Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{12}{13}\right)+\left(\frac{-3}{7}\right)\\= \frac{12}{13}-\frac{3}{7}\\=\frac{84}{91}-\frac{39}{91}\\=\frac{84-39}{91}\\=\frac{45}{91}\)
2. \(-\left(\frac{-3}{7}\right)+\left(\frac{11}{2}\right)\\= \frac{3}{7}+\frac{11}{2}\\=\frac{6}{14}+\frac{77}{14}\\=\frac{6+77}{14}\\=\frac{83}{14}\)
3. \(+\left(\frac{-6}{5}\right)+\left(\frac{-3}{13}\right)\\= \frac{-6}{5}-\frac{3}{13}\\=\frac{-78}{65}-\frac{15}{65}\\=\frac{-78-15}{65}\\=\frac{-93}{65}\)
4. \(-\left(\frac{-4}{5}\right)-\left(\frac{-14}{-9}\right)\\= \frac{4}{5}-\frac{14}{9}\\=\frac{36}{45}-\frac{70}{45}\\=\frac{36-70}{45}\\=\frac{-34}{45}\)
5. \(-\left(\frac{15}{-7}\right)-\left(\frac{-3}{-10}\right)\\= \frac{15}{7}-\frac{3}{10}\\=\frac{150}{70}-\frac{21}{70}\\=\frac{150-21}{70}\\=\frac{129}{70}\)
6. \(+\left(\frac{7}{13}\right)-\left(\frac{-9}{4}\right)\\= \frac{7}{13}+\frac{9}{4}\\=\frac{28}{52}+\frac{117}{52}\\=\frac{28+117}{52}\\=\frac{145}{52}\)
7. \(+\left(\frac{-7}{8}\right)-\left(\frac{10}{-9}\right)\\= \frac{-7}{8}+\frac{10}{9}\\=\frac{-63}{72}+\frac{80}{72}\\=\frac{-63+80}{72}\\=\frac{17}{72}\)
8. \(-\left(\frac{-8}{-3}\right)-\left(\frac{-2}{-13}\right)\\= \frac{-8}{3}-\frac{2}{13}\\=\frac{-104}{39}-\frac{6}{39}\\=\frac{-104-6}{39}\\=\frac{-110}{39}\)
9. \(-\left(\frac{-13}{12}\right)-\left(\frac{14}{-13}\right)\\= \frac{13}{12}+\frac{14}{13}\\=\frac{169}{156}+\frac{168}{156}\\=\frac{169+168}{156}\\=\frac{337}{156}\)
10. \(+\left(\frac{9}{10}\right)+\left(\frac{-10}{-7}\right)\\= \frac{9}{10}+\frac{10}{7}\\=\frac{63}{70}+\frac{100}{70}\\=\frac{63+100}{70}\\=\frac{163}{70}\)
11. \(+\left(\frac{15}{-2}\right)+\left(\frac{14}{-3}\right)\\= \frac{-15}{2}-\frac{14}{3}\\=\frac{-45}{6}-\frac{28}{6}\\=\frac{-45-28}{6}\\=\frac{-73}{6}\)
12. \(-\left(\frac{-11}{-8}\right)+\left(\frac{8}{13}\right)\\= \frac{-11}{8}+\frac{8}{13}\\=\frac{-143}{104}+\frac{64}{104}\\=\frac{-143+64}{104}\\=\frac{-79}{104}\)