Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{-11}\right)-\left(\frac{7}{-11}\right)\\= \frac{-10}{11}+\frac{7}{11}\\=\frac{-10+7}{11}\\=\frac{-3}{11}\)
2. \(+\left(\frac{-5}{-9}\right)-\left(\frac{5}{-6}\right)\\= \frac{5}{9}+\frac{5}{6}\\=\frac{10}{18}+\frac{15}{18}\\=\frac{10+15}{18}\\=\frac{25}{18}\)
3. \(+\left(\frac{11}{-8}\right)+\left(\frac{13}{-11}\right)\\= \frac{-11}{8}-\frac{13}{11}\\=\frac{-121}{88}-\frac{104}{88}\\=\frac{-121-104}{88}\\=\frac{-225}{88}\)
4. \(-\left(\frac{8}{3}\right)+\left(\frac{15}{2}\right)\\= \frac{-8}{3}+\frac{15}{2}\\=\frac{-16}{6}+\frac{45}{6}\\=\frac{-16+45}{6}\\=\frac{29}{6}\)
5. \(+\left(\frac{-13}{-14}\right)-\left(\frac{-8}{-11}\right)\\= \frac{13}{14}-\frac{8}{11}\\=\frac{143}{154}-\frac{112}{154}\\=\frac{143-112}{154}\\=\frac{31}{154}\)
6. \(+\left(\frac{5}{2}\right)+\left(\frac{12}{5}\right)\\= \frac{5}{2}+\frac{12}{5}\\=\frac{25}{10}+\frac{24}{10}\\=\frac{25+24}{10}\\=\frac{49}{10}\)
7. \(+\left(\frac{-14}{-11}\right)-\left(\frac{-10}{3}\right)\\= \frac{14}{11}+\frac{10}{3}\\=\frac{42}{33}+\frac{110}{33}\\=\frac{42+110}{33}\\=\frac{152}{33}\)
8. \(+\left(\frac{-15}{13}\right)+\left(\frac{10}{3}\right)\\= \frac{-15}{13}+\frac{10}{3}\\=\frac{-45}{39}+\frac{130}{39}\\=\frac{-45+130}{39}\\=\frac{85}{39}\)
9. \(-\left(\frac{15}{4}\right)+\left(\frac{10}{-13}\right)\\= \frac{-15}{4}-\frac{10}{13}\\=\frac{-195}{52}-\frac{40}{52}\\=\frac{-195-40}{52}\\=\frac{-235}{52}\)
10. \(-\left(\frac{-10}{7}\right)-\left(\frac{7}{-3}\right)\\= \frac{10}{7}+\frac{7}{3}\\=\frac{30}{21}+\frac{49}{21}\\=\frac{30+49}{21}\\=\frac{79}{21}\)
11. \(-\left(\frac{-2}{3}\right)-\left(\frac{-6}{-11}\right)\\= \frac{2}{3}-\frac{6}{11}\\=\frac{22}{33}-\frac{18}{33}\\=\frac{22-18}{33}\\=\frac{4}{33}\)
12. \(-\left(\frac{10}{-9}\right)+\left(\frac{14}{9}\right)\\= \frac{10}{9}+\frac{14}{9}\\=\frac{10+14}{9}\\=\frac{24}{9}\\=\frac{8}{3}\)