Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{-7}\right) -\left(\frac{-5}{7}\right) +\left(\frac{-5}{-8}\right)\\= \frac{-2}{7}+ \frac{5}{7}+\frac{5}{8}\\=\frac{-16}{56}+\frac{40}{56}+\frac{35}{56}\\=\frac{-16+40+35}{56}\\=\frac{59}{56}\)
2. \(-\left(\frac{7}{-8}\right) +\left(\frac{7}{8}\right) +\left(\frac{11}{10}\right)\\= \frac{7}{8}+ \frac{7}{8}+\frac{11}{10}\\=\frac{35}{40}+\frac{35}{40}+\frac{44}{40}\\=\frac{35+35+44}{40}\\=\frac{114}{40}\\=\frac{57}{20}\)
3. \(+\left(\frac{7}{-8}\right) +\left(\frac{-6}{4}\right) -\left(\frac{12}{-6}\right)\\= \frac{-7}{8}- \frac{6}{4}+\frac{12}{6}\\=\frac{-7}{8}-\frac{3}{2}+\frac{2}{1}\\=\frac{-7-3+2}{8}\\=\frac{-8}{8}\\=\frac{-1}{1}\)
4. \(-\left(\frac{-2}{-5}\right) +\left(\frac{9}{-6}\right) +\left(\frac{-12}{2}\right)\\= \frac{-2}{5}- \frac{9}{6}-\frac{12}{2}\\=\frac{-2}{5}-\frac{3}{2}-\frac{6}{1}\\=\frac{-4}{10}-\frac{15}{10}-\frac{60}{10}\\=\frac{-4-15-60}{10}\\=\frac{-79}{10}\)
5. \(+\left(\frac{-3}{-4}\right) +\left(\frac{-4}{-10}\right) +\left(\frac{-3}{-6}\right)\\= \frac{3}{4}+ \frac{4}{10}+\frac{3}{6}\\=\frac{3}{4}+\frac{2}{5}+\frac{1}{2}\\=\frac{15}{20}+\frac{8}{20}+\frac{10}{20}\\=\frac{15+8+10}{20}\\=\frac{33}{20}\)
6. \(-\left(\frac{-6}{-5}\right) +\left(\frac{2}{-2}\right) +\left(\frac{12}{-2}\right)\\= \frac{-6}{5}- \frac{2}{2}-\frac{12}{2}\\=\frac{-6}{5}-\frac{1}{1}-\frac{6}{1}\\=\frac{-6-1-6}{5}\\=\frac{-13}{5}\)
7. \(+\left(\frac{7}{-9}\right) +\left(\frac{-2}{-7}\right) +\left(\frac{11}{6}\right)\\= \frac{-7}{9}+ \frac{2}{7}+\frac{11}{6}\\=\frac{-98}{126}+\frac{36}{126}+\frac{231}{126}\\=\frac{-98+36+231}{126}\\=\frac{169}{126}\)
8. \(+\left(\frac{3}{-4}\right) +\left(\frac{5}{6}\right) +\left(\frac{-5}{-4}\right)\\= \frac{-3}{4}+ \frac{5}{6}+\frac{5}{4}\\=\frac{-9}{12}+\frac{10}{12}+\frac{15}{12}\\=\frac{-9+10+15}{12}\\=\frac{16}{12}\\=\frac{4}{3}\)
9. \(+\left(\frac{-5}{4}\right) +\left(\frac{-8}{2}\right) +\left(\frac{7}{9}\right)\\= \frac{-5}{4}- \frac{8}{2}+\frac{7}{9}\\=\frac{-5}{4}-\frac{4}{1}+\frac{7}{9}\\=\frac{-45}{36}-\frac{144}{36}+\frac{28}{36}\\=\frac{-45-144+28}{36}\\=\frac{-161}{36}\)
10. \(+\left(\frac{-6}{5}\right) -\left(\frac{2}{7}\right) +\left(\frac{2}{12}\right)\\= \frac{-6}{5}- \frac{2}{7}+\frac{2}{12}\\=\frac{-6}{5}-\frac{2}{7}+\frac{1}{6}\\=\frac{-252}{210}-\frac{60}{210}+\frac{35}{210}\\=\frac{-252-60+35}{210}\\=\frac{-277}{210}\)
11. \(-\left(\frac{6}{-5}\right) +\left(\frac{9}{-10}\right) -\left(\frac{-7}{2}\right)\\= \frac{6}{5}- \frac{9}{10}+\frac{7}{2}\\=\frac{12}{10}-\frac{9}{10}+\frac{35}{10}\\=\frac{12-9+35}{10}\\=\frac{38}{10}\\=\frac{19}{5}\)
12. \(-\left(\frac{4}{-9}\right) -\left(\frac{-9}{-4}\right) -\left(\frac{3}{12}\right)\\= \frac{4}{9}- \frac{9}{4}-\frac{3}{12}\\=\frac{4}{9}-\frac{9}{4}-\frac{1}{4}\\=\frac{16}{36}-\frac{81}{36}-\frac{9}{36}\\=\frac{16-81-9}{36}\\=\frac{-74}{36}\\=\frac{-37}{18}\)