Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{-7}\right)-\left(\frac{15}{-7}\right)\\= \frac{8}{7}+\frac{15}{7}\\=\frac{8+15}{7}\\=\frac{23}{7}\)
2. \(+\left(\frac{5}{3}\right)-\left(\frac{13}{14}\right)\\= \frac{5}{3}-\frac{13}{14}\\=\frac{70}{42}-\frac{39}{42}\\=\frac{70-39}{42}\\=\frac{31}{42}\)
3. \(+\left(\frac{-8}{-7}\right)-\left(\frac{-7}{11}\right)\\= \frac{8}{7}+\frac{7}{11}\\=\frac{88}{77}+\frac{49}{77}\\=\frac{88+49}{77}\\=\frac{137}{77}\)
4. \(+\left(\frac{11}{-6}\right)+\left(\frac{-3}{10}\right)\\= \frac{-11}{6}-\frac{3}{10}\\=\frac{-55}{30}-\frac{9}{30}\\=\frac{-55-9}{30}\\=\frac{-64}{30}\\=\frac{-32}{15}\)
5. \(-\left(\frac{-8}{7}\right)-\left(\frac{12}{5}\right)\\= \frac{8}{7}-\frac{12}{5}\\=\frac{40}{35}-\frac{84}{35}\\=\frac{40-84}{35}\\=\frac{-44}{35}\)
6. \(+\left(\frac{-5}{-2}\right)+\left(\frac{6}{7}\right)\\= \frac{5}{2}+\frac{6}{7}\\=\frac{35}{14}+\frac{12}{14}\\=\frac{35+12}{14}\\=\frac{47}{14}\)
7. \(-\left(\frac{13}{8}\right)-\left(\frac{13}{-5}\right)\\= \frac{-13}{8}+\frac{13}{5}\\=\frac{-65}{40}+\frac{104}{40}\\=\frac{-65+104}{40}\\=\frac{39}{40}\)
8. \(-\left(\frac{2}{-3}\right)-\left(\frac{-8}{-7}\right)\\= \frac{2}{3}-\frac{8}{7}\\=\frac{14}{21}-\frac{24}{21}\\=\frac{14-24}{21}\\=\frac{-10}{21}\)
9. \(+\left(\frac{9}{13}\right)+\left(\frac{-6}{5}\right)\\= \frac{9}{13}-\frac{6}{5}\\=\frac{45}{65}-\frac{78}{65}\\=\frac{45-78}{65}\\=\frac{-33}{65}\)
10. \(-\left(\frac{-15}{2}\right)+\left(\frac{2}{7}\right)\\= \frac{15}{2}+\frac{2}{7}\\=\frac{105}{14}+\frac{4}{14}\\=\frac{105+4}{14}\\=\frac{109}{14}\)
11. \(-\left(\frac{-7}{-2}\right)+\left(\frac{10}{13}\right)\\= \frac{-7}{2}+\frac{10}{13}\\=\frac{-91}{26}+\frac{20}{26}\\=\frac{-91+20}{26}\\=\frac{-71}{26}\)
12. \(+\left(\frac{-3}{7}\right)+\left(\frac{-10}{-3}\right)\\= \frac{-3}{7}+\frac{10}{3}\\=\frac{-9}{21}+\frac{70}{21}\\=\frac{-9+70}{21}\\=\frac{61}{21}\)