Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{-7}\right)+\left(\frac{6}{11}\right)\\= \frac{-5}{7}+\frac{6}{11}\\=\frac{-55}{77}+\frac{42}{77}\\=\frac{-55+42}{77}\\=\frac{-13}{77}\)
2. \(-\left(\frac{13}{-3}\right)+\left(\frac{7}{-11}\right)\\= \frac{13}{3}-\frac{7}{11}\\=\frac{143}{33}-\frac{21}{33}\\=\frac{143-21}{33}\\=\frac{122}{33}\)
3. \(-\left(\frac{10}{-3}\right)+\left(\frac{-15}{-7}\right)\\= \frac{10}{3}+\frac{15}{7}\\=\frac{70}{21}+\frac{45}{21}\\=\frac{70+45}{21}\\=\frac{115}{21}\)
4. \(+\left(\frac{-13}{-3}\right)+\left(\frac{-2}{9}\right)\\= \frac{13}{3}-\frac{2}{9}\\=\frac{39}{9}-\frac{2}{9}\\=\frac{39-2}{9}\\=\frac{37}{9}\)
5. \(-\left(\frac{-10}{7}\right)-\left(\frac{6}{5}\right)\\= \frac{10}{7}-\frac{6}{5}\\=\frac{50}{35}-\frac{42}{35}\\=\frac{50-42}{35}\\=\frac{8}{35}\)
6. \(-\left(\frac{-6}{13}\right)+\left(\frac{-11}{3}\right)\\= \frac{6}{13}-\frac{11}{3}\\=\frac{18}{39}-\frac{143}{39}\\=\frac{18-143}{39}\\=\frac{-125}{39}\)
7. \(+\left(\frac{13}{-12}\right)+\left(\frac{10}{-11}\right)\\= \frac{-13}{12}-\frac{10}{11}\\=\frac{-143}{132}-\frac{120}{132}\\=\frac{-143-120}{132}\\=\frac{-263}{132}\)
8. \(-\left(\frac{-7}{11}\right)-\left(\frac{13}{-14}\right)\\= \frac{7}{11}+\frac{13}{14}\\=\frac{98}{154}+\frac{143}{154}\\=\frac{98+143}{154}\\=\frac{241}{154}\)
9. \(+\left(\frac{-12}{-11}\right)+\left(\frac{-13}{9}\right)\\= \frac{12}{11}-\frac{13}{9}\\=\frac{108}{99}-\frac{143}{99}\\=\frac{108-143}{99}\\=\frac{-35}{99}\)
10. \(-\left(\frac{11}{-2}\right)+\left(\frac{-13}{-2}\right)\\= \frac{11}{2}+\frac{13}{2}\\=\frac{11+13}{2}\\=\frac{24}{2}\\=\frac{12}{1}\)
11. \(+\left(\frac{12}{11}\right)-\left(\frac{-5}{6}\right)\\= \frac{12}{11}+\frac{5}{6}\\=\frac{72}{66}+\frac{55}{66}\\=\frac{72+55}{66}\\=\frac{127}{66}\)
12. \(-\left(\frac{-4}{-3}\right)-\left(\frac{6}{5}\right)\\= \frac{-4}{3}-\frac{6}{5}\\=\frac{-20}{15}-\frac{18}{15}\\=\frac{-20-18}{15}\\=\frac{-38}{15}\)