Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-14}{13}\right)+\left(\frac{-6}{-7}\right)\\= \frac{14}{13}+\frac{6}{7}\\=\frac{98}{91}+\frac{78}{91}\\=\frac{98+78}{91}\\=\frac{176}{91}\)
2. \(+\left(\frac{9}{-5}\right)+\left(\frac{-5}{-2}\right)\\= \frac{-9}{5}+\frac{5}{2}\\=\frac{-18}{10}+\frac{25}{10}\\=\frac{-18+25}{10}\\=\frac{7}{10}\)
3. \(+\left(\frac{-10}{-11}\right)+\left(\frac{-5}{6}\right)\\= \frac{10}{11}-\frac{5}{6}\\=\frac{60}{66}-\frac{55}{66}\\=\frac{60-55}{66}\\=\frac{5}{66}\)
4. \(-\left(\frac{9}{4}\right)+\left(\frac{-8}{3}\right)\\= \frac{-9}{4}-\frac{8}{3}\\=\frac{-27}{12}-\frac{32}{12}\\=\frac{-27-32}{12}\\=\frac{-59}{12}\)
5. \(+\left(\frac{4}{-7}\right)+\left(\frac{-10}{-3}\right)\\= \frac{-4}{7}+\frac{10}{3}\\=\frac{-12}{21}+\frac{70}{21}\\=\frac{-12+70}{21}\\=\frac{58}{21}\)
6. \(+\left(\frac{-6}{-7}\right)-\left(\frac{13}{-4}\right)\\= \frac{6}{7}+\frac{13}{4}\\=\frac{24}{28}+\frac{91}{28}\\=\frac{24+91}{28}\\=\frac{115}{28}\)
7. \(+\left(\frac{7}{13}\right)+\left(\frac{-9}{11}\right)\\= \frac{7}{13}-\frac{9}{11}\\=\frac{77}{143}-\frac{117}{143}\\=\frac{77-117}{143}\\=\frac{-40}{143}\)
8. \(+\left(\frac{5}{6}\right)-\left(\frac{11}{-6}\right)\\= \frac{5}{6}+\frac{11}{6}\\=\frac{5+11}{6}\\=\frac{16}{6}\\=\frac{8}{3}\)
9. \(-\left(\frac{-8}{-9}\right)-\left(\frac{10}{3}\right)\\= \frac{-8}{9}-\frac{10}{3}\\=\frac{-8-10}{9}\\=\frac{-18}{9}\\=\frac{-2}{1}\)
10. \(+\left(\frac{-4}{-7}\right)+\left(\frac{-15}{11}\right)\\= \frac{4}{7}-\frac{15}{11}\\=\frac{44}{77}-\frac{105}{77}\\=\frac{44-105}{77}\\=\frac{-61}{77}\)
11. \(+\left(\frac{-11}{14}\right)+\left(\frac{-5}{-3}\right)\\= \frac{-11}{14}+\frac{5}{3}\\=\frac{-33}{42}+\frac{70}{42}\\=\frac{-33+70}{42}\\=\frac{37}{42}\)
12. \(+\left(\frac{-6}{5}\right)+\left(\frac{7}{-5}\right)\\= \frac{-6}{5}-\frac{7}{5}\\=\frac{-6-7}{5}\\=\frac{-13}{5}\)