Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{4}\right) +\left(\frac{-9}{5}\right) -\left(\frac{11}{-11}\right)\\= \frac{5}{4}- \frac{9}{5}+\frac{11}{11}\\=\frac{5}{4}-\frac{9}{5}+\frac{1}{1}\\=\frac{25}{20}-\frac{36}{20}+\frac{20}{20}\\=\frac{25-36+20}{20}\\=\frac{9}{20}\)
2. \(-\left(\frac{8}{3}\right) +\left(\frac{2}{5}\right) -\left(\frac{8}{-6}\right)\\= \frac{-8}{3}+ \frac{2}{5}+\frac{8}{6}\\=\frac{-8}{3}+\frac{2}{5}+\frac{4}{3}\\=\frac{-40}{15}+\frac{6}{15}+\frac{20}{15}\\=\frac{-40+6+20}{15}\\=\frac{-14}{15}\)
3. \(-\left(\frac{-8}{-7}\right) -\left(\frac{2}{-5}\right) -\left(\frac{-11}{-5}\right)\\= \frac{-8}{7}+ \frac{2}{5}-\frac{11}{5}\\=\frac{-40}{35}+\frac{14}{35}-\frac{77}{35}\\=\frac{-40+14-77}{35}\\=\frac{-103}{35}\)
4. \(+\left(\frac{-6}{-5}\right) -\left(\frac{5}{-9}\right) -\left(\frac{2}{6}\right)\\= \frac{6}{5}+ \frac{5}{9}-\frac{2}{6}\\=\frac{6}{5}+\frac{5}{9}-\frac{1}{3}\\=\frac{54}{45}+\frac{25}{45}-\frac{15}{45}\\=\frac{54+25-15}{45}\\=\frac{64}{45}\)
5. \(-\left(\frac{-6}{-5}\right) +\left(\frac{7}{-2}\right) -\left(\frac{2}{-4}\right)\\= \frac{-6}{5}- \frac{7}{2}+\frac{2}{4}\\=\frac{-6}{5}-\frac{7}{2}+\frac{1}{2}\\=\frac{-12}{10}-\frac{35}{10}+\frac{5}{10}\\=\frac{-12-35+5}{10}\\=\frac{-42}{10}\\=\frac{-21}{5}\)
6. \(+\left(\frac{2}{3}\right) +\left(\frac{-7}{9}\right) -\left(\frac{8}{-9}\right)\\= \frac{2}{3}- \frac{7}{9}+\frac{8}{9}\\=\frac{6}{9}-\frac{7}{9}+\frac{8}{9}\\=\frac{6-7+8}{9}\\=\frac{7}{9}\)
7. \(-\left(\frac{7}{2}\right) -\left(\frac{2}{-8}\right) -\left(\frac{-8}{-11}\right)\\= \frac{-7}{2}+ \frac{2}{8}-\frac{8}{11}\\=\frac{-7}{2}+\frac{1}{4}-\frac{8}{11}\\=\frac{-154}{44}+\frac{11}{44}-\frac{32}{44}\\=\frac{-154+11-32}{44}\\=\frac{-175}{44}\)
8. \(+\left(\frac{10}{9}\right) -\left(\frac{-9}{7}\right) -\left(\frac{2}{-8}\right)\\= \frac{10}{9}+ \frac{9}{7}+\frac{2}{8}\\=\frac{10}{9}+\frac{9}{7}+\frac{1}{4}\\=\frac{280}{252}+\frac{324}{252}+\frac{63}{252}\\=\frac{280+324+63}{252}\\=\frac{667}{252}\)
9. \(+\left(\frac{-7}{-2}\right) +\left(\frac{-7}{-10}\right) +\left(\frac{-7}{-10}\right)\\= \frac{7}{2}+ \frac{7}{10}+\frac{7}{10}\\=\frac{35}{10}+\frac{7}{10}+\frac{7}{10}\\=\frac{35+7+7}{10}\\=\frac{49}{10}\)
10. \(-\left(\frac{3}{4}\right) -\left(\frac{8}{-2}\right) -\left(\frac{9}{-11}\right)\\= \frac{-3}{4}+ \frac{8}{2}+\frac{9}{11}\\=\frac{-3}{4}+\frac{4}{1}+\frac{9}{11}\\=\frac{-33}{44}+\frac{176}{44}+\frac{36}{44}\\=\frac{-33+176+36}{44}\\=\frac{179}{44}\)
11. \(-\left(\frac{-10}{7}\right) -\left(\frac{-2}{-5}\right) -\left(\frac{-3}{3}\right)\\= \frac{10}{7}- \frac{2}{5}+\frac{3}{3}\\=\frac{10}{7}-\frac{2}{5}+\frac{1}{1}\\=\frac{50}{35}-\frac{14}{35}+\frac{35}{35}\\=\frac{50-14+35}{35}\\=\frac{71}{35}\)
12. \(+\left(\frac{10}{-3}\right) -\left(\frac{-3}{5}\right) -\left(\frac{2}{-12}\right)\\= \frac{-10}{3}+ \frac{3}{5}+\frac{2}{12}\\=\frac{-10}{3}+\frac{3}{5}+\frac{1}{6}\\=\frac{-100}{30}+\frac{18}{30}+\frac{5}{30}\\=\frac{-100+18+5}{30}\\=\frac{-77}{30}\)