Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-3}{9}\right) -\left(\frac{-9}{-10}\right)\\= \frac{-10}{7}- \frac{3}{9}-\frac{9}{10}\\=\frac{-10}{7}-\frac{1}{3}-\frac{9}{10}\\=\frac{-300}{210}-\frac{70}{210}-\frac{189}{210}\\=\frac{-300-70-189}{210}\\=\frac{-559}{210}\)
2. \(-\left(\frac{-4}{3}\right) -\left(\frac{-4}{-10}\right) +\left(\frac{-9}{7}\right)\\= \frac{4}{3}- \frac{4}{10}-\frac{9}{7}\\=\frac{4}{3}-\frac{2}{5}-\frac{9}{7}\\=\frac{140}{105}-\frac{42}{105}-\frac{135}{105}\\=\frac{140-42-135}{105}\\=\frac{-37}{105}\)
3. \(+\left(\frac{-2}{-9}\right) -\left(\frac{-8}{-10}\right) -\left(\frac{-9}{-10}\right)\\= \frac{2}{9}- \frac{8}{10}-\frac{9}{10}\\=\frac{2}{9}-\frac{4}{5}-\frac{9}{10}\\=\frac{20}{90}-\frac{72}{90}-\frac{81}{90}\\=\frac{20-72-81}{90}\\=\frac{-133}{90}\)
4. \(+\left(\frac{10}{7}\right) +\left(\frac{-3}{9}\right) +\left(\frac{-6}{2}\right)\\= \frac{10}{7}- \frac{3}{9}-\frac{6}{2}\\=\frac{10}{7}-\frac{1}{3}-\frac{3}{1}\\=\frac{30}{21}-\frac{7}{21}-\frac{63}{21}\\=\frac{30-7-63}{21}\\=\frac{-40}{21}\)
5. \(-\left(\frac{10}{3}\right) +\left(\frac{9}{-9}\right) +\left(\frac{9}{-6}\right)\\= \frac{-10}{3}- \frac{9}{9}-\frac{9}{6}\\=\frac{-10}{3}-\frac{1}{1}-\frac{3}{2}\\=\frac{-20}{6}-\frac{6}{6}-\frac{9}{6}\\=\frac{-20-6-9}{6}\\=\frac{-35}{6}\)
6. \(+\left(\frac{3}{5}\right) -\left(\frac{10}{7}\right) +\left(\frac{3}{-4}\right)\\= \frac{3}{5}- \frac{10}{7}-\frac{3}{4}\\=\frac{84}{140}-\frac{200}{140}-\frac{105}{140}\\=\frac{84-200-105}{140}\\=\frac{-221}{140}\)
7. \(+\left(\frac{-6}{5}\right) -\left(\frac{-4}{5}\right) -\left(\frac{10}{9}\right)\\= \frac{-6}{5}+ \frac{4}{5}-\frac{10}{9}\\=\frac{-54}{45}+\frac{36}{45}-\frac{50}{45}\\=\frac{-54+36-50}{45}\\=\frac{-68}{45}\)
8. \(+\left(\frac{5}{-9}\right) +\left(\frac{-5}{-4}\right) -\left(\frac{9}{-2}\right)\\= \frac{-5}{9}+ \frac{5}{4}+\frac{9}{2}\\=\frac{-20}{36}+\frac{45}{36}+\frac{162}{36}\\=\frac{-20+45+162}{36}\\=\frac{187}{36}\)
9. \(-\left(\frac{8}{3}\right) -\left(\frac{-9}{5}\right) +\left(\frac{-8}{-9}\right)\\= \frac{-8}{3}+ \frac{9}{5}+\frac{8}{9}\\=\frac{-120}{45}+\frac{81}{45}+\frac{40}{45}\\=\frac{-120+81+40}{45}\\=\frac{1}{45}\)
10. \(+\left(\frac{2}{-7}\right) +\left(\frac{2}{-10}\right) -\left(\frac{-10}{-9}\right)\\= \frac{-2}{7}- \frac{2}{10}-\frac{10}{9}\\=\frac{-2}{7}-\frac{1}{5}-\frac{10}{9}\\=\frac{-90}{315}-\frac{63}{315}-\frac{350}{315}\\=\frac{-90-63-350}{315}\\=\frac{-503}{315}\)
11. \(+\left(\frac{-7}{2}\right) +\left(\frac{-9}{-4}\right) -\left(\frac{11}{-3}\right)\\= \frac{-7}{2}+ \frac{9}{4}+\frac{11}{3}\\=\frac{-42}{12}+\frac{27}{12}+\frac{44}{12}\\=\frac{-42+27+44}{12}\\=\frac{29}{12}\)
12. \(+\left(\frac{3}{-7}\right) +\left(\frac{-10}{2}\right) -\left(\frac{2}{6}\right)\\= \frac{-3}{7}- \frac{10}{2}-\frac{2}{6}\\=\frac{-3}{7}-\frac{5}{1}-\frac{1}{3}\\=\frac{-9}{21}-\frac{105}{21}-\frac{7}{21}\\=\frac{-9-105-7}{21}\\=\frac{-121}{21}\)