\left(\frac{7}{8}\right) -\left(\frac{-5}{7}\right) +\left(\frac{7}{4}\right)\\= \frac{7}{8}+ \frac{5}{7}+\frac{7}{4}\\=\frac{49}{56}+\frac{40}{56}+\frac{98}{56}\\=\frac{49+40+98}{56}\\=\frac{187}{56}\)
4. \(+\left(\frac{-10}{-7}\right) -\left(\frac{-2}{-4}\right) +\left(\frac{2}{-5}\right)\\= \frac{10}{7}- \frac{2}{4}-\frac{2}{5}\\=\frac{10}{7}-\frac{1}{2}-\frac{2}{5}\\=\frac{100}{70}-\frac{35}{70}-\frac{28}{70}\\=\frac{100-35-28}{70}\\=\frac{37}{70}\)
5. \(+\left(\frac{2}{3}\right) +\left(\frac{6}{8}\right) +\left(\frac{-7}{2}\right)\\= \frac{2}{3}+ \frac{6}{8}-\frac{7}{2}\\=\frac{2}{3}+\frac{3}{4}-\frac{7}{2}\\=\frac{8}{12}+\frac{9}{12}-\frac{42}{12}\\=\frac{8+9-42}{12}\\=\frac{-25}{12}\)
6. \(-\left(\frac{5}{6}\right) -\left(\frac{-6}{-10}\right) +\left(\frac{-10}{-8}\right)\\= \frac{-5}{6}- \frac{6}{10}+\frac{10}{8}\\=\frac{-5}{6}-\frac{3}{5}+\frac{5}{4}\\=\frac{-50}{60}-\frac{36}{60}+\frac{75}{60}\\=\frac{-50-36+75}{60}\\=\frac{-11}{60}\)
7. \(-\left(\frac{9}{-4}\right) +\left(\frac{5}{-6}\right) +\left(\frac{-11}{10}\right)\\= \frac{9}{4}- \frac{5}{6}-\frac{11}{10}\\=\frac{135}{60}-\frac{50}{60}-\frac{66}{60}\\=\frac{135-50-66}{60}\\=\frac{19}{60}\)
8. \(-\left(\frac{-6}{-5}\right) -\left(\frac{3}{5}\right) -\left(\frac{2}{2}\right)\\= \frac{-6}{5}- \frac{3}{5}-\frac{2}{2}\\=\frac{-6}{5}-\frac{3}{5}-\frac{1}{1}\\=\frac{-6-3-1}{5}\\=\frac{-10}{5}\\=\frac{-2}{1}\)
9. \(+\left(\frac{-10}{7}\right) +\left(\frac{6}{-8}\right) +\left(\frac{-2}{4}\right)\\= \frac{-10}{7}- \frac{6}{8}-\frac{2}{4}\\=\frac{-10}{7}-\frac{3}{4}-\frac{1}{2}\\=\frac{-40}{28}-\frac{21}{28}-\frac{14}{28}\\=\frac{-40-21-14}{28}\\=\frac{-75}{28}\)
10. \(+\left(\frac{-4}{-9}\right) -\left(\frac{-10}{-10}\right) +\left(\frac{-6}{-5}\right)\\= \frac{4}{9}- \frac{10}{10}+\frac{6}{5}\\=\frac{4}{9}-\frac{1}{1}+\frac{6}{5}\\=\frac{20}{45}-\frac{45}{45}+\frac{54}{45}\\=\frac{20-45+54}{45}\\=\frac{29}{45}\)
11. \(+\left(\frac{-6}{-5}\right) -\left(\frac{2}{-4}\right) -\left(\frac{12}{12}\right)\\= \frac{6}{5}+ \frac{2}{4}-\frac{12}{12}\\=\frac{6}{5}+\frac{1}{2}-\frac{1}{1}\\=\frac{12}{10}+\frac{5}{10}-\frac{10}{10}\\=\frac{12+5-10}{10}\\=\frac{7}{10}\)
12. \(-\left(\frac{-9}{-7}\right) +\left(\frac{-5}{3}\right) +\left(\frac{12}{6}\right)\\= \frac{-9}{7}- \frac{5}{3}+\frac{12}{6}\\=\frac{-9}{7}-\frac{5}{3}+\frac{2}{1}\\=\frac{-27}{21}-\frac{35}{21}+\frac{42}{21}\\=\frac{-27-35+42}{21}\\=\frac{-20}{21}\)