Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{3}\right)-\left(\frac{-4}{-5}\right)\\= \frac{5}{3}-\frac{4}{5}\\=\frac{25}{15}-\frac{12}{15}\\=\frac{25-12}{15}\\=\frac{13}{15}\)
2. \(-\left(\frac{-10}{-11}\right)+\left(\frac{-10}{7}\right)\\= \frac{-10}{11}-\frac{10}{7}\\=\frac{-70}{77}-\frac{110}{77}\\=\frac{-70-110}{77}\\=\frac{-180}{77}\)
3. \(+\left(\frac{3}{-13}\right)+\left(\frac{-4}{-7}\right)\\= \frac{-3}{13}+\frac{4}{7}\\=\frac{-21}{91}+\frac{52}{91}\\=\frac{-21+52}{91}\\=\frac{31}{91}\)
4. \(+\left(\frac{-10}{7}\right)+\left(\frac{4}{-3}\right)\\= \frac{-10}{7}-\frac{4}{3}\\=\frac{-30}{21}-\frac{28}{21}\\=\frac{-30-28}{21}\\=\frac{-58}{21}\)
5. \(+\left(\frac{5}{7}\right)-\left(\frac{-4}{7}\right)\\= \frac{5}{7}+\frac{4}{7}\\=\frac{5+4}{7}\\=\frac{9}{7}\)
6. \(-\left(\frac{-6}{7}\right)+\left(\frac{-15}{7}\right)\\= \frac{6}{7}-\frac{15}{7}\\=\frac{6-15}{7}\\=\frac{-9}{7}\)
7. \(+\left(\frac{6}{5}\right)-\left(\frac{9}{13}\right)\\= \frac{6}{5}-\frac{9}{13}\\=\frac{78}{65}-\frac{45}{65}\\=\frac{78-45}{65}\\=\frac{33}{65}\)
8. \(+\left(\frac{-2}{11}\right)+\left(\frac{-5}{7}\right)\\= \frac{-2}{11}-\frac{5}{7}\\=\frac{-14}{77}-\frac{55}{77}\\=\frac{-14-55}{77}\\=\frac{-69}{77}\)
9. \(-\left(\frac{14}{3}\right)-\left(\frac{10}{-7}\right)\\= \frac{-14}{3}+\frac{10}{7}\\=\frac{-98}{21}+\frac{30}{21}\\=\frac{-98+30}{21}\\=\frac{-68}{21}\)
10. \(+\left(\frac{9}{-5}\right)+\left(\frac{12}{5}\right)\\= \frac{-9}{5}+\frac{12}{5}\\=\frac{-9+12}{5}\\=\frac{3}{5}\)
11. \(-\left(\frac{8}{-3}\right)+\left(\frac{-14}{-13}\right)\\= \frac{8}{3}+\frac{14}{13}\\=\frac{104}{39}+\frac{42}{39}\\=\frac{104+42}{39}\\=\frac{146}{39}\)
12. \(-\left(\frac{-3}{-10}\right)+\left(\frac{10}{3}\right)\\= \frac{-3}{10}+\frac{10}{3}\\=\frac{-9}{30}+\frac{100}{30}\\=\frac{-9+100}{30}\\=\frac{91}{30}\)