Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-9}{-13}\right)+\left(\frac{-6}{-5}\right)\\= \frac{-9}{13}+\frac{6}{5}\\=\frac{-45}{65}+\frac{78}{65}\\=\frac{-45+78}{65}\\=\frac{33}{65}\)
2. \(-\left(\frac{-2}{3}\right)+\left(\frac{13}{4}\right)\\= \frac{2}{3}+\frac{13}{4}\\=\frac{8}{12}+\frac{39}{12}\\=\frac{8+39}{12}\\=\frac{47}{12}\)
3. \(+\left(\frac{13}{-5}\right)+\left(\frac{14}{9}\right)\\= \frac{-13}{5}+\frac{14}{9}\\=\frac{-117}{45}+\frac{70}{45}\\=\frac{-117+70}{45}\\=\frac{-47}{45}\)
4. \(+\left(\frac{-9}{8}\right)-\left(\frac{-14}{9}\right)\\= \frac{-9}{8}+\frac{14}{9}\\=\frac{-81}{72}+\frac{112}{72}\\=\frac{-81+112}{72}\\=\frac{31}{72}\)
5. \(+\left(\frac{4}{7}\right)+\left(\frac{-15}{2}\right)\\= \frac{4}{7}-\frac{15}{2}\\=\frac{8}{14}-\frac{105}{14}\\=\frac{8-105}{14}\\=\frac{-97}{14}\)
6. \(+\left(\frac{5}{9}\right)+\left(\frac{-3}{-2}\right)\\= \frac{5}{9}+\frac{3}{2}\\=\frac{10}{18}+\frac{27}{18}\\=\frac{10+27}{18}\\=\frac{37}{18}\)
7. \(-\left(\frac{3}{4}\right)-\left(\frac{9}{4}\right)\\= \frac{-3}{4}-\frac{9}{4}\\=\frac{-3-9}{4}\\=\frac{-12}{4}\\=\frac{-3}{1}\)
8. \(-\left(\frac{-15}{-7}\right)-\left(\frac{2}{-3}\right)\\= \frac{-15}{7}+\frac{2}{3}\\=\frac{-45}{21}+\frac{14}{21}\\=\frac{-45+14}{21}\\=\frac{-31}{21}\)
9. \(+\left(\frac{13}{14}\right)+\left(\frac{-14}{-9}\right)\\= \frac{13}{14}+\frac{14}{9}\\=\frac{117}{126}+\frac{196}{126}\\=\frac{117+196}{126}\\=\frac{313}{126}\)
10. \(+\left(\frac{-13}{10}\right)+\left(\frac{6}{7}\right)\\= \frac{-13}{10}+\frac{6}{7}\\=\frac{-91}{70}+\frac{60}{70}\\=\frac{-91+60}{70}\\=\frac{-31}{70}\)
11. \(-\left(\frac{8}{13}\right)+\left(\frac{-8}{-11}\right)\\= \frac{-8}{13}+\frac{8}{11}\\=\frac{-88}{143}+\frac{104}{143}\\=\frac{-88+104}{143}\\=\frac{16}{143}\)
12. \(+\left(\frac{-6}{11}\right)+\left(\frac{-7}{-8}\right)\\= \frac{-6}{11}+\frac{7}{8}\\=\frac{-48}{88}+\frac{77}{88}\\=\frac{-48+77}{88}\\=\frac{29}{88}\)