Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-8}{7}\right) +\left(\frac{-6}{8}\right) +\left(\frac{10}{7}\right)\\= \frac{8}{7}- \frac{6}{8}+\frac{10}{7}\\=\frac{8}{7}-\frac{3}{4}+\frac{10}{7}\\=\frac{32}{28}-\frac{21}{28}+\frac{40}{28}\\=\frac{32-21+40}{28}\\=\frac{51}{28}\)
2. \(+\left(\frac{-2}{7}\right) -\left(\frac{10}{3}\right) -\left(\frac{4}{-6}\right)\\= \frac{-2}{7}- \frac{10}{3}+\frac{4}{6}\\=\frac{-2}{7}-\frac{10}{3}+\frac{2}{3}\\=\frac{-6}{21}-\frac{70}{21}+\frac{14}{21}\\=\frac{-6-70+14}{21}\\=\frac{-62}{21}\)
3. \(-\left(\frac{-9}{8}\right) +\left(\frac{10}{-3}\right) -\left(\frac{10}{7}\right)\\= \frac{9}{8}- \frac{10}{3}-\frac{10}{7}\\=\frac{189}{168}-\frac{560}{168}-\frac{240}{168}\\=\frac{189-560-240}{168}\\=\frac{-611}{168}\)
4. \(-\left(\frac{-8}{7}\right) +\left(\frac{5}{7}\right) +\left(\frac{11}{6}\right)\\= \frac{8}{7}+ \frac{5}{7}+\frac{11}{6}\\=\frac{48}{42}+\frac{30}{42}+\frac{77}{42}\\=\frac{48+30+77}{42}\\=\frac{155}{42}\)
5. \(-\left(\frac{-5}{-9}\right) +\left(\frac{-8}{-5}\right) -\left(\frac{5}{12}\right)\\= \frac{-5}{9}+ \frac{8}{5}-\frac{5}{12}\\=\frac{-100}{180}+\frac{288}{180}-\frac{75}{180}\\=\frac{-100+288-75}{180}\\=\frac{113}{180}\)
6. \(+\left(\frac{4}{-3}\right) -\left(\frac{-4}{2}\right) -\left(\frac{-10}{8}\right)\\= \frac{-4}{3}+ \frac{4}{2}+\frac{10}{8}\\=\frac{-4}{3}+\frac{2}{1}+\frac{5}{4}\\=\frac{-16}{12}+\frac{24}{12}+\frac{15}{12}\\=\frac{-16+24+15}{12}\\=\frac{23}{12}\)
7. \(-\left(\frac{-7}{2}\right) -\left(\frac{-5}{7}\right) +\left(\frac{-9}{7}\right)\\= \frac{7}{2}+ \frac{5}{7}-\frac{9}{7}\\=\frac{49}{14}+\frac{10}{14}-\frac{18}{14}\\=\frac{49+10-18}{14}\\=\frac{41}{14}\)
8. \(-\left(\frac{3}{-5}\right) -\left(\frac{-3}{5}\right) -\left(\frac{-5}{-12}\right)\\= \frac{3}{5}+ \frac{3}{5}-\frac{5}{12}\\=\frac{36}{60}+\frac{36}{60}-\frac{25}{60}\\=\frac{36+36-25}{60}\\=\frac{47}{60}\)
9. \(-\left(\frac{5}{4}\right) +\left(\frac{-5}{4}\right) +\left(\frac{9}{-7}\right)\\= \frac{-5}{4}- \frac{5}{4}-\frac{9}{7}\\=\frac{-35}{28}-\frac{35}{28}-\frac{36}{28}\\=\frac{-35-35-36}{28}\\=\frac{-106}{28}\\=\frac{-53}{14}\)
10. \(-\left(\frac{5}{2}\right) -\left(\frac{-9}{2}\right) -\left(\frac{6}{6}\right)\\= \frac{-5}{2}+ \frac{9}{2}-\frac{6}{6}\\=\frac{-5}{2}+\frac{9}{2}-\frac{1}{1}\\=\frac{-5+9-1}{2}\\=\frac{3}{2}\)
11. \(-\left(\frac{-7}{2}\right) -\left(\frac{-6}{4}\right) +\left(\frac{5}{-10}\right)\\= \frac{7}{2}+ \frac{6}{4}-\frac{5}{10}\\=\frac{7}{2}+\frac{3}{2}-\frac{1}{2}\\=\frac{7+3-1}{2}\\=\frac{9}{2}\)
12. \(-\left(\frac{2}{3}\right) +\left(\frac{4}{-6}\right) +\left(\frac{-11}{5}\right)\\= \frac{-2}{3}- \frac{4}{6}-\frac{11}{5}\\=\frac{-2}{3}-\frac{2}{3}-\frac{11}{5}\\=\frac{-10}{15}-\frac{10}{15}-\frac{33}{15}\\=\frac{-10-10-33}{15}\\=\frac{-53}{15}\)