Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{6}{5}\right) +\left(\frac{-7}{-6}\right) +\left(\frac{-5}{2}\right)\\= \frac{-6}{5}+ \frac{7}{6}-\frac{5}{2}\\=\frac{-36}{30}+\frac{35}{30}-\frac{75}{30}\\=\frac{-36+35-75}{30}\\=\frac{-76}{30}\\=\frac{-38}{15}\)
2. \(+\left(\frac{-4}{-7}\right) -\left(\frac{-7}{8}\right) +\left(\frac{8}{7}\right)\\= \frac{4}{7}+ \frac{7}{8}+\frac{8}{7}\\=\frac{32}{56}+\frac{49}{56}+\frac{64}{56}\\=\frac{32+49+64}{56}\\=\frac{145}{56}\)
3. \(+\left(\frac{-2}{7}\right) -\left(\frac{-7}{-5}\right) +\left(\frac{-12}{12}\right)\\= \frac{-2}{7}- \frac{7}{5}-\frac{12}{12}\\=\frac{-2}{7}-\frac{7}{5}-\frac{1}{1}\\=\frac{-10}{35}-\frac{49}{35}-\frac{35}{35}\\=\frac{-10-49-35}{35}\\=\frac{-94}{35}\)
4. \(+\left(\frac{-9}{7}\right) -\left(\frac{-10}{-2}\right) -\left(\frac{-10}{-12}\right)\\= \frac{-9}{7}- \frac{10}{2}-\frac{10}{12}\\=\frac{-9}{7}-\frac{5}{1}-\frac{5}{6}\\=\frac{-54}{42}-\frac{210}{42}-\frac{35}{42}\\=\frac{-54-210-35}{42}\\=\frac{-299}{42}\)
5. \(-\left(\frac{6}{5}\right) +\left(\frac{2}{7}\right) +\left(\frac{-2}{12}\right)\\= \frac{-6}{5}+ \frac{2}{7}-\frac{2}{12}\\=\frac{-6}{5}+\frac{2}{7}-\frac{1}{6}\\=\frac{-252}{210}+\frac{60}{210}-\frac{35}{210}\\=\frac{-252+60-35}{210}\\=\frac{-227}{210}\)
6. \(-\left(\frac{8}{-3}\right) -\left(\frac{2}{4}\right) -\left(\frac{-11}{-10}\right)\\= \frac{8}{3}- \frac{2}{4}-\frac{11}{10}\\=\frac{8}{3}-\frac{1}{2}-\frac{11}{10}\\=\frac{80}{30}-\frac{15}{30}-\frac{33}{30}\\=\frac{80-15-33}{30}\\=\frac{32}{30}\\=\frac{16}{15}\)
7. \(+\left(\frac{-5}{6}\right) +\left(\frac{3}{2}\right) +\left(\frac{-5}{-8}\right)\\= \frac{-5}{6}+ \frac{3}{2}+\frac{5}{8}\\=\frac{-20}{24}+\frac{36}{24}+\frac{15}{24}\\=\frac{-20+36+15}{24}\\=\frac{31}{24}\)
8. \(-\left(\frac{-5}{9}\right) -\left(\frac{-6}{10}\right) -\left(\frac{-8}{7}\right)\\= \frac{5}{9}+ \frac{6}{10}+\frac{8}{7}\\=\frac{5}{9}+\frac{3}{5}+\frac{8}{7}\\=\frac{175}{315}+\frac{189}{315}+\frac{360}{315}\\=\frac{175+189+360}{315}\\=\frac{724}{315}\)
9. \(-\left(\frac{-4}{-5}\right) +\left(\frac{-6}{8}\right) -\left(\frac{-11}{7}\right)\\= \frac{-4}{5}- \frac{6}{8}+\frac{11}{7}\\=\frac{-4}{5}-\frac{3}{4}+\frac{11}{7}\\=\frac{-112}{140}-\frac{105}{140}+\frac{220}{140}\\=\frac{-112-105+220}{140}\\=\frac{3}{140}\)
10. \(-\left(\frac{-9}{-8}\right) +\left(\frac{3}{3}\right) +\left(\frac{3}{-8}\right)\\= \frac{-9}{8}+ \frac{3}{3}-\frac{3}{8}\\=\frac{-9}{8}+\frac{1}{1}-\frac{3}{8}\\=\frac{-9+1-3}{8}\\=\frac{-11}{8}\)
11. \(+\left(\frac{2}{-5}\right) +\left(\frac{-9}{3}\right) -\left(\frac{-3}{8}\right)\\= \frac{-2}{5}- \frac{9}{3}+\frac{3}{8}\\=\frac{-2}{5}-\frac{3}{1}+\frac{3}{8}\\=\frac{-16}{40}-\frac{120}{40}+\frac{15}{40}\\=\frac{-16-120+15}{40}\\=\frac{-121}{40}\)
12. \(+\left(\frac{7}{2}\right) +\left(\frac{3}{-7}\right) -\left(\frac{12}{12}\right)\\= \frac{7}{2}- \frac{3}{7}-\frac{12}{12}\\=\frac{7}{2}-\frac{3}{7}-\frac{1}{1}\\=\frac{49}{14}-\frac{6}{14}-\frac{14}{14}\\=\frac{49-6-14}{14}\\=\frac{29}{14}\)