Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{2}\right)+\left(\frac{-13}{-3}\right)\\= \frac{-9}{2}+\frac{13}{3}\\=\frac{-27}{6}+\frac{26}{6}\\=\frac{-27+26}{6}\\=\frac{-1}{6}\)
2. \(-\left(\frac{15}{14}\right)+\left(\frac{-6}{5}\right)\\= \frac{-15}{14}-\frac{6}{5}\\=\frac{-75}{70}-\frac{84}{70}\\=\frac{-75-84}{70}\\=\frac{-159}{70}\)
3. \(+\left(\frac{-10}{3}\right)-\left(\frac{3}{-10}\right)\\= \frac{-10}{3}+\frac{3}{10}\\=\frac{-100}{30}+\frac{9}{30}\\=\frac{-100+9}{30}\\=\frac{-91}{30}\)
4. \(-\left(\frac{-2}{-11}\right)+\left(\frac{-10}{-9}\right)\\= \frac{-2}{11}+\frac{10}{9}\\=\frac{-18}{99}+\frac{110}{99}\\=\frac{-18+110}{99}\\=\frac{92}{99}\)
5. \(-\left(\frac{-2}{13}\right)+\left(\frac{-9}{-7}\right)\\= \frac{2}{13}+\frac{9}{7}\\=\frac{14}{91}+\frac{117}{91}\\=\frac{14+117}{91}\\=\frac{131}{91}\)
6. \(-\left(\frac{15}{-14}\right)-\left(\frac{-8}{-5}\right)\\= \frac{15}{14}-\frac{8}{5}\\=\frac{75}{70}-\frac{112}{70}\\=\frac{75-112}{70}\\=\frac{-37}{70}\)
7. \(-\left(\frac{9}{11}\right)-\left(\frac{15}{-13}\right)\\= \frac{-9}{11}+\frac{15}{13}\\=\frac{-117}{143}+\frac{165}{143}\\=\frac{-117+165}{143}\\=\frac{48}{143}\)
8. \(+\left(\frac{14}{-3}\right)-\left(\frac{-14}{13}\right)\\= \frac{-14}{3}+\frac{14}{13}\\=\frac{-182}{39}+\frac{42}{39}\\=\frac{-182+42}{39}\\=\frac{-140}{39}\)
9. \(-\left(\frac{-12}{5}\right)-\left(\frac{3}{-13}\right)\\= \frac{12}{5}+\frac{3}{13}\\=\frac{156}{65}+\frac{15}{65}\\=\frac{156+15}{65}\\=\frac{171}{65}\)
10. \(+\left(\frac{-9}{-4}\right)+\left(\frac{2}{-13}\right)\\= \frac{9}{4}-\frac{2}{13}\\=\frac{117}{52}-\frac{8}{52}\\=\frac{117-8}{52}\\=\frac{109}{52}\)
11. \(-\left(\frac{13}{5}\right)-\left(\frac{-7}{-9}\right)\\= \frac{-13}{5}-\frac{7}{9}\\=\frac{-117}{45}-\frac{35}{45}\\=\frac{-117-35}{45}\\=\frac{-152}{45}\)
12. \(-\left(\frac{12}{-11}\right)+\left(\frac{-9}{-5}\right)\\= \frac{12}{11}+\frac{9}{5}\\=\frac{60}{55}+\frac{99}{55}\\=\frac{60+99}{55}\\=\frac{159}{55}\)