Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{7}\right) +\left(\frac{-8}{5}\right) -\left(\frac{4}{-9}\right)\\= \frac{4}{7}- \frac{8}{5}+\frac{4}{9}\\=\frac{180}{315}-\frac{504}{315}+\frac{140}{315}\\=\frac{180-504+140}{315}\\=\frac{-184}{315}\)
2. \(+\left(\frac{10}{-7}\right) +\left(\frac{-6}{6}\right) +\left(\frac{-2}{8}\right)\\= \frac{-10}{7}- \frac{6}{6}-\frac{2}{8}\\=\frac{-10}{7}-\frac{1}{1}-\frac{1}{4}\\=\frac{-40}{28}-\frac{28}{28}-\frac{7}{28}\\=\frac{-40-28-7}{28}\\=\frac{-75}{28}\)
3. \(+\left(\frac{-2}{9}\right) -\left(\frac{9}{7}\right) -\left(\frac{4}{2}\right)\\= \frac{-2}{9}- \frac{9}{7}-\frac{4}{2}\\=\frac{-2}{9}-\frac{9}{7}-\frac{2}{1}\\=\frac{-14}{63}-\frac{81}{63}-\frac{126}{63}\\=\frac{-14-81-126}{63}\\=\frac{-221}{63}\)
4. \(-\left(\frac{-6}{5}\right) +\left(\frac{2}{-2}\right) -\left(\frac{-12}{-3}\right)\\= \frac{6}{5}- \frac{2}{2}-\frac{12}{3}\\=\frac{6}{5}-\frac{1}{1}-\frac{4}{1}\\=\frac{6-1-4}{5}\\=\frac{1}{5}\)
5. \(+\left(\frac{-2}{-9}\right) +\left(\frac{-9}{2}\right) -\left(\frac{10}{6}\right)\\= \frac{2}{9}- \frac{9}{2}-\frac{10}{6}\\=\frac{2}{9}-\frac{9}{2}-\frac{5}{3}\\=\frac{4}{18}-\frac{81}{18}-\frac{30}{18}\\=\frac{4-81-30}{18}\\=\frac{-107}{18}\)
6. \(-\left(\frac{-8}{3}\right) +\left(\frac{9}{-3}\right) -\left(\frac{-6}{3}\right)\\= \frac{8}{3}- \frac{9}{3}+\frac{6}{3}\\=\frac{8}{3}-\frac{3}{1}+\frac{2}{1}\\=\frac{8-3+2}{3}\\=\frac{7}{3}\)
7. \(-\left(\frac{-7}{-5}\right) +\left(\frac{-9}{6}\right) -\left(\frac{6}{-9}\right)\\= \frac{-7}{5}- \frac{9}{6}+\frac{6}{9}\\=\frac{-7}{5}-\frac{3}{2}+\frac{2}{3}\\=\frac{-42}{30}-\frac{45}{30}+\frac{20}{30}\\=\frac{-42-45+20}{30}\\=\frac{-67}{30}\)
8. \(-\left(\frac{-10}{9}\right) +\left(\frac{-6}{9}\right) +\left(\frac{2}{8}\right)\\= \frac{10}{9}- \frac{6}{9}+\frac{2}{8}\\=\frac{10}{9}-\frac{2}{3}+\frac{1}{4}\\=\frac{40}{36}-\frac{24}{36}+\frac{9}{36}\\=\frac{40-24+9}{36}\\=\frac{25}{36}\)
9. \(+\left(\frac{6}{5}\right) -\left(\frac{-3}{7}\right) -\left(\frac{-6}{6}\right)\\= \frac{6}{5}+ \frac{3}{7}+\frac{6}{6}\\=\frac{6}{5}+\frac{3}{7}+\frac{1}{1}\\=\frac{42}{35}+\frac{15}{35}+\frac{35}{35}\\=\frac{42+15+35}{35}\\=\frac{92}{35}\)
10. \(-\left(\frac{6}{5}\right) +\left(\frac{4}{-5}\right) +\left(\frac{-8}{-9}\right)\\= \frac{-6}{5}- \frac{4}{5}+\frac{8}{9}\\=\frac{-54}{45}-\frac{36}{45}+\frac{40}{45}\\=\frac{-54-36+40}{45}\\=\frac{-50}{45}\\=\frac{-10}{9}\)
11. \(-\left(\frac{-3}{7}\right) +\left(\frac{-3}{-4}\right) +\left(\frac{-10}{12}\right)\\= \frac{3}{7}+ \frac{3}{4}-\frac{10}{12}\\=\frac{3}{7}+\frac{3}{4}-\frac{5}{6}\\=\frac{36}{84}+\frac{63}{84}-\frac{70}{84}\\=\frac{36+63-70}{84}\\=\frac{29}{84}\)
12. \(-\left(\frac{9}{-7}\right) -\left(\frac{-5}{5}\right) -\left(\frac{8}{-12}\right)\\= \frac{9}{7}+ \frac{5}{5}+\frac{8}{12}\\=\frac{9}{7}+\frac{1}{1}+\frac{2}{3}\\=\frac{27}{21}+\frac{21}{21}+\frac{14}{21}\\=\frac{27+21+14}{21}\\=\frac{62}{21}\)