Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{4}\right) +\left(\frac{-3}{-5}\right) +\left(\frac{11}{9}\right)\\= \frac{-3}{4}+ \frac{3}{5}+\frac{11}{9}\\=\frac{-135}{180}+\frac{108}{180}+\frac{220}{180}\\=\frac{-135+108+220}{180}\\=\frac{193}{180}\)
2. \(-\left(\frac{5}{2}\right) -\left(\frac{10}{-9}\right) -\left(\frac{-7}{2}\right)\\= \frac{-5}{2}+ \frac{10}{9}+\frac{7}{2}\\=\frac{-45}{18}+\frac{20}{18}+\frac{63}{18}\\=\frac{-45+20+63}{18}\\=\frac{38}{18}\\=\frac{19}{9}\)
3. \(+\left(\frac{9}{-7}\right) +\left(\frac{10}{8}\right) +\left(\frac{-2}{2}\right)\\= \frac{-9}{7}+ \frac{10}{8}-\frac{2}{2}\\=\frac{-9}{7}+\frac{5}{4}-\frac{1}{1}\\=\frac{-36}{28}+\frac{35}{28}-\frac{28}{28}\\=\frac{-36+35-28}{28}\\=\frac{-29}{28}\)
4. \(+\left(\frac{6}{-5}\right) +\left(\frac{-9}{-5}\right) +\left(\frac{-11}{-12}\right)\\= \frac{-6}{5}+ \frac{9}{5}+\frac{11}{12}\\=\frac{-72}{60}+\frac{108}{60}+\frac{55}{60}\\=\frac{-72+108+55}{60}\\=\frac{91}{60}\)
5. \(+\left(\frac{-9}{-2}\right) -\left(\frac{-3}{7}\right) +\left(\frac{4}{-6}\right)\\= \frac{9}{2}+ \frac{3}{7}-\frac{4}{6}\\=\frac{9}{2}+\frac{3}{7}-\frac{2}{3}\\=\frac{189}{42}+\frac{18}{42}-\frac{28}{42}\\=\frac{189+18-28}{42}\\=\frac{179}{42}\)
6. \(+\left(\frac{10}{9}\right) -\left(\frac{4}{-10}\right) -\left(\frac{-11}{-5}\right)\\= \frac{10}{9}+ \frac{4}{10}-\frac{11}{5}\\=\frac{10}{9}+\frac{2}{5}-\frac{11}{5}\\=\frac{50}{45}+\frac{18}{45}-\frac{99}{45}\\=\frac{50+18-99}{45}\\=\frac{-31}{45}\)
7. \(-\left(\frac{2}{7}\right) -\left(\frac{9}{5}\right) -\left(\frac{12}{-5}\right)\\= \frac{-2}{7}- \frac{9}{5}+\frac{12}{5}\\=\frac{-10}{35}-\frac{63}{35}+\frac{84}{35}\\=\frac{-10-63+84}{35}\\=\frac{11}{35}\)
8. \(+\left(\frac{6}{5}\right) -\left(\frac{-3}{-5}\right) +\left(\frac{4}{2}\right)\\= \frac{6}{5}- \frac{3}{5}+\frac{4}{2}\\=\frac{6}{5}-\frac{3}{5}+\frac{2}{1}\\=\frac{6-3+2}{5}\\=\frac{5}{5}\\=\frac{1}{1}\)
9. \(-\left(\frac{9}{5}\right) -\left(\frac{5}{3}\right) -\left(\frac{-8}{-9}\right)\\= \frac{-9}{5}- \frac{5}{3}-\frac{8}{9}\\=\frac{-81}{45}-\frac{75}{45}-\frac{40}{45}\\=\frac{-81-75-40}{45}\\=\frac{-196}{45}\)
10. \(+\left(\frac{-4}{-3}\right) -\left(\frac{-9}{-10}\right) -\left(\frac{7}{4}\right)\\= \frac{4}{3}- \frac{9}{10}-\frac{7}{4}\\=\frac{80}{60}-\frac{54}{60}-\frac{105}{60}\\=\frac{80-54-105}{60}\\=\frac{-79}{60}\)
11. \(+\left(\frac{-7}{6}\right) -\left(\frac{9}{6}\right) +\left(\frac{-7}{11}\right)\\= \frac{-7}{6}- \frac{9}{6}-\frac{7}{11}\\=\frac{-7}{6}-\frac{3}{2}-\frac{7}{11}\\=\frac{-77}{66}-\frac{99}{66}-\frac{42}{66}\\=\frac{-77-99-42}{66}\\=\frac{-218}{66}\\=\frac{-109}{33}\)
12. \(+\left(\frac{6}{-5}\right) +\left(\frac{7}{6}\right) +\left(\frac{-11}{8}\right)\\= \frac{-6}{5}+ \frac{7}{6}-\frac{11}{8}\\=\frac{-144}{120}+\frac{140}{120}-\frac{165}{120}\\=\frac{-144+140-165}{120}\\=\frac{-169}{120}\)