Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{-4}\right) -\left(\frac{3}{2}\right) -\left(\frac{8}{-12}\right)\\= \frac{3}{4}- \frac{3}{2}+\frac{8}{12}\\=\frac{3}{4}-\frac{3}{2}+\frac{2}{3}\\=\frac{9}{12}-\frac{18}{12}+\frac{8}{12}\\=\frac{9-18+8}{12}\\=\frac{-1}{12}\)
2. \(+\left(\frac{-6}{5}\right) +\left(\frac{9}{7}\right) -\left(\frac{-6}{-9}\right)\\= \frac{-6}{5}+ \frac{9}{7}-\frac{6}{9}\\=\frac{-6}{5}+\frac{9}{7}-\frac{2}{3}\\=\frac{-126}{105}+\frac{135}{105}-\frac{70}{105}\\=\frac{-126+135-70}{105}\\=\frac{-61}{105}\)
3. \(-\left(\frac{-7}{-4}\right) +\left(\frac{2}{-9}\right) -\left(\frac{2}{6}\right)\\= \frac{-7}{4}- \frac{2}{9}-\frac{2}{6}\\=\frac{-7}{4}-\frac{2}{9}-\frac{1}{3}\\=\frac{-63}{36}-\frac{8}{36}-\frac{12}{36}\\=\frac{-63-8-12}{36}\\=\frac{-83}{36}\)
4. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-2}{-4}\right) -\left(\frac{6}{6}\right)\\= \frac{6}{5}- \frac{2}{4}-\frac{6}{6}\\=\frac{6}{5}-\frac{1}{2}-\frac{1}{1}\\=\frac{12}{10}-\frac{5}{10}-\frac{10}{10}\\=\frac{12-5-10}{10}\\=\frac{-3}{10}\)
5. \(-\left(\frac{2}{3}\right) -\left(\frac{-3}{-7}\right) +\left(\frac{-8}{-4}\right)\\= \frac{-2}{3}- \frac{3}{7}+\frac{8}{4}\\=\frac{-2}{3}-\frac{3}{7}+\frac{2}{1}\\=\frac{-14}{21}-\frac{9}{21}+\frac{42}{21}\\=\frac{-14-9+42}{21}\\=\frac{19}{21}\)
6. \(-\left(\frac{3}{2}\right) +\left(\frac{9}{2}\right) -\left(\frac{5}{-10}\right)\\= \frac{-3}{2}+ \frac{9}{2}+\frac{5}{10}\\=\frac{-3}{2}+\frac{9}{2}+\frac{1}{2}\\=\frac{-3+9+1}{2}\\=\frac{7}{2}\)
7. \(-\left(\frac{-5}{6}\right) -\left(\frac{-7}{2}\right) +\left(\frac{9}{7}\right)\\= \frac{5}{6}+ \frac{7}{2}+\frac{9}{7}\\=\frac{35}{42}+\frac{147}{42}+\frac{54}{42}\\=\frac{35+147+54}{42}\\=\frac{236}{42}\\=\frac{118}{21}\)
8. \(-\left(\frac{-7}{6}\right) +\left(\frac{8}{-10}\right) -\left(\frac{-7}{-9}\right)\\= \frac{7}{6}- \frac{8}{10}-\frac{7}{9}\\=\frac{7}{6}-\frac{4}{5}-\frac{7}{9}\\=\frac{105}{90}-\frac{72}{90}-\frac{70}{90}\\=\frac{105-72-70}{90}\\=\frac{-37}{90}\)
9. \(+\left(\frac{3}{-4}\right) -\left(\frac{8}{9}\right) +\left(\frac{11}{-5}\right)\\= \frac{-3}{4}- \frac{8}{9}-\frac{11}{5}\\=\frac{-135}{180}-\frac{160}{180}-\frac{396}{180}\\=\frac{-135-160-396}{180}\\=\frac{-691}{180}\)
10. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-7}{-10}\right) -\left(\frac{-2}{4}\right)\\= \frac{6}{5}- \frac{7}{10}+\frac{2}{4}\\=\frac{6}{5}-\frac{7}{10}+\frac{1}{2}\\=\frac{12}{10}-\frac{7}{10}+\frac{5}{10}\\=\frac{12-7+5}{10}\\=\frac{10}{10}\\=\frac{1}{1}\)
11. \(-\left(\frac{3}{2}\right) +\left(\frac{-5}{-2}\right) -\left(\frac{-10}{2}\right)\\= \frac{-3}{2}+ \frac{5}{2}+\frac{10}{2}\\=\frac{-3}{2}+\frac{5}{2}+\frac{5}{1}\\=\frac{-3+5+5}{2}\\=\frac{7}{2}\)
12. \(-\left(\frac{-7}{2}\right) +\left(\frac{-6}{4}\right) +\left(\frac{-5}{-9}\right)\\= \frac{7}{2}- \frac{6}{4}+\frac{5}{9}\\=\frac{7}{2}-\frac{3}{2}+\frac{5}{9}\\=\frac{63}{18}-\frac{27}{18}+\frac{10}{18}\\=\frac{63-27+10}{18}\\=\frac{46}{18}\\=\frac{23}{9}\)