Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{3}\right)+\left(\frac{-8}{5}\right)\\= \frac{-10}{3}-\frac{8}{5}\\=\frac{-50}{15}-\frac{24}{15}\\=\frac{-50-24}{15}\\=\frac{-74}{15}\)
2. \(+\left(\frac{9}{-4}\right)+\left(\frac{-9}{-4}\right)\\= \frac{-9}{4}+\frac{9}{4}\\=\frac{-9+9}{4}\\=\frac{0}{4}\\=\frac{0}{1}\)
3. \(+\left(\frac{10}{-13}\right)-\left(\frac{9}{-14}\right)\\= \frac{-10}{13}+\frac{9}{14}\\=\frac{-140}{182}+\frac{117}{182}\\=\frac{-140+117}{182}\\=\frac{-23}{182}\)
4. \(-\left(\frac{-11}{4}\right)+\left(\frac{9}{-7}\right)\\= \frac{11}{4}-\frac{9}{7}\\=\frac{77}{28}-\frac{36}{28}\\=\frac{77-36}{28}\\=\frac{41}{28}\)
5. \(-\left(\frac{13}{-14}\right)+\left(\frac{-4}{3}\right)\\= \frac{13}{14}-\frac{4}{3}\\=\frac{39}{42}-\frac{56}{42}\\=\frac{39-56}{42}\\=\frac{-17}{42}\)
6. \(+\left(\frac{-14}{3}\right)+\left(\frac{9}{-2}\right)\\= \frac{-14}{3}-\frac{9}{2}\\=\frac{-28}{6}-\frac{27}{6}\\=\frac{-28-27}{6}\\=\frac{-55}{6}\)
7. \(+\left(\frac{13}{10}\right)+\left(\frac{6}{-5}\right)\\= \frac{13}{10}-\frac{6}{5}\\=\frac{13-6}{10}\\=\frac{7}{10}\)
8. \(-\left(\frac{-2}{-13}\right)-\left(\frac{6}{5}\right)\\= \frac{-2}{13}-\frac{6}{5}\\=\frac{-10}{65}-\frac{78}{65}\\=\frac{-10-78}{65}\\=\frac{-88}{65}\)
9. \(+\left(\frac{5}{-2}\right)-\left(\frac{-13}{2}\right)\\= \frac{-5}{2}+\frac{13}{2}\\=\frac{-5+13}{2}\\=\frac{8}{2}\\=\frac{4}{1}\)
10. \(-\left(\frac{3}{11}\right)+\left(\frac{8}{7}\right)\\= \frac{-3}{11}+\frac{8}{7}\\=\frac{-21}{77}+\frac{88}{77}\\=\frac{-21+88}{77}\\=\frac{67}{77}\)
11. \(-\left(\frac{6}{5}\right)-\left(\frac{-9}{4}\right)\\= \frac{-6}{5}+\frac{9}{4}\\=\frac{-24}{20}+\frac{45}{20}\\=\frac{-24+45}{20}\\=\frac{21}{20}\)
12. \(-\left(\frac{-4}{-5}\right)+\left(\frac{-7}{3}\right)\\= \frac{-4}{5}-\frac{7}{3}\\=\frac{-12}{15}-\frac{35}{15}\\=\frac{-12-35}{15}\\=\frac{-47}{15}\)