Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-14}{9}\right)+\left(\frac{-6}{5}\right)\\= \frac{14}{9}-\frac{6}{5}\\=\frac{70}{45}-\frac{54}{45}\\=\frac{70-54}{45}\\=\frac{16}{45}\)
2. \(+\left(\frac{-6}{-11}\right)+\left(\frac{-10}{-9}\right)\\= \frac{6}{11}+\frac{10}{9}\\=\frac{54}{99}+\frac{110}{99}\\=\frac{54+110}{99}\\=\frac{164}{99}\)
3. \(-\left(\frac{15}{-7}\right)+\left(\frac{-12}{-5}\right)\\= \frac{15}{7}+\frac{12}{5}\\=\frac{75}{35}+\frac{84}{35}\\=\frac{75+84}{35}\\=\frac{159}{35}\)
4. \(+\left(\frac{10}{-3}\right)+\left(\frac{14}{11}\right)\\= \frac{-10}{3}+\frac{14}{11}\\=\frac{-110}{33}+\frac{42}{33}\\=\frac{-110+42}{33}\\=\frac{-68}{33}\)
5. \(+\left(\frac{-10}{-7}\right)+\left(\frac{11}{14}\right)\\= \frac{10}{7}+\frac{11}{14}\\=\frac{20}{14}+\frac{11}{14}\\=\frac{20+11}{14}\\=\frac{31}{14}\)
6. \(-\left(\frac{-5}{7}\right)-\left(\frac{8}{3}\right)\\= \frac{5}{7}-\frac{8}{3}\\=\frac{15}{21}-\frac{56}{21}\\=\frac{15-56}{21}\\=\frac{-41}{21}\)
7. \(-\left(\frac{8}{11}\right)-\left(\frac{14}{-9}\right)\\= \frac{-8}{11}+\frac{14}{9}\\=\frac{-72}{99}+\frac{154}{99}\\=\frac{-72+154}{99}\\=\frac{82}{99}\)
8. \(-\left(\frac{-15}{11}\right)+\left(\frac{-4}{3}\right)\\= \frac{15}{11}-\frac{4}{3}\\=\frac{45}{33}-\frac{44}{33}\\=\frac{45-44}{33}\\=\frac{1}{33}\)
9. \(-\left(\frac{15}{11}\right)-\left(\frac{3}{13}\right)\\= \frac{-15}{11}-\frac{3}{13}\\=\frac{-195}{143}-\frac{33}{143}\\=\frac{-195-33}{143}\\=\frac{-228}{143}\)
10. \(+\left(\frac{4}{3}\right)+\left(\frac{9}{13}\right)\\= \frac{4}{3}+\frac{9}{13}\\=\frac{52}{39}+\frac{27}{39}\\=\frac{52+27}{39}\\=\frac{79}{39}\)
11. \(-\left(\frac{-10}{3}\right)+\left(\frac{-8}{-13}\right)\\= \frac{10}{3}+\frac{8}{13}\\=\frac{130}{39}+\frac{24}{39}\\=\frac{130+24}{39}\\=\frac{154}{39}\)
12. \(+\left(\frac{-4}{-11}\right)+\left(\frac{-10}{3}\right)\\= \frac{4}{11}-\frac{10}{3}\\=\frac{12}{33}-\frac{110}{33}\\=\frac{12-110}{33}\\=\frac{-98}{33}\)