Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{12}{13}\right)+\left(\frac{-10}{-7}\right)\\= \frac{12}{13}+\frac{10}{7}\\=\frac{84}{91}+\frac{130}{91}\\=\frac{84+130}{91}\\=\frac{214}{91}\)
2. \(-\left(\frac{2}{3}\right)+\left(\frac{-13}{5}\right)\\= \frac{-2}{3}-\frac{13}{5}\\=\frac{-10}{15}-\frac{39}{15}\\=\frac{-10-39}{15}\\=\frac{-49}{15}\)
3. \(+\left(\frac{-14}{5}\right)+\left(\frac{14}{11}\right)\\= \frac{-14}{5}+\frac{14}{11}\\=\frac{-154}{55}+\frac{70}{55}\\=\frac{-154+70}{55}\\=\frac{-84}{55}\)
4. \(+\left(\frac{-9}{10}\right)-\left(\frac{12}{-7}\right)\\= \frac{-9}{10}+\frac{12}{7}\\=\frac{-63}{70}+\frac{120}{70}\\=\frac{-63+120}{70}\\=\frac{57}{70}\)
5. \(-\left(\frac{-6}{-7}\right)+\left(\frac{-6}{-5}\right)\\= \frac{-6}{7}+\frac{6}{5}\\=\frac{-30}{35}+\frac{42}{35}\\=\frac{-30+42}{35}\\=\frac{12}{35}\)
6. \(+\left(\frac{-9}{7}\right)+\left(\frac{5}{2}\right)\\= \frac{-9}{7}+\frac{5}{2}\\=\frac{-18}{14}+\frac{35}{14}\\=\frac{-18+35}{14}\\=\frac{17}{14}\)
7. \(-\left(\frac{7}{-8}\right)+\left(\frac{6}{-7}\right)\\= \frac{7}{8}-\frac{6}{7}\\=\frac{49}{56}-\frac{48}{56}\\=\frac{49-48}{56}\\=\frac{1}{56}\)
8. \(-\left(\frac{-11}{-10}\right)+\left(\frac{12}{-7}\right)\\= \frac{-11}{10}-\frac{12}{7}\\=\frac{-77}{70}-\frac{120}{70}\\=\frac{-77-120}{70}\\=\frac{-197}{70}\)
9. \(+\left(\frac{9}{-2}\right)-\left(\frac{2}{3}\right)\\= \frac{-9}{2}-\frac{2}{3}\\=\frac{-27}{6}-\frac{4}{6}\\=\frac{-27-4}{6}\\=\frac{-31}{6}\)
10. \(+\left(\frac{3}{10}\right)+\left(\frac{-4}{-3}\right)\\= \frac{3}{10}+\frac{4}{3}\\=\frac{9}{30}+\frac{40}{30}\\=\frac{9+40}{30}\\=\frac{49}{30}\)
11. \(-\left(\frac{12}{11}\right)-\left(\frac{2}{11}\right)\\= \frac{-12}{11}-\frac{2}{11}\\=\frac{-12-2}{11}\\=\frac{-14}{11}\)
12. \(-\left(\frac{8}{13}\right)-\left(\frac{-12}{11}\right)\\= \frac{-8}{13}+\frac{12}{11}\\=\frac{-88}{143}+\frac{156}{143}\\=\frac{-88+156}{143}\\=\frac{68}{143}\)