Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{-9}\right)-\left(\frac{-13}{2}\right)\\= \frac{10}{9}+\frac{13}{2}\\=\frac{20}{18}+\frac{117}{18}\\=\frac{20+117}{18}\\=\frac{137}{18}\)
2. \(+\left(\frac{-3}{10}\right)+\left(\frac{9}{-10}\right)\\= \frac{-3}{10}-\frac{9}{10}\\=\frac{-3-9}{10}\\=\frac{-12}{10}\\=\frac{-6}{5}\)
3. \(+\left(\frac{-11}{-9}\right)+\left(\frac{3}{7}\right)\\= \frac{11}{9}+\frac{3}{7}\\=\frac{77}{63}+\frac{27}{63}\\=\frac{77+27}{63}\\=\frac{104}{63}\)
4. \(+\left(\frac{12}{-11}\right)+\left(\frac{-7}{-12}\right)\\= \frac{-12}{11}+\frac{7}{12}\\=\frac{-144}{132}+\frac{77}{132}\\=\frac{-144+77}{132}\\=\frac{-67}{132}\)
5. \(-\left(\frac{8}{7}\right)+\left(\frac{2}{3}\right)\\= \frac{-8}{7}+\frac{2}{3}\\=\frac{-24}{21}+\frac{14}{21}\\=\frac{-24+14}{21}\\=\frac{-10}{21}\)
6. \(-\left(\frac{14}{9}\right)+\left(\frac{-6}{-11}\right)\\= \frac{-14}{9}+\frac{6}{11}\\=\frac{-154}{99}+\frac{54}{99}\\=\frac{-154+54}{99}\\=\frac{-100}{99}\)
7. \(+\left(\frac{-8}{-5}\right)+\left(\frac{-2}{9}\right)\\= \frac{8}{5}-\frac{2}{9}\\=\frac{72}{45}-\frac{10}{45}\\=\frac{72-10}{45}\\=\frac{62}{45}\)
8. \(+\left(\frac{13}{9}\right)-\left(\frac{-3}{-2}\right)\\= \frac{13}{9}-\frac{3}{2}\\=\frac{26}{18}-\frac{27}{18}\\=\frac{26-27}{18}\\=\frac{-1}{18}\)
9. \(+\left(\frac{10}{3}\right)+\left(\frac{-4}{3}\right)\\= \frac{10}{3}-\frac{4}{3}\\=\frac{10-4}{3}\\=\frac{6}{3}\\=\frac{2}{1}\)
10. \(+\left(\frac{15}{11}\right)+\left(\frac{-6}{11}\right)\\= \frac{15}{11}-\frac{6}{11}\\=\frac{15-6}{11}\\=\frac{9}{11}\)
11. \(+\left(\frac{5}{-11}\right)+\left(\frac{2}{5}\right)\\= \frac{-5}{11}+\frac{2}{5}\\=\frac{-25}{55}+\frac{22}{55}\\=\frac{-25+22}{55}\\=\frac{-3}{55}\)
12. \(+\left(\frac{-13}{3}\right)+\left(\frac{5}{-8}\right)\\= \frac{-13}{3}-\frac{5}{8}\\=\frac{-104}{24}-\frac{15}{24}\\=\frac{-104-15}{24}\\=\frac{-119}{24}\)