Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{6}{11}\right)-\left(\frac{-15}{-11}\right)\\= \frac{-6}{11}-\frac{15}{11}\\=\frac{-6-15}{11}\\=\frac{-21}{11}\)
2. \(+\left(\frac{5}{8}\right)-\left(\frac{-14}{9}\right)\\= \frac{5}{8}+\frac{14}{9}\\=\frac{45}{72}+\frac{112}{72}\\=\frac{45+112}{72}\\=\frac{157}{72}\)
3. \(+\left(\frac{13}{-2}\right)+\left(\frac{10}{7}\right)\\= \frac{-13}{2}+\frac{10}{7}\\=\frac{-91}{14}+\frac{20}{14}\\=\frac{-91+20}{14}\\=\frac{-71}{14}\)
4. \(+\left(\frac{14}{-9}\right)-\left(\frac{13}{10}\right)\\= \frac{-14}{9}-\frac{13}{10}\\=\frac{-140}{90}-\frac{117}{90}\\=\frac{-140-117}{90}\\=\frac{-257}{90}\)
5. \(+\left(\frac{11}{-3}\right)-\left(\frac{-12}{13}\right)\\= \frac{-11}{3}+\frac{12}{13}\\=\frac{-143}{39}+\frac{36}{39}\\=\frac{-143+36}{39}\\=\frac{-107}{39}\)
6. \(-\left(\frac{-12}{-5}\right)+\left(\frac{-2}{-5}\right)\\= \frac{-12}{5}+\frac{2}{5}\\=\frac{-12+2}{5}\\=\frac{-10}{5}\\=\frac{-2}{1}\)
7. \(+\left(\frac{-6}{5}\right)-\left(\frac{7}{-3}\right)\\= \frac{-6}{5}+\frac{7}{3}\\=\frac{-18}{15}+\frac{35}{15}\\=\frac{-18+35}{15}\\=\frac{17}{15}\)
8. \(-\left(\frac{6}{7}\right)-\left(\frac{-10}{-9}\right)\\= \frac{-6}{7}-\frac{10}{9}\\=\frac{-54}{63}-\frac{70}{63}\\=\frac{-54-70}{63}\\=\frac{-124}{63}\)
9. \(-\left(\frac{-14}{-5}\right)+\left(\frac{10}{7}\right)\\= \frac{-14}{5}+\frac{10}{7}\\=\frac{-98}{35}+\frac{50}{35}\\=\frac{-98+50}{35}\\=\frac{-48}{35}\)
10. \(+\left(\frac{-8}{-9}\right)-\left(\frac{3}{-10}\right)\\= \frac{8}{9}+\frac{3}{10}\\=\frac{80}{90}+\frac{27}{90}\\=\frac{80+27}{90}\\=\frac{107}{90}\)
11. \(+\left(\frac{5}{-2}\right)-\left(\frac{10}{-9}\right)\\= \frac{-5}{2}+\frac{10}{9}\\=\frac{-45}{18}+\frac{20}{18}\\=\frac{-45+20}{18}\\=\frac{-25}{18}\)
12. \(-\left(\frac{-5}{7}\right)+\left(\frac{6}{-5}\right)\\= \frac{5}{7}-\frac{6}{5}\\=\frac{25}{35}-\frac{42}{35}\\=\frac{25-42}{35}\\=\frac{-17}{35}\)