Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{9}\right) -\left(\frac{-9}{9}\right) -\left(\frac{-6}{8}\right)\\= \frac{-8}{9}+ \frac{9}{9}+\frac{6}{8}\\=\frac{-8}{9}+\frac{1}{1}+\frac{3}{4}\\=\frac{-32}{36}+\frac{36}{36}+\frac{27}{36}\\=\frac{-32+36+27}{36}\\=\frac{31}{36}\)
2. \(-\left(\frac{-3}{-5}\right) +\left(\frac{10}{4}\right) +\left(\frac{10}{10}\right)\\= \frac{-3}{5}+ \frac{10}{4}+\frac{10}{10}\\=\frac{-3}{5}+\frac{5}{2}+\frac{1}{1}\\=\frac{-6}{10}+\frac{25}{10}+\frac{10}{10}\\=\frac{-6+25+10}{10}\\=\frac{29}{10}\)
3. \(-\left(\frac{7}{9}\right) -\left(\frac{-9}{-6}\right) -\left(\frac{5}{7}\right)\\= \frac{-7}{9}- \frac{9}{6}-\frac{5}{7}\\=\frac{-7}{9}-\frac{3}{2}-\frac{5}{7}\\=\frac{-98}{126}-\frac{189}{126}-\frac{90}{126}\\=\frac{-98-189-90}{126}\\=\frac{-377}{126}\)
4. \(-\left(\frac{-3}{-7}\right) -\left(\frac{-5}{-3}\right) +\left(\frac{-12}{-11}\right)\\= \frac{-3}{7}- \frac{5}{3}+\frac{12}{11}\\=\frac{-99}{231}-\frac{385}{231}+\frac{252}{231}\\=\frac{-99-385+252}{231}\\=\frac{-232}{231}\)
5. \(+\left(\frac{-3}{4}\right) -\left(\frac{-3}{6}\right) +\left(\frac{-3}{-2}\right)\\= \frac{-3}{4}+ \frac{3}{6}+\frac{3}{2}\\=\frac{-3}{4}+\frac{1}{2}+\frac{3}{2}\\=\frac{-3+1+3}{4}\\=\frac{1}{4}\)
6. \(+\left(\frac{6}{5}\right) +\left(\frac{-10}{9}\right) +\left(\frac{9}{5}\right)\\= \frac{6}{5}- \frac{10}{9}+\frac{9}{5}\\=\frac{54}{45}-\frac{50}{45}+\frac{81}{45}\\=\frac{54-50+81}{45}\\=\frac{85}{45}\\=\frac{17}{9}\)
7. \(-\left(\frac{10}{9}\right) -\left(\frac{-9}{-2}\right) +\left(\frac{-11}{12}\right)\\= \frac{-10}{9}- \frac{9}{2}-\frac{11}{12}\\=\frac{-40}{36}-\frac{162}{36}-\frac{33}{36}\\=\frac{-40-162-33}{36}\\=\frac{-235}{36}\)
8. \(-\left(\frac{8}{-5}\right) -\left(\frac{-10}{-5}\right) +\left(\frac{-4}{-8}\right)\\= \frac{8}{5}- \frac{10}{5}+\frac{4}{8}\\=\frac{8}{5}-\frac{2}{1}+\frac{1}{2}\\=\frac{16}{10}-\frac{20}{10}+\frac{5}{10}\\=\frac{16-20+5}{10}\\=\frac{1}{10}\)
9. \(+\left(\frac{-9}{7}\right) -\left(\frac{7}{3}\right) +\left(\frac{2}{11}\right)\\= \frac{-9}{7}- \frac{7}{3}+\frac{2}{11}\\=\frac{-297}{231}-\frac{539}{231}+\frac{42}{231}\\=\frac{-297-539+42}{231}\\=\frac{-794}{231}\)
10. \(-\left(\frac{-4}{5}\right) +\left(\frac{2}{-7}\right) -\left(\frac{-8}{-5}\right)\\= \frac{4}{5}- \frac{2}{7}-\frac{8}{5}\\=\frac{28}{35}-\frac{10}{35}-\frac{56}{35}\\=\frac{28-10-56}{35}\\=\frac{-38}{35}\)
11. \(+\left(\frac{2}{5}\right) +\left(\frac{-5}{-6}\right) -\left(\frac{-11}{4}\right)\\= \frac{2}{5}+ \frac{5}{6}+\frac{11}{4}\\=\frac{24}{60}+\frac{50}{60}+\frac{165}{60}\\=\frac{24+50+165}{60}\\=\frac{239}{60}\)
12. \(-\left(\frac{9}{-4}\right) +\left(\frac{6}{6}\right) +\left(\frac{-10}{11}\right)\\= \frac{9}{4}+ \frac{6}{6}-\frac{10}{11}\\=\frac{9}{4}+\frac{1}{1}-\frac{10}{11}\\=\frac{99}{44}+\frac{44}{44}-\frac{40}{44}\\=\frac{99+44-40}{44}\\=\frac{103}{44}\)