Breuken haakjesregel (reeks 1)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{13}\right)+\left(\frac{13}{14}\right)\\= \frac{5}{13}+\frac{13}{14}\\=\frac{70}{182}+\frac{169}{182}\\=\frac{70+169}{182}\\=\frac{239}{182}\)
2. \(+\left(\frac{-9}{5}\right)-\left(\frac{-6}{11}\right)\\= \frac{-9}{5}+\frac{6}{11}\\=\frac{-99}{55}+\frac{30}{55}\\=\frac{-99+30}{55}\\=\frac{-69}{55}\)
3. \(-\left(\frac{3}{4}\right)+\left(\frac{-13}{6}\right)\\= \frac{-3}{4}-\frac{13}{6}\\=\frac{-9}{12}-\frac{26}{12}\\=\frac{-9-26}{12}\\=\frac{-35}{12}\)
4. \(+\left(\frac{-9}{-2}\right)+\left(\frac{-11}{7}\right)\\= \frac{9}{2}-\frac{11}{7}\\=\frac{63}{14}-\frac{22}{14}\\=\frac{63-22}{14}\\=\frac{41}{14}\)
5. \(-\left(\frac{3}{-4}\right)-\left(\frac{-9}{-2}\right)\\= \frac{3}{4}-\frac{9}{2}\\=\frac{3-9}{4}\\=\frac{-6}{4}\\=\frac{-3}{2}\)
6. \(+\left(\frac{-10}{-3}\right)-\left(\frac{-13}{2}\right)\\= \frac{10}{3}+\frac{13}{2}\\=\frac{20}{6}+\frac{39}{6}\\=\frac{20+39}{6}\\=\frac{59}{6}\)
7. \(+\left(\frac{12}{5}\right)-\left(\frac{7}{-11}\right)\\= \frac{12}{5}+\frac{7}{11}\\=\frac{132}{55}+\frac{35}{55}\\=\frac{132+35}{55}\\=\frac{167}{55}\)
8. \(+\left(\frac{-4}{-3}\right)+\left(\frac{-15}{7}\right)\\= \frac{4}{3}-\frac{15}{7}\\=\frac{28}{21}-\frac{45}{21}\\=\frac{28-45}{21}\\=\frac{-17}{21}\)
9. \(-\left(\frac{-6}{-5}\right)+\left(\frac{2}{5}\right)\\= \frac{-6}{5}+\frac{2}{5}\\=\frac{-6+2}{5}\\=\frac{-4}{5}\)
10. \(+\left(\frac{-7}{8}\right)+\left(\frac{-3}{14}\right)\\= \frac{-7}{8}-\frac{3}{14}\\=\frac{-49}{56}-\frac{12}{56}\\=\frac{-49-12}{56}\\=\frac{-61}{56}\)
11. \(+\left(\frac{5}{2}\right)+\left(\frac{-7}{-4}\right)\\= \frac{5}{2}+\frac{7}{4}\\=\frac{10}{4}+\frac{7}{4}\\=\frac{10+7}{4}\\=\frac{17}{4}\)
12. \(+\left(\frac{11}{12}\right)-\left(\frac{9}{14}\right)\\= \frac{11}{12}-\frac{9}{14}\\=\frac{77}{84}-\frac{54}{84}\\=\frac{77-54}{84}\\=\frac{23}{84}\)