Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{2}\right) +\left(\frac{-2}{4}\right) +\left(\frac{4}{-12}\right)\\= \frac{9}{2}- \frac{2}{4}-\frac{4}{12}\\=\frac{9}{2}-\frac{1}{2}-\frac{1}{3}\\=\frac{27}{6}-\frac{3}{6}-\frac{2}{6}\\=\frac{27-3-2}{6}\\=\frac{22}{6}\\=\frac{11}{3}\)
2. \(+\left(\frac{4}{-5}\right) +\left(\frac{-3}{-5}\right) -\left(\frac{2}{-6}\right)\\= \frac{-4}{5}+ \frac{3}{5}+\frac{2}{6}\\=\frac{-4}{5}+\frac{3}{5}+\frac{1}{3}\\=\frac{-12}{15}+\frac{9}{15}+\frac{5}{15}\\=\frac{-12+9+5}{15}\\=\frac{2}{15}\)
3. \(-\left(\frac{-5}{-3}\right) -\left(\frac{2}{-6}\right) +\left(\frac{-5}{9}\right)\\= \frac{-5}{3}+ \frac{2}{6}-\frac{5}{9}\\=\frac{-5}{3}+\frac{1}{3}-\frac{5}{9}\\=\frac{-15}{9}+\frac{3}{9}-\frac{5}{9}\\=\frac{-15+3-5}{9}\\=\frac{-17}{9}\)
4. \(-\left(\frac{-4}{-9}\right) +\left(\frac{10}{-3}\right) +\left(\frac{-6}{12}\right)\\= \frac{-4}{9}- \frac{10}{3}-\frac{6}{12}\\=\frac{-4}{9}-\frac{10}{3}-\frac{1}{2}\\=\frac{-8}{18}-\frac{60}{18}-\frac{9}{18}\\=\frac{-8-60-9}{18}\\=\frac{-77}{18}\)
5. \(-\left(\frac{6}{5}\right) -\left(\frac{-6}{-6}\right) +\left(\frac{-10}{2}\right)\\= \frac{-6}{5}- \frac{6}{6}-\frac{10}{2}\\=\frac{-6}{5}-\frac{1}{1}-\frac{5}{1}\\=\frac{-6-1-5}{5}\\=\frac{-12}{5}\)
6. \(-\left(\frac{10}{-7}\right) -\left(\frac{4}{-10}\right) +\left(\frac{-8}{-2}\right)\\= \frac{10}{7}+ \frac{4}{10}+\frac{8}{2}\\=\frac{10}{7}+\frac{2}{5}+\frac{4}{1}\\=\frac{50}{35}+\frac{14}{35}+\frac{140}{35}\\=\frac{50+14+140}{35}\\=\frac{204}{35}\)
7. \(-\left(\frac{-8}{3}\right) -\left(\frac{-3}{5}\right) +\left(\frac{2}{8}\right)\\= \frac{8}{3}+ \frac{3}{5}+\frac{2}{8}\\=\frac{8}{3}+\frac{3}{5}+\frac{1}{4}\\=\frac{160}{60}+\frac{36}{60}+\frac{15}{60}\\=\frac{160+36+15}{60}\\=\frac{211}{60}\)
8. \(+\left(\frac{-9}{8}\right) +\left(\frac{-7}{-6}\right) +\left(\frac{-11}{6}\right)\\= \frac{-9}{8}+ \frac{7}{6}-\frac{11}{6}\\=\frac{-27}{24}+\frac{28}{24}-\frac{44}{24}\\=\frac{-27+28-44}{24}\\=\frac{-43}{24}\)
9. \(+\left(\frac{7}{8}\right) -\left(\frac{-8}{4}\right) -\left(\frac{4}{11}\right)\\= \frac{7}{8}+ \frac{8}{4}-\frac{4}{11}\\=\frac{7}{8}+\frac{2}{1}-\frac{4}{11}\\=\frac{77}{88}+\frac{176}{88}-\frac{32}{88}\\=\frac{77+176-32}{88}\\=\frac{221}{88}\)
10. \(-\left(\frac{6}{7}\right) -\left(\frac{-3}{-9}\right) +\left(\frac{-6}{-11}\right)\\= \frac{-6}{7}- \frac{3}{9}+\frac{6}{11}\\=\frac{-6}{7}-\frac{1}{3}+\frac{6}{11}\\=\frac{-198}{231}-\frac{77}{231}+\frac{126}{231}\\=\frac{-198-77+126}{231}\\=\frac{-149}{231}\)
11. \(-\left(\frac{-4}{-7}\right) -\left(\frac{2}{8}\right) -\left(\frac{9}{-4}\right)\\= \frac{-4}{7}- \frac{2}{8}+\frac{9}{4}\\=\frac{-4}{7}-\frac{1}{4}+\frac{9}{4}\\=\frac{-16}{28}-\frac{7}{28}+\frac{63}{28}\\=\frac{-16-7+63}{28}\\=\frac{40}{28}\\=\frac{10}{7}\)
12. \(+\left(\frac{-8}{9}\right) -\left(\frac{5}{-7}\right) +\left(\frac{-6}{-11}\right)\\= \frac{-8}{9}+ \frac{5}{7}+\frac{6}{11}\\=\frac{-616}{693}+\frac{495}{693}+\frac{378}{693}\\=\frac{-616+495+378}{693}\\=\frac{257}{693}\)