Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{4}{9}\right)+\left(\frac{14}{11}\right)\\= \frac{4}{9}+\frac{14}{11}\\=\frac{44}{99}+\frac{126}{99}\\=\frac{44+126}{99}\\=\frac{170}{99}\)
2. \(-\left(\frac{-11}{-3}\right)-\left(\frac{14}{11}\right)\\= \frac{-11}{3}-\frac{14}{11}\\=\frac{-121}{33}-\frac{42}{33}\\=\frac{-121-42}{33}\\=\frac{-163}{33}\)
3. \(-\left(\frac{7}{-5}\right)-\left(\frac{15}{-2}\right)\\= \frac{7}{5}+\frac{15}{2}\\=\frac{14}{10}+\frac{75}{10}\\=\frac{14+75}{10}\\=\frac{89}{10}\)
4. \(-\left(\frac{-7}{9}\right)+\left(\frac{-2}{-9}\right)\\= \frac{7}{9}+\frac{2}{9}\\=\frac{7+2}{9}\\=\frac{9}{9}\\=\frac{1}{1}\)
5. \(+\left(\frac{10}{-3}\right)+\left(\frac{15}{7}\right)\\= \frac{-10}{3}+\frac{15}{7}\\=\frac{-70}{21}+\frac{45}{21}\\=\frac{-70+45}{21}\\=\frac{-25}{21}\)
6. \(+\left(\frac{13}{11}\right)+\left(\frac{-10}{13}\right)\\= \frac{13}{11}-\frac{10}{13}\\=\frac{169}{143}-\frac{110}{143}\\=\frac{169-110}{143}\\=\frac{59}{143}\)
7. \(-\left(\frac{-7}{10}\right)-\left(\frac{3}{-2}\right)\\= \frac{7}{10}+\frac{3}{2}\\=\frac{7+3}{10}\\=\frac{10}{10}\\=\frac{1}{1}\)
8. \(+\left(\frac{-9}{-2}\right)+\left(\frac{3}{2}\right)\\= \frac{9}{2}+\frac{3}{2}\\=\frac{9+3}{2}\\=\frac{12}{2}\\=\frac{6}{1}\)
9. \(+\left(\frac{15}{13}\right)+\left(\frac{14}{9}\right)\\= \frac{15}{13}+\frac{14}{9}\\=\frac{135}{117}+\frac{182}{117}\\=\frac{135+182}{117}\\=\frac{317}{117}\)
10. \(+\left(\frac{11}{9}\right)-\left(\frac{-8}{-3}\right)\\= \frac{11}{9}-\frac{8}{3}\\=\frac{11-8}{9}\\=\frac{3}{9}\\=\frac{1}{3}\)
11. \(+\left(\frac{3}{-7}\right)-\left(\frac{7}{-2}\right)\\= \frac{-3}{7}+\frac{7}{2}\\=\frac{-6}{14}+\frac{49}{14}\\=\frac{-6+49}{14}\\=\frac{43}{14}\)
12. \(+\left(\frac{4}{5}\right)-\left(\frac{-9}{-4}\right)\\= \frac{4}{5}-\frac{9}{4}\\=\frac{16}{20}-\frac{45}{20}\\=\frac{16-45}{20}\\=\frac{-29}{20}\)