Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-14}{13}\right)+\left(\frac{15}{2}\right)\\= \frac{14}{13}+\frac{15}{2}\\=\frac{28}{26}+\frac{195}{26}\\=\frac{28+195}{26}\\=\frac{223}{26}\)
2. \(+\left(\frac{-6}{5}\right)+\left(\frac{7}{2}\right)\\= \frac{-6}{5}+\frac{7}{2}\\=\frac{-12}{10}+\frac{35}{10}\\=\frac{-12+35}{10}\\=\frac{23}{10}\)
3. \(+\left(\frac{8}{-11}\right)+\left(\frac{6}{-5}\right)\\= \frac{-8}{11}-\frac{6}{5}\\=\frac{-40}{55}-\frac{66}{55}\\=\frac{-40-66}{55}\\=\frac{-106}{55}\)
4. \(-\left(\frac{4}{11}\right)-\left(\frac{15}{13}\right)\\= \frac{-4}{11}-\frac{15}{13}\\=\frac{-52}{143}-\frac{165}{143}\\=\frac{-52-165}{143}\\=\frac{-217}{143}\)
5. \(-\left(\frac{-7}{2}\right)-\left(\frac{2}{3}\right)\\= \frac{7}{2}-\frac{2}{3}\\=\frac{21}{6}-\frac{4}{6}\\=\frac{21-4}{6}\\=\frac{17}{6}\)
6. \(+\left(\frac{-15}{-13}\right)-\left(\frac{-7}{6}\right)\\= \frac{15}{13}+\frac{7}{6}\\=\frac{90}{78}+\frac{91}{78}\\=\frac{90+91}{78}\\=\frac{181}{78}\)
7. \(+\left(\frac{-2}{7}\right)+\left(\frac{-7}{-4}\right)\\= \frac{-2}{7}+\frac{7}{4}\\=\frac{-8}{28}+\frac{49}{28}\\=\frac{-8+49}{28}\\=\frac{41}{28}\)
8. \(+\left(\frac{-9}{-4}\right)-\left(\frac{-6}{11}\right)\\= \frac{9}{4}+\frac{6}{11}\\=\frac{99}{44}+\frac{24}{44}\\=\frac{99+24}{44}\\=\frac{123}{44}\)
9. \(+\left(\frac{-14}{-13}\right)-\left(\frac{-4}{-13}\right)\\= \frac{14}{13}-\frac{4}{13}\\=\frac{14-4}{13}\\=\frac{10}{13}\)
10. \(-\left(\frac{12}{-5}\right)+\left(\frac{-14}{13}\right)\\= \frac{12}{5}-\frac{14}{13}\\=\frac{156}{65}-\frac{70}{65}\\=\frac{156-70}{65}\\=\frac{86}{65}\)
11. \(+\left(\frac{-3}{14}\right)-\left(\frac{-9}{-10}\right)\\= \frac{-3}{14}-\frac{9}{10}\\=\frac{-15}{70}-\frac{63}{70}\\=\frac{-15-63}{70}\\=\frac{-78}{70}\\=\frac{-39}{35}\)
12. \(-\left(\frac{-11}{12}\right)-\left(\frac{9}{10}\right)\\= \frac{11}{12}-\frac{9}{10}\\=\frac{55}{60}-\frac{54}{60}\\=\frac{55-54}{60}\\=\frac{1}{60}\)