Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{7}\right) -\left(\frac{7}{-4}\right) +\left(\frac{-8}{-3}\right)\\= \frac{-9}{7}+ \frac{7}{4}+\frac{8}{3}\\=\frac{-108}{84}+\frac{147}{84}+\frac{224}{84}\\=\frac{-108+147+224}{84}\\=\frac{263}{84}\)
2. \(+\left(\frac{-5}{7}\right) +\left(\frac{9}{-5}\right) -\left(\frac{5}{-6}\right)\\= \frac{-5}{7}- \frac{9}{5}+\frac{5}{6}\\=\frac{-150}{210}-\frac{378}{210}+\frac{175}{210}\\=\frac{-150-378+175}{210}\\=\frac{-353}{210}\)
3. \(-\left(\frac{-2}{9}\right) -\left(\frac{2}{-5}\right) -\left(\frac{-4}{12}\right)\\= \frac{2}{9}+ \frac{2}{5}+\frac{4}{12}\\=\frac{2}{9}+\frac{2}{5}+\frac{1}{3}\\=\frac{10}{45}+\frac{18}{45}+\frac{15}{45}\\=\frac{10+18+15}{45}\\=\frac{43}{45}\)
4. \(+\left(\frac{3}{-5}\right) +\left(\frac{-6}{-7}\right) -\left(\frac{7}{-4}\right)\\= \frac{-3}{5}+ \frac{6}{7}+\frac{7}{4}\\=\frac{-84}{140}+\frac{120}{140}+\frac{245}{140}\\=\frac{-84+120+245}{140}\\=\frac{281}{140}\)
5. \(-\left(\frac{-3}{-4}\right) +\left(\frac{-2}{-9}\right) +\left(\frac{-12}{2}\right)\\= \frac{-3}{4}+ \frac{2}{9}-\frac{12}{2}\\=\frac{-3}{4}+\frac{2}{9}-\frac{6}{1}\\=\frac{-27}{36}+\frac{8}{36}-\frac{216}{36}\\=\frac{-27+8-216}{36}\\=\frac{-235}{36}\)
6. \(+\left(\frac{3}{-2}\right) +\left(\frac{-7}{6}\right) -\left(\frac{-8}{-4}\right)\\= \frac{-3}{2}- \frac{7}{6}-\frac{8}{4}\\=\frac{-3}{2}-\frac{7}{6}-\frac{2}{1}\\=\frac{-9}{6}-\frac{7}{6}-\frac{12}{6}\\=\frac{-9-7-12}{6}\\=\frac{-28}{6}\\=\frac{-14}{3}\)
7. \(-\left(\frac{6}{5}\right) -\left(\frac{-4}{4}\right) -\left(\frac{-12}{2}\right)\\= \frac{-6}{5}+ \frac{4}{4}+\frac{12}{2}\\=\frac{-6}{5}+\frac{1}{1}+\frac{6}{1}\\=\frac{-6+1+6}{5}\\=\frac{1}{5}\)
8. \(-\left(\frac{9}{2}\right) +\left(\frac{-2}{-4}\right) -\left(\frac{5}{-3}\right)\\= \frac{-9}{2}+ \frac{2}{4}+\frac{5}{3}\\=\frac{-9}{2}+\frac{1}{2}+\frac{5}{3}\\=\frac{-27}{6}+\frac{3}{6}+\frac{10}{6}\\=\frac{-27+3+10}{6}\\=\frac{-14}{6}\\=\frac{-7}{3}\)
9. \(-\left(\frac{-9}{-5}\right) -\left(\frac{2}{7}\right) -\left(\frac{-7}{-5}\right)\\= \frac{-9}{5}- \frac{2}{7}-\frac{7}{5}\\=\frac{-63}{35}-\frac{10}{35}-\frac{49}{35}\\=\frac{-63-10-49}{35}\\=\frac{-122}{35}\)
10. \(-\left(\frac{-4}{9}\right) -\left(\frac{-9}{8}\right) -\left(\frac{10}{-2}\right)\\= \frac{4}{9}+ \frac{9}{8}+\frac{10}{2}\\=\frac{4}{9}+\frac{9}{8}+\frac{5}{1}\\=\frac{32}{72}+\frac{81}{72}+\frac{360}{72}\\=\frac{32+81+360}{72}\\=\frac{473}{72}\)
11. \(-\left(\frac{-10}{9}\right) +\left(\frac{10}{8}\right) -\left(\frac{-6}{-6}\right)\\= \frac{10}{9}+ \frac{10}{8}-\frac{6}{6}\\=\frac{10}{9}+\frac{5}{4}-\frac{1}{1}\\=\frac{40}{36}+\frac{45}{36}-\frac{36}{36}\\=\frac{40+45-36}{36}\\=\frac{49}{36}\)
12. \(-\left(\frac{-6}{5}\right) +\left(\frac{-2}{-9}\right) +\left(\frac{11}{5}\right)\\= \frac{6}{5}+ \frac{2}{9}+\frac{11}{5}\\=\frac{54}{45}+\frac{10}{45}+\frac{99}{45}\\=\frac{54+10+99}{45}\\=\frac{163}{45}\)