Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{6}{-13}\right)+\left(\frac{10}{-7}\right)\\= \frac{6}{13}-\frac{10}{7}\\=\frac{42}{91}-\frac{130}{91}\\=\frac{42-130}{91}\\=\frac{-88}{91}\)
2. \(+\left(\frac{-14}{3}\right)+\left(\frac{8}{-5}\right)\\= \frac{-14}{3}-\frac{8}{5}\\=\frac{-70}{15}-\frac{24}{15}\\=\frac{-70-24}{15}\\=\frac{-94}{15}\)
3. \(-\left(\frac{-11}{14}\right)+\left(\frac{-13}{-2}\right)\\= \frac{11}{14}+\frac{13}{2}\\=\frac{11+13}{14}\\=\frac{24}{14}\\=\frac{12}{7}\)
4. \(-\left(\frac{7}{-6}\right)-\left(\frac{-9}{8}\right)\\= \frac{7}{6}+\frac{9}{8}\\=\frac{28}{24}+\frac{27}{24}\\=\frac{28+27}{24}\\=\frac{55}{24}\)
5. \(+\left(\frac{3}{10}\right)+\left(\frac{13}{-2}\right)\\= \frac{3}{10}-\frac{13}{2}\\=\frac{3-13}{10}\\=\frac{-10}{10}\\=\frac{-1}{1}\)
6. \(-\left(\frac{-14}{-11}\right)+\left(\frac{7}{-2}\right)\\= \frac{-14}{11}-\frac{7}{2}\\=\frac{-28}{22}-\frac{77}{22}\\=\frac{-28-77}{22}\\=\frac{-105}{22}\)
7. \(-\left(\frac{-12}{5}\right)-\left(\frac{-7}{-8}\right)\\= \frac{12}{5}-\frac{7}{8}\\=\frac{96}{40}-\frac{35}{40}\\=\frac{96-35}{40}\\=\frac{61}{40}\)
8. \(+\left(\frac{-9}{-2}\right)-\left(\frac{-13}{8}\right)\\= \frac{9}{2}+\frac{13}{8}\\=\frac{36}{8}+\frac{13}{8}\\=\frac{36+13}{8}\\=\frac{49}{8}\)
9. \(-\left(\frac{-15}{-14}\right)-\left(\frac{7}{-10}\right)\\= \frac{-15}{14}+\frac{7}{10}\\=\frac{-75}{70}+\frac{49}{70}\\=\frac{-75+49}{70}\\=\frac{-26}{70}\\=\frac{-13}{35}\)
10. \(+\left(\frac{-11}{2}\right)+\left(\frac{-15}{-11}\right)\\= \frac{-11}{2}+\frac{15}{11}\\=\frac{-121}{22}+\frac{30}{22}\\=\frac{-121+30}{22}\\=\frac{-91}{22}\)
11. \(-\left(\frac{4}{-11}\right)+\left(\frac{-15}{-2}\right)\\= \frac{4}{11}+\frac{15}{2}\\=\frac{8}{22}+\frac{165}{22}\\=\frac{8+165}{22}\\=\frac{173}{22}\)
12. \(+\left(\frac{11}{-2}\right)-\left(\frac{-9}{11}\right)\\= \frac{-11}{2}+\frac{9}{11}\\=\frac{-121}{22}+\frac{18}{22}\\=\frac{-121+18}{22}\\=\frac{-103}{22}\)