Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{15}\right)+\left(\frac{2}{-7}\right)\\= \frac{2}{15}-\frac{2}{7}\\=\frac{14}{105}-\frac{30}{105}\\=\frac{14-30}{105}\\=\frac{-16}{105}\)
2. \(+\left(\frac{-4}{9}\right)+\left(\frac{8}{-9}\right)\\= \frac{-4}{9}-\frac{8}{9}\\=\frac{-4-8}{9}\\=\frac{-12}{9}\\=\frac{-4}{3}\)
3. \(+\left(\frac{-5}{-11}\right)-\left(\frac{-3}{4}\right)\\= \frac{5}{11}+\frac{3}{4}\\=\frac{20}{44}+\frac{33}{44}\\=\frac{20+33}{44}\\=\frac{53}{44}\)
4. \(-\left(\frac{-7}{2}\right)-\left(\frac{2}{-11}\right)\\= \frac{7}{2}+\frac{2}{11}\\=\frac{77}{22}+\frac{4}{22}\\=\frac{77+4}{22}\\=\frac{81}{22}\)
5. \(+\left(\frac{-9}{-14}\right)-\left(\frac{-5}{3}\right)\\= \frac{9}{14}+\frac{5}{3}\\=\frac{27}{42}+\frac{70}{42}\\=\frac{27+70}{42}\\=\frac{97}{42}\)
6. \(+\left(\frac{-5}{7}\right)+\left(\frac{-12}{13}\right)\\= \frac{-5}{7}-\frac{12}{13}\\=\frac{-65}{91}-\frac{84}{91}\\=\frac{-65-84}{91}\\=\frac{-149}{91}\)
7. \(-\left(\frac{2}{-3}\right)+\left(\frac{-11}{-7}\right)\\= \frac{2}{3}+\frac{11}{7}\\=\frac{14}{21}+\frac{33}{21}\\=\frac{14+33}{21}\\=\frac{47}{21}\)
8. \(+\left(\frac{3}{8}\right)-\left(\frac{-8}{-3}\right)\\= \frac{3}{8}-\frac{8}{3}\\=\frac{9}{24}-\frac{64}{24}\\=\frac{9-64}{24}\\=\frac{-55}{24}\)
9. \(-\left(\frac{-11}{-5}\right)-\left(\frac{-8}{-15}\right)\\= \frac{-11}{5}-\frac{8}{15}\\=\frac{-33}{15}-\frac{8}{15}\\=\frac{-33-8}{15}\\=\frac{-41}{15}\)
10. \(+\left(\frac{-10}{3}\right)-\left(\frac{13}{6}\right)\\= \frac{-10}{3}-\frac{13}{6}\\=\frac{-20}{6}-\frac{13}{6}\\=\frac{-20-13}{6}\\=\frac{-33}{6}\\=\frac{-11}{2}\)
11. \(-\left(\frac{-10}{13}\right)+\left(\frac{-5}{6}\right)\\= \frac{10}{13}-\frac{5}{6}\\=\frac{60}{78}-\frac{65}{78}\\=\frac{60-65}{78}\\=\frac{-5}{78}\)
12. \(+\left(\frac{-3}{7}\right)+\left(\frac{-7}{-9}\right)\\= \frac{-3}{7}+\frac{7}{9}\\=\frac{-27}{63}+\frac{49}{63}\\=\frac{-27+49}{63}\\=\frac{22}{63}\)