Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{-2}\right) +\left(\frac{-2}{3}\right) -\left(\frac{6}{-2}\right)\\= \frac{3}{2}- \frac{2}{3}+\frac{6}{2}\\=\frac{3}{2}-\frac{2}{3}+\frac{3}{1}\\=\frac{9}{6}-\frac{4}{6}+\frac{18}{6}\\=\frac{9-4+18}{6}\\=\frac{23}{6}\)
2. \(+\left(\frac{-3}{-2}\right) +\left(\frac{-4}{-7}\right) -\left(\frac{-9}{8}\right)\\= \frac{3}{2}+ \frac{4}{7}+\frac{9}{8}\\=\frac{84}{56}+\frac{32}{56}+\frac{63}{56}\\=\frac{84+32+63}{56}\\=\frac{179}{56}\)
3. \(-\left(\frac{-7}{2}\right) +\left(\frac{-2}{-2}\right) +\left(\frac{7}{-8}\right)\\= \frac{7}{2}+ \frac{2}{2}-\frac{7}{8}\\=\frac{7}{2}+\frac{1}{1}-\frac{7}{8}\\=\frac{28}{8}+\frac{8}{8}-\frac{7}{8}\\=\frac{28+8-7}{8}\\=\frac{29}{8}\)
4. \(+\left(\frac{6}{7}\right) -\left(\frac{3}{-7}\right) -\left(\frac{-3}{-5}\right)\\= \frac{6}{7}+ \frac{3}{7}-\frac{3}{5}\\=\frac{30}{35}+\frac{15}{35}-\frac{21}{35}\\=\frac{30+15-21}{35}\\=\frac{24}{35}\)
5. \(+\left(\frac{-3}{-8}\right) -\left(\frac{6}{4}\right) +\left(\frac{-5}{12}\right)\\= \frac{3}{8}- \frac{6}{4}-\frac{5}{12}\\=\frac{3}{8}-\frac{3}{2}-\frac{5}{12}\\=\frac{9}{24}-\frac{36}{24}-\frac{10}{24}\\=\frac{9-36-10}{24}\\=\frac{-37}{24}\)
6. \(+\left(\frac{-3}{-2}\right) -\left(\frac{2}{-4}\right) -\left(\frac{5}{5}\right)\\= \frac{3}{2}+ \frac{2}{4}-\frac{5}{5}\\=\frac{3}{2}+\frac{1}{2}-\frac{1}{1}\\=\frac{3+1-1}{2}\\=\frac{3}{2}\)
7. \(-\left(\frac{-6}{5}\right) -\left(\frac{2}{-10}\right) -\left(\frac{6}{8}\right)\\= \frac{6}{5}+ \frac{2}{10}-\frac{6}{8}\\=\frac{6}{5}+\frac{1}{5}-\frac{3}{4}\\=\frac{24}{20}+\frac{4}{20}-\frac{15}{20}\\=\frac{24+4-15}{20}\\=\frac{13}{20}\)
8. \(+\left(\frac{-8}{9}\right) -\left(\frac{9}{-4}\right) -\left(\frac{-6}{-6}\right)\\= \frac{-8}{9}+ \frac{9}{4}-\frac{6}{6}\\=\frac{-8}{9}+\frac{9}{4}-\frac{1}{1}\\=\frac{-32}{36}+\frac{81}{36}-\frac{36}{36}\\=\frac{-32+81-36}{36}\\=\frac{13}{36}\)
9. \(+\left(\frac{5}{7}\right) -\left(\frac{-8}{2}\right) +\left(\frac{2}{-8}\right)\\= \frac{5}{7}+ \frac{8}{2}-\frac{2}{8}\\=\frac{5}{7}+\frac{4}{1}-\frac{1}{4}\\=\frac{20}{28}+\frac{112}{28}-\frac{7}{28}\\=\frac{20+112-7}{28}\\=\frac{125}{28}\)
10. \(-\left(\frac{10}{3}\right) +\left(\frac{-7}{-8}\right) +\left(\frac{11}{7}\right)\\= \frac{-10}{3}+ \frac{7}{8}+\frac{11}{7}\\=\frac{-560}{168}+\frac{147}{168}+\frac{264}{168}\\=\frac{-560+147+264}{168}\\=\frac{-149}{168}\)
11. \(+\left(\frac{-4}{-3}\right) -\left(\frac{-2}{7}\right) +\left(\frac{10}{6}\right)\\= \frac{4}{3}+ \frac{2}{7}+\frac{10}{6}\\=\frac{4}{3}+\frac{2}{7}+\frac{5}{3}\\=\frac{28}{21}+\frac{6}{21}+\frac{35}{21}\\=\frac{28+6+35}{21}\\=\frac{69}{21}\\=\frac{23}{7}\)
12. \(-\left(\frac{7}{4}\right) -\left(\frac{-8}{-6}\right) +\left(\frac{8}{11}\right)\\= \frac{-7}{4}- \frac{8}{6}+\frac{8}{11}\\=\frac{-7}{4}-\frac{4}{3}+\frac{8}{11}\\=\frac{-231}{132}-\frac{176}{132}+\frac{96}{132}\\=\frac{-231-176+96}{132}\\=\frac{-311}{132}\)