Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{6}{7}\right) -\left(\frac{3}{3}\right) -\left(\frac{9}{12}\right)\\= \frac{6}{7}- \frac{3}{3}-\frac{9}{12}\\=\frac{6}{7}-\frac{1}{1}-\frac{3}{4}\\=\frac{24}{28}-\frac{28}{28}-\frac{21}{28}\\=\frac{24-28-21}{28}\\=\frac{-25}{28}\)
2. \(+\left(\frac{4}{5}\right) +\left(\frac{3}{2}\right) +\left(\frac{5}{10}\right)\\= \frac{4}{5}+ \frac{3}{2}+\frac{5}{10}\\=\frac{4}{5}+\frac{3}{2}+\frac{1}{2}\\=\frac{8}{10}+\frac{15}{10}+\frac{5}{10}\\=\frac{8+15+5}{10}\\=\frac{28}{10}\\=\frac{14}{5}\)
3. \(-\left(\frac{-10}{-7}\right) -\left(\frac{-7}{8}\right) -\left(\frac{-8}{12}\right)\\= \frac{-10}{7}+ \frac{7}{8}+\frac{8}{12}\\=\frac{-10}{7}+\frac{7}{8}+\frac{2}{3}\\=\frac{-240}{168}+\frac{147}{168}+\frac{112}{168}\\=\frac{-240+147+112}{168}\\=\frac{19}{168}\)
4. \(-\left(\frac{6}{5}\right) +\left(\frac{-8}{-2}\right) -\left(\frac{2}{3}\right)\\= \frac{-6}{5}+ \frac{8}{2}-\frac{2}{3}\\=\frac{-6}{5}+\frac{4}{1}-\frac{2}{3}\\=\frac{-18}{15}+\frac{60}{15}-\frac{10}{15}\\=\frac{-18+60-10}{15}\\=\frac{32}{15}\)
5. \(+\left(\frac{8}{-7}\right) -\left(\frac{8}{-2}\right) +\left(\frac{-5}{6}\right)\\= \frac{-8}{7}+ \frac{8}{2}-\frac{5}{6}\\=\frac{-8}{7}+\frac{4}{1}-\frac{5}{6}\\=\frac{-48}{42}+\frac{168}{42}-\frac{35}{42}\\=\frac{-48+168-35}{42}\\=\frac{85}{42}\)
6. \(-\left(\frac{-9}{4}\right) +\left(\frac{-10}{-9}\right) +\left(\frac{11}{-2}\right)\\= \frac{9}{4}+ \frac{10}{9}-\frac{11}{2}\\=\frac{81}{36}+\frac{40}{36}-\frac{198}{36}\\=\frac{81+40-198}{36}\\=\frac{-77}{36}\)
7. \(-\left(\frac{-10}{3}\right) -\left(\frac{-10}{-8}\right) +\left(\frac{-12}{10}\right)\\= \frac{10}{3}- \frac{10}{8}-\frac{12}{10}\\=\frac{10}{3}-\frac{5}{4}-\frac{6}{5}\\=\frac{200}{60}-\frac{75}{60}-\frac{72}{60}\\=\frac{200-75-72}{60}\\=\frac{53}{60}\)
8. \(-\left(\frac{3}{2}\right) -\left(\frac{-9}{5}\right) -\left(\frac{9}{8}\right)\\= \frac{-3}{2}+ \frac{9}{5}-\frac{9}{8}\\=\frac{-60}{40}+\frac{72}{40}-\frac{45}{40}\\=\frac{-60+72-45}{40}\\=\frac{-33}{40}\)
9. \(-\left(\frac{7}{5}\right) +\left(\frac{-9}{3}\right) +\left(\frac{3}{-5}\right)\\= \frac{-7}{5}- \frac{9}{3}-\frac{3}{5}\\=\frac{-7}{5}-\frac{3}{1}-\frac{3}{5}\\=\frac{-7-3-3}{5}\\=\frac{-13}{5}\)
10. \(-\left(\frac{7}{8}\right) -\left(\frac{-8}{-6}\right) +\left(\frac{9}{-7}\right)\\= \frac{-7}{8}- \frac{8}{6}-\frac{9}{7}\\=\frac{-7}{8}-\frac{4}{3}-\frac{9}{7}\\=\frac{-147}{168}-\frac{224}{168}-\frac{216}{168}\\=\frac{-147-224-216}{168}\\=\frac{-587}{168}\)
11. \(+\left(\frac{-4}{-5}\right) +\left(\frac{6}{-2}\right) -\left(\frac{4}{-10}\right)\\= \frac{4}{5}- \frac{6}{2}+\frac{4}{10}\\=\frac{4}{5}-\frac{3}{1}+\frac{2}{5}\\=\frac{4-3+2}{5}\\=\frac{3}{5}\)
12. \(-\left(\frac{-2}{-3}\right) -\left(\frac{9}{2}\right) +\left(\frac{3}{4}\right)\\= \frac{-2}{3}- \frac{9}{2}+\frac{3}{4}\\=\frac{-8}{12}-\frac{54}{12}+\frac{9}{12}\\=\frac{-8-54+9}{12}\\=\frac{-53}{12}\)