Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{2}{-3}\right)-\left(\frac{12}{-5}\right)\\= \frac{2}{3}+\frac{12}{5}\\=\frac{10}{15}+\frac{36}{15}\\=\frac{10+36}{15}\\=\frac{46}{15}\)
2. \(+\left(\frac{-12}{5}\right)+\left(\frac{-10}{3}\right)\\= \frac{-12}{5}-\frac{10}{3}\\=\frac{-36}{15}-\frac{50}{15}\\=\frac{-36-50}{15}\\=\frac{-86}{15}\)
3. \(-\left(\frac{-2}{13}\right)-\left(\frac{-12}{-11}\right)\\= \frac{2}{13}-\frac{12}{11}\\=\frac{22}{143}-\frac{156}{143}\\=\frac{22-156}{143}\\=\frac{-134}{143}\)
4. \(+\left(\frac{-5}{7}\right)+\left(\frac{-13}{10}\right)\\= \frac{-5}{7}-\frac{13}{10}\\=\frac{-50}{70}-\frac{91}{70}\\=\frac{-50-91}{70}\\=\frac{-141}{70}\)
5. \(-\left(\frac{5}{2}\right)+\left(\frac{7}{-11}\right)\\= \frac{-5}{2}-\frac{7}{11}\\=\frac{-55}{22}-\frac{14}{22}\\=\frac{-55-14}{22}\\=\frac{-69}{22}\)
6. \(+\left(\frac{3}{2}\right)+\left(\frac{10}{-3}\right)\\= \frac{3}{2}-\frac{10}{3}\\=\frac{9}{6}-\frac{20}{6}\\=\frac{9-20}{6}\\=\frac{-11}{6}\)
7. \(-\left(\frac{14}{-9}\right)+\left(\frac{-7}{9}\right)\\= \frac{14}{9}-\frac{7}{9}\\=\frac{14-7}{9}\\=\frac{7}{9}\)
8. \(+\left(\frac{-9}{2}\right)+\left(\frac{3}{-5}\right)\\= \frac{-9}{2}-\frac{3}{5}\\=\frac{-45}{10}-\frac{6}{10}\\=\frac{-45-6}{10}\\=\frac{-51}{10}\)
9. \(-\left(\frac{6}{11}\right)+\left(\frac{6}{11}\right)\\= \frac{-6}{11}+\frac{6}{11}\\=\frac{-6+6}{11}\\=\frac{0}{11}\\=\frac{0}{1}\)
10. \(+\left(\frac{-14}{-3}\right)-\left(\frac{7}{10}\right)\\= \frac{14}{3}-\frac{7}{10}\\=\frac{140}{30}-\frac{21}{30}\\=\frac{140-21}{30}\\=\frac{119}{30}\)
11. \(-\left(\frac{-6}{-13}\right)-\left(\frac{13}{9}\right)\\= \frac{-6}{13}-\frac{13}{9}\\=\frac{-54}{117}-\frac{169}{117}\\=\frac{-54-169}{117}\\=\frac{-223}{117}\)
12. \(-\left(\frac{-12}{-5}\right)-\left(\frac{8}{-9}\right)\\= \frac{-12}{5}+\frac{8}{9}\\=\frac{-108}{45}+\frac{40}{45}\\=\frac{-108+40}{45}\\=\frac{-68}{45}\)