Breuken haakjesregel (reeks 1)

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Bereken

1. \(-\left(\frac{13}{-4}\right)+\left(\frac{9}{-10}\right)\)
2. \(+\left(\frac{-14}{9}\right)+\left(\frac{7}{6}\right)\)
3. \(-\left(\frac{10}{3}\right)-\left(\frac{4}{3}\right)\)
4. \(-\left(\frac{13}{-11}\right)-\left(\frac{-11}{-4}\right)\)
5. \(-\left(\frac{-9}{-2}\right)-\left(\frac{2}{3}\right)\)
6. \(-\left(\frac{15}{-13}\right)-\left(\frac{-13}{-10}\right)\)
7. \(+\left(\frac{5}{6}\right)+\left(\frac{-2}{-7}\right)\)
8. \(-\left(\frac{-15}{-13}\right)-\left(\frac{-4}{7}\right)\)
9. \(+\left(\frac{14}{-9}\right)+\left(\frac{-10}{-7}\right)\)
10. \(+\left(\frac{-2}{7}\right)+\left(\frac{-14}{3}\right)\)
11. \(+\left(\frac{-11}{10}\right)-\left(\frac{-15}{-7}\right)\)
12. \(-\left(\frac{-7}{-8}\right)-\left(\frac{-8}{7}\right)\)

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Bereken

Verbetersleutel

1. \(-\left(\frac{13}{-4}\right)+\left(\frac{9}{-10}\right)\\= \frac{13}{4}-\frac{9}{10}\\=\frac{65}{20}-\frac{18}{20}\\=\frac{65-18}{20}\\=\frac{47}{20}\)
2. \(+\left(\frac{-14}{9}\right)+\left(\frac{7}{6}\right)\\= \frac{-14}{9}+\frac{7}{6}\\=\frac{-28}{18}+\frac{21}{18}\\=\frac{-28+21}{18}\\=\frac{-7}{18}\)
3. \(-\left(\frac{10}{3}\right)-\left(\frac{4}{3}\right)\\= \frac{-10}{3}-\frac{4}{3}\\=\frac{-10-4}{3}\\=\frac{-14}{3}\)
4. \(-\left(\frac{13}{-11}\right)-\left(\frac{-11}{-4}\right)\\= \frac{13}{11}-\frac{11}{4}\\=\frac{52}{44}-\frac{121}{44}\\=\frac{52-121}{44}\\=\frac{-69}{44}\)
5. \(-\left(\frac{-9}{-2}\right)-\left(\frac{2}{3}\right)\\= \frac{-9}{2}-\frac{2}{3}\\=\frac{-27}{6}-\frac{4}{6}\\=\frac{-27-4}{6}\\=\frac{-31}{6}\)
6. \(-\left(\frac{15}{-13}\right)-\left(\frac{-13}{-10}\right)\\= \frac{15}{13}-\frac{13}{10}\\=\frac{150}{130}-\frac{169}{130}\\=\frac{150-169}{130}\\=\frac{-19}{130}\)
7. \(+\left(\frac{5}{6}\right)+\left(\frac{-2}{-7}\right)\\= \frac{5}{6}+\frac{2}{7}\\=\frac{35}{42}+\frac{12}{42}\\=\frac{35+12}{42}\\=\frac{47}{42}\)
8. \(-\left(\frac{-15}{-13}\right)-\left(\frac{-4}{7}\right)\\= \frac{-15}{13}+\frac{4}{7}\\=\frac{-105}{91}+\frac{52}{91}\\=\frac{-105+52}{91}\\=\frac{-53}{91}\)
9. \(+\left(\frac{14}{-9}\right)+\left(\frac{-10}{-7}\right)\\= \frac{-14}{9}+\frac{10}{7}\\=\frac{-98}{63}+\frac{90}{63}\\=\frac{-98+90}{63}\\=\frac{-8}{63}\)
10. \(+\left(\frac{-2}{7}\right)+\left(\frac{-14}{3}\right)\\= \frac{-2}{7}-\frac{14}{3}\\=\frac{-6}{21}-\frac{98}{21}\\=\frac{-6-98}{21}\\=\frac{-104}{21}\)
11. \(+\left(\frac{-11}{10}\right)-\left(\frac{-15}{-7}\right)\\= \frac{-11}{10}-\frac{15}{7}\\=\frac{-77}{70}-\frac{150}{70}\\=\frac{-77-150}{70}\\=\frac{-227}{70}\)
12. \(-\left(\frac{-7}{-8}\right)-\left(\frac{-8}{7}\right)\\= \frac{-7}{8}+\frac{8}{7}\\=\frac{-49}{56}+\frac{64}{56}\\=\frac{-49+64}{56}\\=\frac{15}{56}\)