Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{13}\right)+\left(\frac{12}{-5}\right)\\= \frac{9}{13}-\frac{12}{5}\\=\frac{45}{65}-\frac{156}{65}\\=\frac{45-156}{65}\\=\frac{-111}{65}\)
2. \(+\left(\frac{5}{-8}\right)+\left(\frac{10}{7}\right)\\= \frac{-5}{8}+\frac{10}{7}\\=\frac{-35}{56}+\frac{80}{56}\\=\frac{-35+80}{56}\\=\frac{45}{56}\)
3. \(+\left(\frac{2}{-3}\right)-\left(\frac{-7}{8}\right)\\= \frac{-2}{3}+\frac{7}{8}\\=\frac{-16}{24}+\frac{21}{24}\\=\frac{-16+21}{24}\\=\frac{5}{24}\)
4. \(+\left(\frac{12}{-11}\right)+\left(\frac{-7}{-2}\right)\\= \frac{-12}{11}+\frac{7}{2}\\=\frac{-24}{22}+\frac{77}{22}\\=\frac{-24+77}{22}\\=\frac{53}{22}\)
5. \(-\left(\frac{-10}{-13}\right)+\left(\frac{6}{7}\right)\\= \frac{-10}{13}+\frac{6}{7}\\=\frac{-70}{91}+\frac{78}{91}\\=\frac{-70+78}{91}\\=\frac{8}{91}\)
6. \(-\left(\frac{-5}{-2}\right)-\left(\frac{-14}{11}\right)\\= \frac{-5}{2}+\frac{14}{11}\\=\frac{-55}{22}+\frac{28}{22}\\=\frac{-55+28}{22}\\=\frac{-27}{22}\)
7. \(+\left(\frac{-11}{7}\right)-\left(\frac{-6}{5}\right)\\= \frac{-11}{7}+\frac{6}{5}\\=\frac{-55}{35}+\frac{42}{35}\\=\frac{-55+42}{35}\\=\frac{-13}{35}\)
8. \(-\left(\frac{-5}{7}\right)-\left(\frac{-12}{5}\right)\\= \frac{5}{7}+\frac{12}{5}\\=\frac{25}{35}+\frac{84}{35}\\=\frac{25+84}{35}\\=\frac{109}{35}\)
9. \(+\left(\frac{-5}{2}\right)-\left(\frac{15}{-11}\right)\\= \frac{-5}{2}+\frac{15}{11}\\=\frac{-55}{22}+\frac{30}{22}\\=\frac{-55+30}{22}\\=\frac{-25}{22}\)
10. \(-\left(\frac{-10}{-3}\right)+\left(\frac{5}{-6}\right)\\= \frac{-10}{3}-\frac{5}{6}\\=\frac{-20}{6}-\frac{5}{6}\\=\frac{-20-5}{6}\\=\frac{-25}{6}\)
11. \(+\left(\frac{15}{-11}\right)+\left(\frac{3}{-7}\right)\\= \frac{-15}{11}-\frac{3}{7}\\=\frac{-105}{77}-\frac{33}{77}\\=\frac{-105-33}{77}\\=\frac{-138}{77}\)
12. \(-\left(\frac{-8}{11}\right)+\left(\frac{12}{-11}\right)\\= \frac{8}{11}-\frac{12}{11}\\=\frac{8-12}{11}\\=\frac{-4}{11}\)