Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{-7}\right) -\left(\frac{8}{-6}\right) -\left(\frac{2}{-12}\right)\\= \frac{-10}{7}+ \frac{8}{6}+\frac{2}{12}\\=\frac{-10}{7}+\frac{4}{3}+\frac{1}{6}\\=\frac{-60}{42}+\frac{56}{42}+\frac{7}{42}\\=\frac{-60+56+7}{42}\\=\frac{3}{42}\\=\frac{1}{14}\)
2. \(+\left(\frac{-6}{-7}\right) +\left(\frac{6}{5}\right) -\left(\frac{6}{8}\right)\\= \frac{6}{7}+ \frac{6}{5}-\frac{6}{8}\\=\frac{6}{7}+\frac{6}{5}-\frac{3}{4}\\=\frac{120}{140}+\frac{168}{140}-\frac{105}{140}\\=\frac{120+168-105}{140}\\=\frac{183}{140}\)
3. \(-\left(\frac{4}{5}\right) -\left(\frac{-8}{7}\right) +\left(\frac{3}{3}\right)\\= \frac{-4}{5}+ \frac{8}{7}+\frac{3}{3}\\=\frac{-4}{5}+\frac{8}{7}+\frac{1}{1}\\=\frac{-28}{35}+\frac{40}{35}+\frac{35}{35}\\=\frac{-28+40+35}{35}\\=\frac{47}{35}\)
4. \(-\left(\frac{8}{3}\right) -\left(\frac{10}{-4}\right) -\left(\frac{-10}{12}\right)\\= \frac{-8}{3}+ \frac{10}{4}+\frac{10}{12}\\=\frac{-8}{3}+\frac{5}{2}+\frac{5}{6}\\=\frac{-16}{6}+\frac{15}{6}+\frac{5}{6}\\=\frac{-16+15+5}{6}\\=\frac{4}{6}\\=\frac{2}{3}\)
5. \(+\left(\frac{7}{9}\right) -\left(\frac{-6}{-7}\right) -\left(\frac{5}{2}\right)\\= \frac{7}{9}- \frac{6}{7}-\frac{5}{2}\\=\frac{98}{126}-\frac{108}{126}-\frac{315}{126}\\=\frac{98-108-315}{126}\\=\frac{-325}{126}\)
6. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-10}{-5}\right) +\left(\frac{-3}{-3}\right)\\= \frac{-10}{7}+ \frac{10}{5}+\frac{3}{3}\\=\frac{-10}{7}+\frac{2}{1}+\frac{1}{1}\\=\frac{-10+2+1}{7}\\=\frac{-7}{7}\\=\frac{-1}{1}\)
7. \(-\left(\frac{4}{-3}\right) -\left(\frac{-10}{7}\right) +\left(\frac{-3}{-5}\right)\\= \frac{4}{3}+ \frac{10}{7}+\frac{3}{5}\\=\frac{140}{105}+\frac{150}{105}+\frac{63}{105}\\=\frac{140+150+63}{105}\\=\frac{353}{105}\)
8. \(+\left(\frac{2}{-5}\right) -\left(\frac{7}{-9}\right) +\left(\frac{9}{5}\right)\\= \frac{-2}{5}+ \frac{7}{9}+\frac{9}{5}\\=\frac{-18}{45}+\frac{35}{45}+\frac{81}{45}\\=\frac{-18+35+81}{45}\\=\frac{98}{45}\)
9. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-6}{-6}\right) +\left(\frac{11}{4}\right)\\= \frac{-10}{7}+ \frac{6}{6}+\frac{11}{4}\\=\frac{-10}{7}+\frac{1}{1}+\frac{11}{4}\\=\frac{-40}{28}+\frac{28}{28}+\frac{77}{28}\\=\frac{-40+28+77}{28}\\=\frac{65}{28}\)
10. \(+\left(\frac{7}{-5}\right) -\left(\frac{-4}{-4}\right) +\left(\frac{-5}{-12}\right)\\= \frac{-7}{5}- \frac{4}{4}+\frac{5}{12}\\=\frac{-7}{5}-\frac{1}{1}+\frac{5}{12}\\=\frac{-84}{60}-\frac{60}{60}+\frac{25}{60}\\=\frac{-84-60+25}{60}\\=\frac{-119}{60}\)
11. \(+\left(\frac{5}{-2}\right) +\left(\frac{-7}{6}\right) -\left(\frac{-9}{6}\right)\\= \frac{-5}{2}- \frac{7}{6}+\frac{9}{6}\\=\frac{-5}{2}-\frac{7}{6}+\frac{3}{2}\\=\frac{-15}{6}-\frac{7}{6}+\frac{9}{6}\\=\frac{-15-7+9}{6}\\=\frac{-13}{6}\)
12. \(-\left(\frac{5}{-3}\right) +\left(\frac{-3}{3}\right) +\left(\frac{5}{-7}\right)\\= \frac{5}{3}- \frac{3}{3}-\frac{5}{7}\\=\frac{5}{3}-\frac{1}{1}-\frac{5}{7}\\=\frac{35}{21}-\frac{21}{21}-\frac{15}{21}\\=\frac{35-21-15}{21}\\=\frac{-1}{21}\)