Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{14}{-5}\right)+\left(\frac{11}{3}\right)\\= \frac{-14}{5}+\frac{11}{3}\\=\frac{-42}{15}+\frac{55}{15}\\=\frac{-42+55}{15}\\=\frac{13}{15}\)
2. \(+\left(\frac{10}{-11}\right)+\left(\frac{-11}{-12}\right)\\= \frac{-10}{11}+\frac{11}{12}\\=\frac{-120}{132}+\frac{121}{132}\\=\frac{-120+121}{132}\\=\frac{1}{132}\)
3. \(+\left(\frac{-15}{-11}\right)-\left(\frac{3}{-10}\right)\\= \frac{15}{11}+\frac{3}{10}\\=\frac{150}{110}+\frac{33}{110}\\=\frac{150+33}{110}\\=\frac{183}{110}\)
4. \(+\left(\frac{-12}{-5}\right)-\left(\frac{15}{14}\right)\\= \frac{12}{5}-\frac{15}{14}\\=\frac{168}{70}-\frac{75}{70}\\=\frac{168-75}{70}\\=\frac{93}{70}\)
5. \(-\left(\frac{-8}{-13}\right)+\left(\frac{-10}{11}\right)\\= \frac{-8}{13}-\frac{10}{11}\\=\frac{-88}{143}-\frac{130}{143}\\=\frac{-88-130}{143}\\=\frac{-218}{143}\)
6. \(+\left(\frac{7}{-10}\right)+\left(\frac{-3}{10}\right)\\= \frac{-7}{10}-\frac{3}{10}\\=\frac{-7-3}{10}\\=\frac{-10}{10}\\=\frac{-1}{1}\)
7. \(+\left(\frac{12}{5}\right)-\left(\frac{4}{5}\right)\\= \frac{12}{5}-\frac{4}{5}\\=\frac{12-4}{5}\\=\frac{8}{5}\)
8. \(+\left(\frac{2}{3}\right)-\left(\frac{-10}{-7}\right)\\= \frac{2}{3}-\frac{10}{7}\\=\frac{14}{21}-\frac{30}{21}\\=\frac{14-30}{21}\\=\frac{-16}{21}\)
9. \(-\left(\frac{12}{-5}\right)-\left(\frac{4}{9}\right)\\= \frac{12}{5}-\frac{4}{9}\\=\frac{108}{45}-\frac{20}{45}\\=\frac{108-20}{45}\\=\frac{88}{45}\)
10. \(+\left(\frac{-4}{-13}\right)+\left(\frac{12}{-11}\right)\\= \frac{4}{13}-\frac{12}{11}\\=\frac{44}{143}-\frac{156}{143}\\=\frac{44-156}{143}\\=\frac{-112}{143}\)
11. \(+\left(\frac{-7}{-8}\right)+\left(\frac{-14}{-9}\right)\\= \frac{7}{8}+\frac{14}{9}\\=\frac{63}{72}+\frac{112}{72}\\=\frac{63+112}{72}\\=\frac{175}{72}\)
12. \(+\left(\frac{-3}{14}\right)-\left(\frac{12}{5}\right)\\= \frac{-3}{14}-\frac{12}{5}\\=\frac{-15}{70}-\frac{168}{70}\\=\frac{-15-168}{70}\\=\frac{-183}{70}\)