Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{3}\right)-\left(\frac{-14}{13}\right)\\= \frac{4}{3}+\frac{14}{13}\\=\frac{52}{39}+\frac{42}{39}\\=\frac{52+42}{39}\\=\frac{94}{39}\)
2. \(+\left(\frac{4}{3}\right)+\left(\frac{-8}{3}\right)\\= \frac{4}{3}-\frac{8}{3}\\=\frac{4-8}{3}\\=\frac{-4}{3}\)
3. \(+\left(\frac{-5}{-2}\right)+\left(\frac{3}{-2}\right)\\= \frac{5}{2}-\frac{3}{2}\\=\frac{5-3}{2}\\=\frac{2}{2}\\=\frac{1}{1}\)
4. \(-\left(\frac{12}{-13}\right)-\left(\frac{11}{6}\right)\\= \frac{12}{13}-\frac{11}{6}\\=\frac{72}{78}-\frac{143}{78}\\=\frac{72-143}{78}\\=\frac{-71}{78}\)
5. \(+\left(\frac{-8}{3}\right)+\left(\frac{-9}{-4}\right)\\= \frac{-8}{3}+\frac{9}{4}\\=\frac{-32}{12}+\frac{27}{12}\\=\frac{-32+27}{12}\\=\frac{-5}{12}\)
6. \(-\left(\frac{12}{13}\right)-\left(\frac{3}{10}\right)\\= \frac{-12}{13}-\frac{3}{10}\\=\frac{-120}{130}-\frac{39}{130}\\=\frac{-120-39}{130}\\=\frac{-159}{130}\)
7. \(-\left(\frac{11}{-5}\right)+\left(\frac{15}{14}\right)\\= \frac{11}{5}+\frac{15}{14}\\=\frac{154}{70}+\frac{75}{70}\\=\frac{154+75}{70}\\=\frac{229}{70}\)
8. \(+\left(\frac{15}{-4}\right)+\left(\frac{3}{-11}\right)\\= \frac{-15}{4}-\frac{3}{11}\\=\frac{-165}{44}-\frac{12}{44}\\=\frac{-165-12}{44}\\=\frac{-177}{44}\)
9. \(+\left(\frac{-12}{-5}\right)+\left(\frac{-9}{5}\right)\\= \frac{12}{5}-\frac{9}{5}\\=\frac{12-9}{5}\\=\frac{3}{5}\)
10. \(+\left(\frac{14}{3}\right)+\left(\frac{2}{-9}\right)\\= \frac{14}{3}-\frac{2}{9}\\=\frac{42}{9}-\frac{2}{9}\\=\frac{42-2}{9}\\=\frac{40}{9}\)
11. \(+\left(\frac{5}{-11}\right)-\left(\frac{-3}{13}\right)\\= \frac{-5}{11}+\frac{3}{13}\\=\frac{-65}{143}+\frac{33}{143}\\=\frac{-65+33}{143}\\=\frac{-32}{143}\)
12. \(+\left(\frac{7}{5}\right)-\left(\frac{6}{-5}\right)\\= \frac{7}{5}+\frac{6}{5}\\=\frac{7+6}{5}\\=\frac{13}{5}\)