Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{15}{13}\right)+\left(\frac{7}{5}\right)\\= \frac{-15}{13}+\frac{7}{5}\\=\frac{-75}{65}+\frac{91}{65}\\=\frac{-75+91}{65}\\=\frac{16}{65}\)
2. \(-\left(\frac{-12}{-5}\right)+\left(\frac{-6}{11}\right)\\= \frac{-12}{5}-\frac{6}{11}\\=\frac{-132}{55}-\frac{30}{55}\\=\frac{-132-30}{55}\\=\frac{-162}{55}\)
3. \(+\left(\frac{-8}{7}\right)+\left(\frac{-2}{-3}\right)\\= \frac{-8}{7}+\frac{2}{3}\\=\frac{-24}{21}+\frac{14}{21}\\=\frac{-24+14}{21}\\=\frac{-10}{21}\)
4. \(+\left(\frac{-12}{5}\right)-\left(\frac{12}{11}\right)\\= \frac{-12}{5}-\frac{12}{11}\\=\frac{-132}{55}-\frac{60}{55}\\=\frac{-132-60}{55}\\=\frac{-192}{55}\)
5. \(+\left(\frac{3}{-2}\right)-\left(\frac{-6}{-11}\right)\\= \frac{-3}{2}-\frac{6}{11}\\=\frac{-33}{22}-\frac{12}{22}\\=\frac{-33-12}{22}\\=\frac{-45}{22}\)
6. \(-\left(\frac{15}{13}\right)-\left(\frac{6}{11}\right)\\= \frac{-15}{13}-\frac{6}{11}\\=\frac{-165}{143}-\frac{78}{143}\\=\frac{-165-78}{143}\\=\frac{-243}{143}\)
7. \(+\left(\frac{14}{3}\right)+\left(\frac{-15}{8}\right)\\= \frac{14}{3}-\frac{15}{8}\\=\frac{112}{24}-\frac{45}{24}\\=\frac{112-45}{24}\\=\frac{67}{24}\)
8. \(-\left(\frac{6}{11}\right)-\left(\frac{3}{13}\right)\\= \frac{-6}{11}-\frac{3}{13}\\=\frac{-78}{143}-\frac{33}{143}\\=\frac{-78-33}{143}\\=\frac{-111}{143}\)
9. \(+\left(\frac{-3}{13}\right)-\left(\frac{-3}{10}\right)\\= \frac{-3}{13}+\frac{3}{10}\\=\frac{-30}{130}+\frac{39}{130}\\=\frac{-30+39}{130}\\=\frac{9}{130}\)
10. \(+\left(\frac{-5}{4}\right)+\left(\frac{12}{7}\right)\\= \frac{-5}{4}+\frac{12}{7}\\=\frac{-35}{28}+\frac{48}{28}\\=\frac{-35+48}{28}\\=\frac{13}{28}\)
11. \(+\left(\frac{5}{7}\right)+\left(\frac{-8}{7}\right)\\= \frac{5}{7}-\frac{8}{7}\\=\frac{5-8}{7}\\=\frac{-3}{7}\)
12. \(-\left(\frac{-7}{-3}\right)-\left(\frac{12}{-5}\right)\\= \frac{-7}{3}+\frac{12}{5}\\=\frac{-35}{15}+\frac{36}{15}\\=\frac{-35+36}{15}\\=\frac{1}{15}\)