Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{6}\right) -\left(\frac{6}{8}\right) -\left(\frac{9}{-4}\right)\\= \frac{5}{6}- \frac{6}{8}+\frac{9}{4}\\=\frac{5}{6}-\frac{3}{4}+\frac{9}{4}\\=\frac{10}{12}-\frac{9}{12}+\frac{27}{12}\\=\frac{10-9+27}{12}\\=\frac{28}{12}\\=\frac{7}{3}\)
2. \(-\left(\frac{-6}{-5}\right) +\left(\frac{-5}{-7}\right) -\left(\frac{-7}{10}\right)\\= \frac{-6}{5}+ \frac{5}{7}+\frac{7}{10}\\=\frac{-84}{70}+\frac{50}{70}+\frac{49}{70}\\=\frac{-84+50+49}{70}\\=\frac{15}{70}\\=\frac{3}{14}\)
3. \(+\left(\frac{3}{2}\right) -\left(\frac{-6}{9}\right) -\left(\frac{-4}{4}\right)\\= \frac{3}{2}+ \frac{6}{9}+\frac{4}{4}\\=\frac{3}{2}+\frac{2}{3}+\frac{1}{1}\\=\frac{9}{6}+\frac{4}{6}+\frac{6}{6}\\=\frac{9+4+6}{6}\\=\frac{19}{6}\)
4. \(-\left(\frac{-3}{4}\right) -\left(\frac{5}{-4}\right) +\left(\frac{-7}{9}\right)\\= \frac{3}{4}+ \frac{5}{4}-\frac{7}{9}\\=\frac{27}{36}+\frac{45}{36}-\frac{28}{36}\\=\frac{27+45-28}{36}\\=\frac{44}{36}\\=\frac{11}{9}\)
5. \(-\left(\frac{-10}{-3}\right) -\left(\frac{-4}{-5}\right) +\left(\frac{8}{9}\right)\\= \frac{-10}{3}- \frac{4}{5}+\frac{8}{9}\\=\frac{-150}{45}-\frac{36}{45}+\frac{40}{45}\\=\frac{-150-36+40}{45}\\=\frac{-146}{45}\)
6. \(+\left(\frac{9}{4}\right) -\left(\frac{-7}{-2}\right) +\left(\frac{-5}{7}\right)\\= \frac{9}{4}- \frac{7}{2}-\frac{5}{7}\\=\frac{63}{28}-\frac{98}{28}-\frac{20}{28}\\=\frac{63-98-20}{28}\\=\frac{-55}{28}\)
7. \(+\left(\frac{-6}{5}\right) -\left(\frac{-8}{5}\right) +\left(\frac{3}{-2}\right)\\= \frac{-6}{5}+ \frac{8}{5}-\frac{3}{2}\\=\frac{-12}{10}+\frac{16}{10}-\frac{15}{10}\\=\frac{-12+16-15}{10}\\=\frac{-11}{10}\)
8. \(-\left(\frac{-6}{-5}\right) -\left(\frac{4}{-2}\right) -\left(\frac{4}{5}\right)\\= \frac{-6}{5}+ \frac{4}{2}-\frac{4}{5}\\=\frac{-6}{5}+\frac{2}{1}-\frac{4}{5}\\=\frac{-6+2-4}{5}\\=\frac{-8}{5}\)
9. \(+\left(\frac{-9}{-8}\right) -\left(\frac{-5}{3}\right) -\left(\frac{12}{-2}\right)\\= \frac{9}{8}+ \frac{5}{3}+\frac{12}{2}\\=\frac{9}{8}+\frac{5}{3}+\frac{6}{1}\\=\frac{27}{24}+\frac{40}{24}+\frac{144}{24}\\=\frac{27+40+144}{24}\\=\frac{211}{24}\)
10. \(-\left(\frac{-9}{-5}\right) +\left(\frac{-9}{6}\right) -\left(\frac{-4}{6}\right)\\= \frac{-9}{5}- \frac{9}{6}+\frac{4}{6}\\=\frac{-9}{5}-\frac{3}{2}+\frac{2}{3}\\=\frac{-54}{30}-\frac{45}{30}+\frac{20}{30}\\=\frac{-54-45+20}{30}\\=\frac{-79}{30}\)
11. \(-\left(\frac{4}{-3}\right) +\left(\frac{-3}{-6}\right) +\left(\frac{-10}{-5}\right)\\= \frac{4}{3}+ \frac{3}{6}+\frac{10}{5}\\=\frac{4}{3}+\frac{1}{2}+\frac{2}{1}\\=\frac{8}{6}+\frac{3}{6}+\frac{12}{6}\\=\frac{8+3+12}{6}\\=\frac{23}{6}\)
12. \(-\left(\frac{-5}{-6}\right) -\left(\frac{5}{2}\right) -\left(\frac{5}{8}\right)\\= \frac{-5}{6}- \frac{5}{2}-\frac{5}{8}\\=\frac{-20}{24}-\frac{60}{24}-\frac{15}{24}\\=\frac{-20-60-15}{24}\\=\frac{-95}{24}\)