Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-7}{2}\right)+\left(\frac{8}{-3}\right)\\= \frac{7}{2}-\frac{8}{3}\\=\frac{21}{6}-\frac{16}{6}\\=\frac{21-16}{6}\\=\frac{5}{6}\)
2. \(+\left(\frac{14}{13}\right)-\left(\frac{-7}{6}\right)\\= \frac{14}{13}+\frac{7}{6}\\=\frac{84}{78}+\frac{91}{78}\\=\frac{84+91}{78}\\=\frac{175}{78}\)
3. \(-\left(\frac{4}{-5}\right)-\left(\frac{-12}{11}\right)\\= \frac{4}{5}+\frac{12}{11}\\=\frac{44}{55}+\frac{60}{55}\\=\frac{44+60}{55}\\=\frac{104}{55}\)
4. \(+\left(\frac{-2}{5}\right)-\left(\frac{-15}{11}\right)\\= \frac{-2}{5}+\frac{15}{11}\\=\frac{-22}{55}+\frac{75}{55}\\=\frac{-22+75}{55}\\=\frac{53}{55}\)
5. \(-\left(\frac{-8}{-13}\right)-\left(\frac{3}{-13}\right)\\= \frac{-8}{13}+\frac{3}{13}\\=\frac{-8+3}{13}\\=\frac{-5}{13}\)
6. \(-\left(\frac{-8}{3}\right)+\left(\frac{9}{2}\right)\\= \frac{8}{3}+\frac{9}{2}\\=\frac{16}{6}+\frac{27}{6}\\=\frac{16+27}{6}\\=\frac{43}{6}\)
7. \(-\left(\frac{10}{3}\right)-\left(\frac{-15}{11}\right)\\= \frac{-10}{3}+\frac{15}{11}\\=\frac{-110}{33}+\frac{45}{33}\\=\frac{-110+45}{33}\\=\frac{-65}{33}\)
8. \(-\left(\frac{-9}{-7}\right)-\left(\frac{-12}{-13}\right)\\= \frac{-9}{7}-\frac{12}{13}\\=\frac{-117}{91}-\frac{84}{91}\\=\frac{-117-84}{91}\\=\frac{-201}{91}\)
9. \(-\left(\frac{15}{-4}\right)-\left(\frac{15}{-7}\right)\\= \frac{15}{4}+\frac{15}{7}\\=\frac{105}{28}+\frac{60}{28}\\=\frac{105+60}{28}\\=\frac{165}{28}\)
10. \(-\left(\frac{-8}{5}\right)-\left(\frac{-15}{7}\right)\\= \frac{8}{5}+\frac{15}{7}\\=\frac{56}{35}+\frac{75}{35}\\=\frac{56+75}{35}\\=\frac{131}{35}\)
11. \(+\left(\frac{3}{-4}\right)-\left(\frac{7}{-5}\right)\\= \frac{-3}{4}+\frac{7}{5}\\=\frac{-15}{20}+\frac{28}{20}\\=\frac{-15+28}{20}\\=\frac{13}{20}\)
12. \(+\left(\frac{6}{5}\right)+\left(\frac{2}{-9}\right)\\= \frac{6}{5}-\frac{2}{9}\\=\frac{54}{45}-\frac{10}{45}\\=\frac{54-10}{45}\\=\frac{44}{45}\)