Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{8}\right) -\left(\frac{7}{-8}\right) +\left(\frac{-3}{9}\right)\\= \frac{-7}{8}+ \frac{7}{8}-\frac{3}{9}\\=\frac{-7}{8}+\frac{7}{8}-\frac{1}{3}\\=\frac{-21}{24}+\frac{21}{24}-\frac{8}{24}\\=\frac{-21+21-8}{24}\\=\frac{-8}{24}\\=\frac{-1}{3}\)
2. \(-\left(\frac{7}{2}\right) -\left(\frac{6}{-9}\right) +\left(\frac{-3}{-2}\right)\\= \frac{-7}{2}+ \frac{6}{9}+\frac{3}{2}\\=\frac{-7}{2}+\frac{2}{3}+\frac{3}{2}\\=\frac{-21}{6}+\frac{4}{6}+\frac{9}{6}\\=\frac{-21+4+9}{6}\\=\frac{-8}{6}\\=\frac{-4}{3}\)
3. \(+\left(\frac{9}{2}\right) +\left(\frac{4}{10}\right) +\left(\frac{-7}{-2}\right)\\= \frac{9}{2}+ \frac{4}{10}+\frac{7}{2}\\=\frac{9}{2}+\frac{2}{5}+\frac{7}{2}\\=\frac{45}{10}+\frac{4}{10}+\frac{35}{10}\\=\frac{45+4+35}{10}\\=\frac{84}{10}\\=\frac{42}{5}\)
4. \(+\left(\frac{-3}{-4}\right) -\left(\frac{7}{-9}\right) -\left(\frac{5}{10}\right)\\= \frac{3}{4}+ \frac{7}{9}-\frac{5}{10}\\=\frac{3}{4}+\frac{7}{9}-\frac{1}{2}\\=\frac{27}{36}+\frac{28}{36}-\frac{18}{36}\\=\frac{27+28-18}{36}\\=\frac{37}{36}\)
5. \(-\left(\frac{3}{-2}\right) +\left(\frac{2}{-4}\right) -\left(\frac{-9}{-4}\right)\\= \frac{3}{2}- \frac{2}{4}-\frac{9}{4}\\=\frac{3}{2}-\frac{1}{2}-\frac{9}{4}\\=\frac{6}{4}-\frac{2}{4}-\frac{9}{4}\\=\frac{6-2-9}{4}\\=\frac{-5}{4}\)
6. \(-\left(\frac{-8}{7}\right) +\left(\frac{-5}{-10}\right) +\left(\frac{-2}{-4}\right)\\= \frac{8}{7}+ \frac{5}{10}+\frac{2}{4}\\=\frac{8}{7}+\frac{1}{2}+\frac{1}{2}\\=\frac{16}{14}+\frac{7}{14}+\frac{7}{14}\\=\frac{16+7+7}{14}\\=\frac{30}{14}\\=\frac{15}{7}\)
7. \(-\left(\frac{10}{-9}\right) +\left(\frac{2}{-10}\right) +\left(\frac{11}{4}\right)\\= \frac{10}{9}- \frac{2}{10}+\frac{11}{4}\\=\frac{10}{9}-\frac{1}{5}+\frac{11}{4}\\=\frac{200}{180}-\frac{36}{180}+\frac{495}{180}\\=\frac{200-36+495}{180}\\=\frac{659}{180}\)
8. \(-\left(\frac{9}{2}\right) +\left(\frac{-10}{7}\right) +\left(\frac{6}{-11}\right)\\= \frac{-9}{2}- \frac{10}{7}-\frac{6}{11}\\=\frac{-693}{154}-\frac{220}{154}-\frac{84}{154}\\=\frac{-693-220-84}{154}\\=\frac{-997}{154}\)
9. \(-\left(\frac{-8}{3}\right) -\left(\frac{6}{-4}\right) -\left(\frac{-4}{12}\right)\\= \frac{8}{3}+ \frac{6}{4}+\frac{4}{12}\\=\frac{8}{3}+\frac{3}{2}+\frac{1}{3}\\=\frac{16}{6}+\frac{9}{6}+\frac{2}{6}\\=\frac{16+9+2}{6}\\=\frac{27}{6}\\=\frac{9}{2}\)
10. \(-\left(\frac{9}{-7}\right) -\left(\frac{-8}{7}\right) -\left(\frac{3}{-11}\right)\\= \frac{9}{7}+ \frac{8}{7}+\frac{3}{11}\\=\frac{99}{77}+\frac{88}{77}+\frac{21}{77}\\=\frac{99+88+21}{77}\\=\frac{208}{77}\)
11. \(+\left(\frac{9}{2}\right) -\left(\frac{-10}{8}\right) -\left(\frac{-2}{-7}\right)\\= \frac{9}{2}+ \frac{10}{8}-\frac{2}{7}\\=\frac{9}{2}+\frac{5}{4}-\frac{2}{7}\\=\frac{126}{28}+\frac{35}{28}-\frac{8}{28}\\=\frac{126+35-8}{28}\\=\frac{153}{28}\)
12. \(-\left(\frac{-4}{3}\right) -\left(\frac{7}{-6}\right) -\left(\frac{-9}{-5}\right)\\= \frac{4}{3}+ \frac{7}{6}-\frac{9}{5}\\=\frac{40}{30}+\frac{35}{30}-\frac{54}{30}\\=\frac{40+35-54}{30}\\=\frac{21}{30}\\=\frac{7}{10}\)