Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{12}{13}\right)-\left(\frac{9}{-4}\right)\\= \frac{-12}{13}+\frac{9}{4}\\=\frac{-48}{52}+\frac{117}{52}\\=\frac{-48+117}{52}\\=\frac{69}{52}\)
2. \(+\left(\frac{4}{-11}\right)+\left(\frac{3}{13}\right)\\= \frac{-4}{11}+\frac{3}{13}\\=\frac{-52}{143}+\frac{33}{143}\\=\frac{-52+33}{143}\\=\frac{-19}{143}\)
3. \(-\left(\frac{9}{11}\right)+\left(\frac{-5}{-6}\right)\\= \frac{-9}{11}+\frac{5}{6}\\=\frac{-54}{66}+\frac{55}{66}\\=\frac{-54+55}{66}\\=\frac{1}{66}\)
4. \(-\left(\frac{-12}{11}\right)-\left(\frac{9}{10}\right)\\= \frac{12}{11}-\frac{9}{10}\\=\frac{120}{110}-\frac{99}{110}\\=\frac{120-99}{110}\\=\frac{21}{110}\)
5. \(-\left(\frac{-10}{7}\right)+\left(\frac{12}{5}\right)\\= \frac{10}{7}+\frac{12}{5}\\=\frac{50}{35}+\frac{84}{35}\\=\frac{50+84}{35}\\=\frac{134}{35}\)
6. \(-\left(\frac{-4}{-3}\right)+\left(\frac{-6}{-5}\right)\\= \frac{-4}{3}+\frac{6}{5}\\=\frac{-20}{15}+\frac{18}{15}\\=\frac{-20+18}{15}\\=\frac{-2}{15}\)
7. \(+\left(\frac{10}{-9}\right)+\left(\frac{-13}{-3}\right)\\= \frac{-10}{9}+\frac{13}{3}\\=\frac{-10+13}{9}\\=\frac{3}{9}\\=\frac{1}{3}\)
8. \(+\left(\frac{2}{5}\right)+\left(\frac{-9}{7}\right)\\= \frac{2}{5}-\frac{9}{7}\\=\frac{14}{35}-\frac{45}{35}\\=\frac{14-45}{35}\\=\frac{-31}{35}\)
9. \(+\left(\frac{5}{-12}\right)-\left(\frac{-15}{-7}\right)\\= \frac{-5}{12}-\frac{15}{7}\\=\frac{-35}{84}-\frac{180}{84}\\=\frac{-35-180}{84}\\=\frac{-215}{84}\)
10. \(-\left(\frac{-11}{-3}\right)+\left(\frac{-15}{-2}\right)\\= \frac{-11}{3}+\frac{15}{2}\\=\frac{-22}{6}+\frac{45}{6}\\=\frac{-22+45}{6}\\=\frac{23}{6}\)
11. \(-\left(\frac{4}{13}\right)+\left(\frac{-13}{10}\right)\\= \frac{-4}{13}-\frac{13}{10}\\=\frac{-40}{130}-\frac{169}{130}\\=\frac{-40-169}{130}\\=\frac{-209}{130}\)
12. \(+\left(\frac{-15}{-13}\right)+\left(\frac{9}{-7}\right)\\= \frac{15}{13}-\frac{9}{7}\\=\frac{105}{91}-\frac{117}{91}\\=\frac{105-117}{91}\\=\frac{-12}{91}\)