Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{-11}\right)+\left(\frac{-7}{2}\right)\\= \frac{-2}{11}-\frac{7}{2}\\=\frac{-4}{22}-\frac{77}{22}\\=\frac{-4-77}{22}\\=\frac{-81}{22}\)
2. \(-\left(\frac{2}{-3}\right)+\left(\frac{14}{13}\right)\\= \frac{2}{3}+\frac{14}{13}\\=\frac{26}{39}+\frac{42}{39}\\=\frac{26+42}{39}\\=\frac{68}{39}\)
3. \(+\left(\frac{9}{13}\right)+\left(\frac{-2}{13}\right)\\= \frac{9}{13}-\frac{2}{13}\\=\frac{9-2}{13}\\=\frac{7}{13}\)
4. \(-\left(\frac{-3}{-7}\right)-\left(\frac{-5}{6}\right)\\= \frac{-3}{7}+\frac{5}{6}\\=\frac{-18}{42}+\frac{35}{42}\\=\frac{-18+35}{42}\\=\frac{17}{42}\)
5. \(+\left(\frac{-6}{-13}\right)+\left(\frac{-11}{-2}\right)\\= \frac{6}{13}+\frac{11}{2}\\=\frac{12}{26}+\frac{143}{26}\\=\frac{12+143}{26}\\=\frac{155}{26}\)
6. \(+\left(\frac{-15}{-14}\right)-\left(\frac{10}{9}\right)\\= \frac{15}{14}-\frac{10}{9}\\=\frac{135}{126}-\frac{140}{126}\\=\frac{135-140}{126}\\=\frac{-5}{126}\)
7. \(+\left(\frac{-6}{-13}\right)+\left(\frac{-10}{7}\right)\\= \frac{6}{13}-\frac{10}{7}\\=\frac{42}{91}-\frac{130}{91}\\=\frac{42-130}{91}\\=\frac{-88}{91}\)
8. \(-\left(\frac{5}{11}\right)-\left(\frac{-6}{5}\right)\\= \frac{-5}{11}+\frac{6}{5}\\=\frac{-25}{55}+\frac{66}{55}\\=\frac{-25+66}{55}\\=\frac{41}{55}\)
9. \(-\left(\frac{-11}{4}\right)-\left(\frac{-2}{-9}\right)\\= \frac{11}{4}-\frac{2}{9}\\=\frac{99}{36}-\frac{8}{36}\\=\frac{99-8}{36}\\=\frac{91}{36}\)
10. \(+\left(\frac{-10}{-3}\right)-\left(\frac{-10}{7}\right)\\= \frac{10}{3}+\frac{10}{7}\\=\frac{70}{21}+\frac{30}{21}\\=\frac{70+30}{21}\\=\frac{100}{21}\)
11. \(-\left(\frac{-12}{7}\right)+\left(\frac{-12}{11}\right)\\= \frac{12}{7}-\frac{12}{11}\\=\frac{132}{77}-\frac{84}{77}\\=\frac{132-84}{77}\\=\frac{48}{77}\)
12. \(+\left(\frac{-11}{-12}\right)-\left(\frac{10}{-3}\right)\\= \frac{11}{12}+\frac{10}{3}\\=\frac{11+10}{12}\\=\frac{21}{12}\\=\frac{7}{4}\)