Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-14}{5}\right)-\left(\frac{-13}{3}\right)\\= \frac{14}{5}+\frac{13}{3}\\=\frac{42}{15}+\frac{65}{15}\\=\frac{42+65}{15}\\=\frac{107}{15}\)
2. \(+\left(\frac{-11}{-7}\right)-\left(\frac{-15}{-13}\right)\\= \frac{11}{7}-\frac{15}{13}\\=\frac{143}{91}-\frac{105}{91}\\=\frac{143-105}{91}\\=\frac{38}{91}\)
3. \(-\left(\frac{8}{-11}\right)-\left(\frac{14}{-5}\right)\\= \frac{8}{11}+\frac{14}{5}\\=\frac{40}{55}+\frac{154}{55}\\=\frac{40+154}{55}\\=\frac{194}{55}\)
4. \(+\left(\frac{2}{-11}\right)-\left(\frac{-4}{11}\right)\\= \frac{-2}{11}+\frac{4}{11}\\=\frac{-2+4}{11}\\=\frac{2}{11}\)
5. \(-\left(\frac{-4}{13}\right)+\left(\frac{-2}{-15}\right)\\= \frac{4}{13}+\frac{2}{15}\\=\frac{60}{195}+\frac{26}{195}\\=\frac{60+26}{195}\\=\frac{86}{195}\)
6. \(-\left(\frac{-2}{-11}\right)-\left(\frac{12}{-11}\right)\\= \frac{-2}{11}+\frac{12}{11}\\=\frac{-2+12}{11}\\=\frac{10}{11}\)
7. \(+\left(\frac{6}{-13}\right)+\left(\frac{-3}{10}\right)\\= \frac{-6}{13}-\frac{3}{10}\\=\frac{-60}{130}-\frac{39}{130}\\=\frac{-60-39}{130}\\=\frac{-99}{130}\)
8. \(+\left(\frac{15}{8}\right)-\left(\frac{-10}{3}\right)\\= \frac{15}{8}+\frac{10}{3}\\=\frac{45}{24}+\frac{80}{24}\\=\frac{45+80}{24}\\=\frac{125}{24}\)
9. \(-\left(\frac{3}{-8}\right)+\left(\frac{-2}{-3}\right)\\= \frac{3}{8}+\frac{2}{3}\\=\frac{9}{24}+\frac{16}{24}\\=\frac{9+16}{24}\\=\frac{25}{24}\)
10. \(+\left(\frac{2}{7}\right)+\left(\frac{9}{-5}\right)\\= \frac{2}{7}-\frac{9}{5}\\=\frac{10}{35}-\frac{63}{35}\\=\frac{10-63}{35}\\=\frac{-53}{35}\)
11. \(+\left(\frac{6}{7}\right)+\left(\frac{-9}{-5}\right)\\= \frac{6}{7}+\frac{9}{5}\\=\frac{30}{35}+\frac{63}{35}\\=\frac{30+63}{35}\\=\frac{93}{35}\)
12. \(+\left(\frac{5}{12}\right)-\left(\frac{-6}{5}\right)\\= \frac{5}{12}+\frac{6}{5}\\=\frac{25}{60}+\frac{72}{60}\\=\frac{25+72}{60}\\=\frac{97}{60}\)