Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{-2}\right) -\left(\frac{-10}{-2}\right) +\left(\frac{2}{12}\right)\\= \frac{3}{2}- \frac{10}{2}+\frac{2}{12}\\=\frac{3}{2}-\frac{5}{1}+\frac{1}{6}\\=\frac{9}{6}-\frac{30}{6}+\frac{1}{6}\\=\frac{9-30+1}{6}\\=\frac{-20}{6}\\=\frac{-10}{3}\)
2. \(+\left(\frac{-8}{-9}\right) +\left(\frac{-9}{-3}\right) +\left(\frac{-11}{8}\right)\\= \frac{8}{9}+ \frac{9}{3}-\frac{11}{8}\\=\frac{8}{9}+\frac{3}{1}-\frac{11}{8}\\=\frac{64}{72}+\frac{216}{72}-\frac{99}{72}\\=\frac{64+216-99}{72}\\=\frac{181}{72}\)
3. \(-\left(\frac{8}{-5}\right) -\left(\frac{8}{-6}\right) -\left(\frac{7}{12}\right)\\= \frac{8}{5}+ \frac{8}{6}-\frac{7}{12}\\=\frac{8}{5}+\frac{4}{3}-\frac{7}{12}\\=\frac{96}{60}+\frac{80}{60}-\frac{35}{60}\\=\frac{96+80-35}{60}\\=\frac{141}{60}\\=\frac{47}{20}\)
4. \(+\left(\frac{4}{-3}\right) -\left(\frac{-6}{-2}\right) +\left(\frac{11}{-8}\right)\\= \frac{-4}{3}- \frac{6}{2}-\frac{11}{8}\\=\frac{-4}{3}-\frac{3}{1}-\frac{11}{8}\\=\frac{-32}{24}-\frac{72}{24}-\frac{33}{24}\\=\frac{-32-72-33}{24}\\=\frac{-137}{24}\)
5. \(-\left(\frac{8}{3}\right) -\left(\frac{4}{4}\right) +\left(\frac{-11}{-2}\right)\\= \frac{-8}{3}- \frac{4}{4}+\frac{11}{2}\\=\frac{-8}{3}-\frac{1}{1}+\frac{11}{2}\\=\frac{-16}{6}-\frac{6}{6}+\frac{33}{6}\\=\frac{-16-6+33}{6}\\=\frac{11}{6}\)
6. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-5}{-10}\right) -\left(\frac{5}{11}\right)\\= \frac{-10}{7}+ \frac{5}{10}-\frac{5}{11}\\=\frac{-10}{7}+\frac{1}{2}-\frac{5}{11}\\=\frac{-220}{154}+\frac{77}{154}-\frac{70}{154}\\=\frac{-220+77-70}{154}\\=\frac{-213}{154}\)
7. \(-\left(\frac{9}{-7}\right) +\left(\frac{4}{-5}\right) +\left(\frac{-3}{-3}\right)\\= \frac{9}{7}- \frac{4}{5}+\frac{3}{3}\\=\frac{9}{7}-\frac{4}{5}+\frac{1}{1}\\=\frac{45}{35}-\frac{28}{35}+\frac{35}{35}\\=\frac{45-28+35}{35}\\=\frac{52}{35}\)
8. \(+\left(\frac{6}{-5}\right) +\left(\frac{-9}{5}\right) -\left(\frac{11}{6}\right)\\= \frac{-6}{5}- \frac{9}{5}-\frac{11}{6}\\=\frac{-36}{30}-\frac{54}{30}-\frac{55}{30}\\=\frac{-36-54-55}{30}\\=\frac{-145}{30}\\=\frac{-29}{6}\)
9. \(-\left(\frac{3}{-2}\right) -\left(\frac{-5}{-5}\right) +\left(\frac{5}{4}\right)\\= \frac{3}{2}- \frac{5}{5}+\frac{5}{4}\\=\frac{3}{2}-\frac{1}{1}+\frac{5}{4}\\=\frac{6}{4}-\frac{4}{4}+\frac{5}{4}\\=\frac{6-4+5}{4}\\=\frac{7}{4}\)
10. \(-\left(\frac{-4}{-3}\right) +\left(\frac{-7}{-3}\right) -\left(\frac{-5}{12}\right)\\= \frac{-4}{3}+ \frac{7}{3}+\frac{5}{12}\\=\frac{-16}{12}+\frac{28}{12}+\frac{5}{12}\\=\frac{-16+28+5}{12}\\=\frac{17}{12}\)
11. \(-\left(\frac{10}{7}\right) -\left(\frac{9}{-8}\right) +\left(\frac{2}{4}\right)\\= \frac{-10}{7}+ \frac{9}{8}+\frac{2}{4}\\=\frac{-10}{7}+\frac{9}{8}+\frac{1}{2}\\=\frac{-80}{56}+\frac{63}{56}+\frac{28}{56}\\=\frac{-80+63+28}{56}\\=\frac{11}{56}\)
12. \(-\left(\frac{9}{-5}\right) +\left(\frac{6}{-8}\right) -\left(\frac{-9}{-2}\right)\\= \frac{9}{5}- \frac{6}{8}-\frac{9}{2}\\=\frac{9}{5}-\frac{3}{4}-\frac{9}{2}\\=\frac{36}{20}-\frac{15}{20}-\frac{90}{20}\\=\frac{36-15-90}{20}\\=\frac{-69}{20}\)