Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{2}\right) +\left(\frac{-2}{-9}\right) +\left(\frac{-2}{5}\right)\\= \frac{5}{2}+ \frac{2}{9}-\frac{2}{5}\\=\frac{225}{90}+\frac{20}{90}-\frac{36}{90}\\=\frac{225+20-36}{90}\\=\frac{209}{90}\)
2. \(+\left(\frac{9}{-7}\right) +\left(\frac{8}{-10}\right) -\left(\frac{12}{-12}\right)\\= \frac{-9}{7}- \frac{8}{10}+\frac{12}{12}\\=\frac{-9}{7}-\frac{4}{5}+\frac{1}{1}\\=\frac{-45}{35}-\frac{28}{35}+\frac{35}{35}\\=\frac{-45-28+35}{35}\\=\frac{-38}{35}\)
3. \(+\left(\frac{7}{2}\right) +\left(\frac{-8}{-9}\right) -\left(\frac{7}{11}\right)\\= \frac{7}{2}+ \frac{8}{9}-\frac{7}{11}\\=\frac{693}{198}+\frac{176}{198}-\frac{126}{198}\\=\frac{693+176-126}{198}\\=\frac{743}{198}\)
4. \(-\left(\frac{6}{-5}\right) +\left(\frac{-7}{-8}\right) -\left(\frac{8}{-6}\right)\\= \frac{6}{5}+ \frac{7}{8}+\frac{8}{6}\\=\frac{6}{5}+\frac{7}{8}+\frac{4}{3}\\=\frac{144}{120}+\frac{105}{120}+\frac{160}{120}\\=\frac{144+105+160}{120}\\=\frac{409}{120}\)
5. \(-\left(\frac{-2}{-9}\right) +\left(\frac{-9}{-3}\right) +\left(\frac{-11}{5}\right)\\= \frac{-2}{9}+ \frac{9}{3}-\frac{11}{5}\\=\frac{-2}{9}+\frac{3}{1}-\frac{11}{5}\\=\frac{-10}{45}+\frac{135}{45}-\frac{99}{45}\\=\frac{-10+135-99}{45}\\=\frac{26}{45}\)
6. \(+\left(\frac{-9}{2}\right) -\left(\frac{-6}{-2}\right) -\left(\frac{4}{7}\right)\\= \frac{-9}{2}- \frac{6}{2}-\frac{4}{7}\\=\frac{-9}{2}-\frac{3}{1}-\frac{4}{7}\\=\frac{-63}{14}-\frac{42}{14}-\frac{8}{14}\\=\frac{-63-42-8}{14}\\=\frac{-113}{14}\)
7. \(+\left(\frac{-7}{4}\right) +\left(\frac{-5}{3}\right) -\left(\frac{-7}{-7}\right)\\= \frac{-7}{4}- \frac{5}{3}-\frac{7}{7}\\=\frac{-7}{4}-\frac{5}{3}-\frac{1}{1}\\=\frac{-21}{12}-\frac{20}{12}-\frac{12}{12}\\=\frac{-21-20-12}{12}\\=\frac{-53}{12}\)
8. \(+\left(\frac{-4}{9}\right) -\left(\frac{-9}{7}\right) -\left(\frac{-5}{3}\right)\\= \frac{-4}{9}+ \frac{9}{7}+\frac{5}{3}\\=\frac{-28}{63}+\frac{81}{63}+\frac{105}{63}\\=\frac{-28+81+105}{63}\\=\frac{158}{63}\)
9. \(+\left(\frac{-8}{7}\right) -\left(\frac{7}{10}\right) +\left(\frac{-5}{4}\right)\\= \frac{-8}{7}- \frac{7}{10}-\frac{5}{4}\\=\frac{-160}{140}-\frac{98}{140}-\frac{175}{140}\\=\frac{-160-98-175}{140}\\=\frac{-433}{140}\)
10. \(+\left(\frac{4}{9}\right) -\left(\frac{5}{-6}\right) -\left(\frac{-2}{-9}\right)\\= \frac{4}{9}+ \frac{5}{6}-\frac{2}{9}\\=\frac{8}{18}+\frac{15}{18}-\frac{4}{18}\\=\frac{8+15-4}{18}\\=\frac{19}{18}\)
11. \(-\left(\frac{-6}{5}\right) -\left(\frac{-2}{-3}\right) +\left(\frac{-2}{-8}\right)\\= \frac{6}{5}- \frac{2}{3}+\frac{2}{8}\\=\frac{6}{5}-\frac{2}{3}+\frac{1}{4}\\=\frac{72}{60}-\frac{40}{60}+\frac{15}{60}\\=\frac{72-40+15}{60}\\=\frac{47}{60}\)
12. \(+\left(\frac{2}{9}\right) -\left(\frac{-6}{-5}\right) +\left(\frac{-2}{-4}\right)\\= \frac{2}{9}- \frac{6}{5}+\frac{2}{4}\\=\frac{2}{9}-\frac{6}{5}+\frac{1}{2}\\=\frac{20}{90}-\frac{108}{90}+\frac{45}{90}\\=\frac{20-108+45}{90}\\=\frac{-43}{90}\)