Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{13}\right)-\left(\frac{15}{-11}\right)\\= \frac{-10}{13}+\frac{15}{11}\\=\frac{-110}{143}+\frac{195}{143}\\=\frac{-110+195}{143}\\=\frac{85}{143}\)
2. \(-\left(\frac{-9}{-8}\right)+\left(\frac{7}{2}\right)\\= \frac{-9}{8}+\frac{7}{2}\\=\frac{-9+7}{8}\\=\frac{-2}{8}\\=\frac{-1}{4}\)
3. \(+\left(\frac{4}{9}\right)-\left(\frac{-6}{11}\right)\\= \frac{4}{9}+\frac{6}{11}\\=\frac{44}{99}+\frac{54}{99}\\=\frac{44+54}{99}\\=\frac{98}{99}\)
4. \(-\left(\frac{15}{14}\right)-\left(\frac{-8}{-5}\right)\\= \frac{-15}{14}-\frac{8}{5}\\=\frac{-75}{70}-\frac{112}{70}\\=\frac{-75-112}{70}\\=\frac{-187}{70}\)
5. \(+\left(\frac{15}{-11}\right)+\left(\frac{2}{-7}\right)\\= \frac{-15}{11}-\frac{2}{7}\\=\frac{-105}{77}-\frac{22}{77}\\=\frac{-105-22}{77}\\=\frac{-127}{77}\)
6. \(+\left(\frac{-13}{-11}\right)-\left(\frac{-13}{-11}\right)\\= \frac{13}{11}-\frac{13}{11}\\=\frac{13-13}{11}\\=\frac{0}{11}\\=\frac{0}{1}\)
7. \(-\left(\frac{-10}{3}\right)-\left(\frac{7}{-4}\right)\\= \frac{10}{3}+\frac{7}{4}\\=\frac{40}{12}+\frac{21}{12}\\=\frac{40+21}{12}\\=\frac{61}{12}\)
8. \(-\left(\frac{6}{5}\right)-\left(\frac{-5}{-12}\right)\\= \frac{-6}{5}-\frac{5}{12}\\=\frac{-72}{60}-\frac{25}{60}\\=\frac{-72-25}{60}\\=\frac{-97}{60}\)
9. \(+\left(\frac{-6}{11}\right)+\left(\frac{12}{11}\right)\\= \frac{-6}{11}+\frac{12}{11}\\=\frac{-6+12}{11}\\=\frac{6}{11}\)
10. \(+\left(\frac{-6}{7}\right)+\left(\frac{3}{14}\right)\\= \frac{-6}{7}+\frac{3}{14}\\=\frac{-12}{14}+\frac{3}{14}\\=\frac{-12+3}{14}\\=\frac{-9}{14}\)
11. \(-\left(\frac{-9}{-2}\right)-\left(\frac{-6}{-7}\right)\\= \frac{-9}{2}-\frac{6}{7}\\=\frac{-63}{14}-\frac{12}{14}\\=\frac{-63-12}{14}\\=\frac{-75}{14}\)
12. \(+\left(\frac{9}{-8}\right)+\left(\frac{-5}{-6}\right)\\= \frac{-9}{8}+\frac{5}{6}\\=\frac{-27}{24}+\frac{20}{24}\\=\frac{-27+20}{24}\\=\frac{-7}{24}\)