Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{7}\right) -\left(\frac{-2}{6}\right) +\left(\frac{-7}{5}\right)\\= \frac{9}{7}+ \frac{2}{6}-\frac{7}{5}\\=\frac{9}{7}+\frac{1}{3}-\frac{7}{5}\\=\frac{135}{105}+\frac{35}{105}-\frac{147}{105}\\=\frac{135+35-147}{105}\\=\frac{23}{105}\)
2. \(-\left(\frac{9}{2}\right) -\left(\frac{5}{7}\right) -\left(\frac{-9}{-12}\right)\\= \frac{-9}{2}- \frac{5}{7}-\frac{9}{12}\\=\frac{-9}{2}-\frac{5}{7}-\frac{3}{4}\\=\frac{-126}{28}-\frac{20}{28}-\frac{21}{28}\\=\frac{-126-20-21}{28}\\=\frac{-167}{28}\)
3. \(+\left(\frac{-8}{9}\right) -\left(\frac{2}{-6}\right) +\left(\frac{-2}{3}\right)\\= \frac{-8}{9}+ \frac{2}{6}-\frac{2}{3}\\=\frac{-8}{9}+\frac{1}{3}-\frac{2}{3}\\=\frac{-8+1-2}{9}\\=\frac{-9}{9}\\=\frac{-1}{1}\)
4. \(+\left(\frac{6}{-5}\right) +\left(\frac{9}{-3}\right) +\left(\frac{-7}{-7}\right)\\= \frac{-6}{5}- \frac{9}{3}+\frac{7}{7}\\=\frac{-6}{5}-\frac{3}{1}+\frac{1}{1}\\=\frac{-6-3+1}{5}\\=\frac{-8}{5}\)
5. \(+\left(\frac{3}{2}\right) -\left(\frac{7}{-9}\right) -\left(\frac{9}{-8}\right)\\= \frac{3}{2}+ \frac{7}{9}+\frac{9}{8}\\=\frac{108}{72}+\frac{56}{72}+\frac{81}{72}\\=\frac{108+56+81}{72}\\=\frac{245}{72}\)
6. \(-\left(\frac{-10}{3}\right) -\left(\frac{-5}{9}\right) -\left(\frac{9}{10}\right)\\= \frac{10}{3}+ \frac{5}{9}-\frac{9}{10}\\=\frac{300}{90}+\frac{50}{90}-\frac{81}{90}\\=\frac{300+50-81}{90}\\=\frac{269}{90}\)
7. \(+\left(\frac{-10}{3}\right) +\left(\frac{-9}{-4}\right) -\left(\frac{9}{-12}\right)\\= \frac{-10}{3}+ \frac{9}{4}+\frac{9}{12}\\=\frac{-10}{3}+\frac{9}{4}+\frac{3}{4}\\=\frac{-40}{12}+\frac{27}{12}+\frac{9}{12}\\=\frac{-40+27+9}{12}\\=\frac{-4}{12}\\=\frac{-1}{3}\)
8. \(-\left(\frac{4}{-5}\right) -\left(\frac{-7}{6}\right) -\left(\frac{-6}{12}\right)\\= \frac{4}{5}+ \frac{7}{6}+\frac{6}{12}\\=\frac{4}{5}+\frac{7}{6}+\frac{1}{2}\\=\frac{24}{30}+\frac{35}{30}+\frac{15}{30}\\=\frac{24+35+15}{30}\\=\frac{74}{30}\\=\frac{37}{15}\)
9. \(+\left(\frac{-9}{4}\right) -\left(\frac{5}{-9}\right) -\left(\frac{4}{5}\right)\\= \frac{-9}{4}+ \frac{5}{9}-\frac{4}{5}\\=\frac{-405}{180}+\frac{100}{180}-\frac{144}{180}\\=\frac{-405+100-144}{180}\\=\frac{-449}{180}\)
10. \(+\left(\frac{-5}{2}\right) -\left(\frac{-9}{10}\right) -\left(\frac{3}{-12}\right)\\= \frac{-5}{2}+ \frac{9}{10}+\frac{3}{12}\\=\frac{-5}{2}+\frac{9}{10}+\frac{1}{4}\\=\frac{-50}{20}+\frac{18}{20}+\frac{5}{20}\\=\frac{-50+18+5}{20}\\=\frac{-27}{20}\)
11. \(+\left(\frac{2}{3}\right) +\left(\frac{5}{7}\right) +\left(\frac{2}{2}\right)\\= \frac{2}{3}+ \frac{5}{7}+\frac{2}{2}\\=\frac{2}{3}+\frac{5}{7}+\frac{1}{1}\\=\frac{14}{21}+\frac{15}{21}+\frac{21}{21}\\=\frac{14+15+21}{21}\\=\frac{50}{21}\)
12. \(-\left(\frac{7}{-5}\right) -\left(\frac{-9}{-5}\right) +\left(\frac{-11}{-4}\right)\\= \frac{7}{5}- \frac{9}{5}+\frac{11}{4}\\=\frac{28}{20}-\frac{36}{20}+\frac{55}{20}\\=\frac{28-36+55}{20}\\=\frac{47}{20}\)