Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-8}{-7}\right)+\left(\frac{-15}{-14}\right)\\= \frac{-8}{7}+\frac{15}{14}\\=\frac{-16}{14}+\frac{15}{14}\\=\frac{-16+15}{14}\\=\frac{-1}{14}\)
2. \(-\left(\frac{12}{11}\right)-\left(\frac{3}{10}\right)\\= \frac{-12}{11}-\frac{3}{10}\\=\frac{-120}{110}-\frac{33}{110}\\=\frac{-120-33}{110}\\=\frac{-153}{110}\)
3. \(+\left(\frac{6}{11}\right)+\left(\frac{-12}{5}\right)\\= \frac{6}{11}-\frac{12}{5}\\=\frac{30}{55}-\frac{132}{55}\\=\frac{30-132}{55}\\=\frac{-102}{55}\)
4. \(+\left(\frac{15}{2}\right)-\left(\frac{9}{7}\right)\\= \frac{15}{2}-\frac{9}{7}\\=\frac{105}{14}-\frac{18}{14}\\=\frac{105-18}{14}\\=\frac{87}{14}\)
5. \(-\left(\frac{4}{3}\right)-\left(\frac{-11}{-4}\right)\\= \frac{-4}{3}-\frac{11}{4}\\=\frac{-16}{12}-\frac{33}{12}\\=\frac{-16-33}{12}\\=\frac{-49}{12}\)
6. \(+\left(\frac{-2}{15}\right)-\left(\frac{-2}{5}\right)\\= \frac{-2}{15}+\frac{2}{5}\\=\frac{-2+2}{15}\\=\frac{0}{15}\\=\frac{0}{1}\)
7. \(-\left(\frac{10}{9}\right)+\left(\frac{-2}{-15}\right)\\= \frac{-10}{9}+\frac{2}{15}\\=\frac{-50}{45}+\frac{6}{45}\\=\frac{-50+6}{45}\\=\frac{-44}{45}\)
8. \(+\left(\frac{-7}{6}\right)-\left(\frac{-2}{-5}\right)\\= \frac{-7}{6}-\frac{2}{5}\\=\frac{-35}{30}-\frac{12}{30}\\=\frac{-35-12}{30}\\=\frac{-47}{30}\)
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. \(+\left(\frac{9}{7}\right)-\left(\frac{5}{7}\right)\\= \frac{9}{7}-\frac{5}{7}\\=\frac{9-5}{7}\\=\frac{4}{7}\)
11. \(-\left(\frac{-6}{7}\right)+\left(\frac{-11}{5}\right)\\= \frac{6}{7}-\frac{11}{5}\\=\frac{30}{35}-\frac{77}{35}\\=\frac{30-77}{35}\\=\frac{-47}{35}\)
12. \(-\left(\frac{-6}{-13}\right)+\left(\frac{-11}{-9}\right)\\= \frac{-6}{13}+\frac{11}{9}\\=\frac{-54}{117}+\frac{143}{117}\\=\frac{-54+143}{117}\\=\frac{89}{117}\)