Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-7}{8}\right)-\left(\frac{-15}{13}\right)\\= \frac{7}{8}+\frac{15}{13}\\=\frac{91}{104}+\frac{120}{104}\\=\frac{91+120}{104}\\=\frac{211}{104}\)
2. \(+\left(\frac{5}{-7}\right)-\left(\frac{8}{3}\right)\\= \frac{-5}{7}-\frac{8}{3}\\=\frac{-15}{21}-\frac{56}{21}\\=\frac{-15-56}{21}\\=\frac{-71}{21}\)
3. \(-\left(\frac{8}{-7}\right)+\left(\frac{-10}{-3}\right)\\= \frac{8}{7}+\frac{10}{3}\\=\frac{24}{21}+\frac{70}{21}\\=\frac{24+70}{21}\\=\frac{94}{21}\)
4. \(+\left(\frac{-10}{-3}\right)-\left(\frac{15}{7}\right)\\= \frac{10}{3}-\frac{15}{7}\\=\frac{70}{21}-\frac{45}{21}\\=\frac{70-45}{21}\\=\frac{25}{21}\)
5. \(+\left(\frac{9}{-7}\right)-\left(\frac{9}{-10}\right)\\= \frac{-9}{7}+\frac{9}{10}\\=\frac{-90}{70}+\frac{63}{70}\\=\frac{-90+63}{70}\\=\frac{-27}{70}\)
6. \(+\left(\frac{8}{13}\right)+\left(\frac{-5}{-2}\right)\\= \frac{8}{13}+\frac{5}{2}\\=\frac{16}{26}+\frac{65}{26}\\=\frac{16+65}{26}\\=\frac{81}{26}\)
7. \(+\left(\frac{14}{-3}\right)+\left(\frac{-8}{7}\right)\\= \frac{-14}{3}-\frac{8}{7}\\=\frac{-98}{21}-\frac{24}{21}\\=\frac{-98-24}{21}\\=\frac{-122}{21}\)
8. \(-\left(\frac{2}{13}\right)+\left(\frac{-6}{-7}\right)\\= \frac{-2}{13}+\frac{6}{7}\\=\frac{-14}{91}+\frac{78}{91}\\=\frac{-14+78}{91}\\=\frac{64}{91}\)
9. \(-\left(\frac{10}{13}\right)-\left(\frac{10}{-11}\right)\\= \frac{-10}{13}+\frac{10}{11}\\=\frac{-110}{143}+\frac{130}{143}\\=\frac{-110+130}{143}\\=\frac{20}{143}\)
10. \(+\left(\frac{4}{-5}\right)-\left(\frac{-4}{-5}\right)\\= \frac{-4}{5}-\frac{4}{5}\\=\frac{-4-4}{5}\\=\frac{-8}{5}\)
11. \(-\left(\frac{8}{3}\right)-\left(\frac{-6}{-7}\right)\\= \frac{-8}{3}-\frac{6}{7}\\=\frac{-56}{21}-\frac{18}{21}\\=\frac{-56-18}{21}\\=\frac{-74}{21}\)
12. \(-\left(\frac{6}{13}\right)-\left(\frac{-4}{3}\right)\\= \frac{-6}{13}+\frac{4}{3}\\=\frac{-18}{39}+\frac{52}{39}\\=\frac{-18+52}{39}\\=\frac{34}{39}\)