Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-7}\right) +\left(\frac{-8}{2}\right) -\left(\frac{-9}{4}\right)\\= \frac{10}{7}- \frac{8}{2}+\frac{9}{4}\\=\frac{10}{7}-\frac{4}{1}+\frac{9}{4}\\=\frac{40}{28}-\frac{112}{28}+\frac{63}{28}\\=\frac{40-112+63}{28}\\=\frac{-9}{28}\)
2. \(+\left(\frac{5}{-7}\right) -\left(\frac{5}{2}\right) -\left(\frac{-2}{-5}\right)\\= \frac{-5}{7}- \frac{5}{2}-\frac{2}{5}\\=\frac{-50}{70}-\frac{175}{70}-\frac{28}{70}\\=\frac{-50-175-28}{70}\\=\frac{-253}{70}\)
3. \(+\left(\frac{8}{5}\right) -\left(\frac{-6}{7}\right) +\left(\frac{-10}{8}\right)\\= \frac{8}{5}+ \frac{6}{7}-\frac{10}{8}\\=\frac{8}{5}+\frac{6}{7}-\frac{5}{4}\\=\frac{224}{140}+\frac{120}{140}-\frac{175}{140}\\=\frac{224+120-175}{140}\\=\frac{169}{140}\)
4. \(-\left(\frac{-10}{9}\right) +\left(\frac{6}{-2}\right) +\left(\frac{5}{-9}\right)\\= \frac{10}{9}- \frac{6}{2}-\frac{5}{9}\\=\frac{10}{9}-\frac{3}{1}-\frac{5}{9}\\=\frac{10-3-5}{9}\\=\frac{2}{9}\)
5. \(-\left(\frac{5}{-7}\right) +\left(\frac{-8}{-9}\right) +\left(\frac{6}{-3}\right)\\= \frac{5}{7}+ \frac{8}{9}-\frac{6}{3}\\=\frac{5}{7}+\frac{8}{9}-\frac{2}{1}\\=\frac{45}{63}+\frac{56}{63}-\frac{126}{63}\\=\frac{45+56-126}{63}\\=\frac{-25}{63}\)
6. \(-\left(\frac{-7}{6}\right) +\left(\frac{-8}{-7}\right) -\left(\frac{-8}{11}\right)\\= \frac{7}{6}+ \frac{8}{7}+\frac{8}{11}\\=\frac{539}{462}+\frac{528}{462}+\frac{336}{462}\\=\frac{539+528+336}{462}\\=\frac{1403}{462}\)
7. \(-\left(\frac{8}{-5}\right) +\left(\frac{-8}{-4}\right) -\left(\frac{-5}{-10}\right)\\= \frac{8}{5}+ \frac{8}{4}-\frac{5}{10}\\=\frac{8}{5}+\frac{2}{1}-\frac{1}{2}\\=\frac{16}{10}+\frac{20}{10}-\frac{5}{10}\\=\frac{16+20-5}{10}\\=\frac{31}{10}\)
8. \(-\left(\frac{-8}{9}\right) -\left(\frac{-6}{10}\right) +\left(\frac{7}{12}\right)\\= \frac{8}{9}+ \frac{6}{10}+\frac{7}{12}\\=\frac{8}{9}+\frac{3}{5}+\frac{7}{12}\\=\frac{160}{180}+\frac{108}{180}+\frac{105}{180}\\=\frac{160+108+105}{180}\\=\frac{373}{180}\)
9. \(+\left(\frac{5}{-2}\right) -\left(\frac{5}{-5}\right) -\left(\frac{-2}{-10}\right)\\= \frac{-5}{2}+ \frac{5}{5}-\frac{2}{10}\\=\frac{-5}{2}+\frac{1}{1}-\frac{1}{5}\\=\frac{-25}{10}+\frac{10}{10}-\frac{2}{10}\\=\frac{-25+10-2}{10}\\=\frac{-17}{10}\)
10. \(-\left(\frac{2}{-5}\right) -\left(\frac{-10}{-10}\right) -\left(\frac{7}{-4}\right)\\= \frac{2}{5}- \frac{10}{10}+\frac{7}{4}\\=\frac{2}{5}-\frac{1}{1}+\frac{7}{4}\\=\frac{8}{20}-\frac{20}{20}+\frac{35}{20}\\=\frac{8-20+35}{20}\\=\frac{23}{20}\)
11. \(+\left(\frac{-10}{7}\right) +\left(\frac{-2}{7}\right) -\left(\frac{-3}{-5}\right)\\= \frac{-10}{7}- \frac{2}{7}-\frac{3}{5}\\=\frac{-50}{35}-\frac{10}{35}-\frac{21}{35}\\=\frac{-50-10-21}{35}\\=\frac{-81}{35}\)
12. \(+\left(\frac{-7}{-9}\right) +\left(\frac{9}{-9}\right) -\left(\frac{-10}{-2}\right)\\= \frac{7}{9}- \frac{9}{9}-\frac{10}{2}\\=\frac{7}{9}-\frac{1}{1}-\frac{5}{1}\\=\frac{7-1-5}{9}\\=\frac{1}{9}\)