Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{2}\right) +\left(\frac{-3}{5}\right) -\left(\frac{-4}{-11}\right)\\= \frac{-3}{2}- \frac{3}{5}-\frac{4}{11}\\=\frac{-165}{110}-\frac{66}{110}-\frac{40}{110}\\=\frac{-165-66-40}{110}\\=\frac{-271}{110}\)
2. \(+\left(\frac{-7}{-9}\right) -\left(\frac{-3}{-6}\right) +\left(\frac{10}{8}\right)\\= \frac{7}{9}- \frac{3}{6}+\frac{10}{8}\\=\frac{7}{9}-\frac{1}{2}+\frac{5}{4}\\=\frac{28}{36}-\frac{18}{36}+\frac{45}{36}\\=\frac{28-18+45}{36}\\=\frac{55}{36}\)
3. \(+\left(\frac{-2}{3}\right) +\left(\frac{4}{-10}\right) -\left(\frac{10}{2}\right)\\= \frac{-2}{3}- \frac{4}{10}-\frac{10}{2}\\=\frac{-2}{3}-\frac{2}{5}-\frac{5}{1}\\=\frac{-10}{15}-\frac{6}{15}-\frac{75}{15}\\=\frac{-10-6-75}{15}\\=\frac{-91}{15}\)
4. \(-\left(\frac{9}{2}\right) -\left(\frac{8}{-7}\right) -\left(\frac{6}{5}\right)\\= \frac{-9}{2}+ \frac{8}{7}-\frac{6}{5}\\=\frac{-315}{70}+\frac{80}{70}-\frac{84}{70}\\=\frac{-315+80-84}{70}\\=\frac{-319}{70}\)
5. \(+\left(\frac{-8}{-9}\right) -\left(\frac{7}{-10}\right) -\left(\frac{7}{-6}\right)\\= \frac{8}{9}+ \frac{7}{10}+\frac{7}{6}\\=\frac{80}{90}+\frac{63}{90}+\frac{105}{90}\\=\frac{80+63+105}{90}\\=\frac{248}{90}\\=\frac{124}{45}\)
6. \(-\left(\frac{-7}{8}\right) +\left(\frac{-4}{-4}\right) -\left(\frac{-10}{-8}\right)\\= \frac{7}{8}+ \frac{4}{4}-\frac{10}{8}\\=\frac{7}{8}+\frac{1}{1}-\frac{5}{4}\\=\frac{7+1-5}{8}\\=\frac{3}{8}\)
7. \(+\left(\frac{8}{-9}\right) -\left(\frac{8}{3}\right) +\left(\frac{8}{-2}\right)\\= \frac{-8}{9}- \frac{8}{3}-\frac{8}{2}\\=\frac{-8}{9}-\frac{8}{3}-\frac{4}{1}\\=\frac{-8-8-4}{9}\\=\frac{-20}{9}\)
8. \(+\left(\frac{-3}{-7}\right) +\left(\frac{7}{3}\right) +\left(\frac{-3}{-6}\right)\\= \frac{3}{7}+ \frac{7}{3}+\frac{3}{6}\\=\frac{3}{7}+\frac{7}{3}+\frac{1}{2}\\=\frac{18}{42}+\frac{98}{42}+\frac{21}{42}\\=\frac{18+98+21}{42}\\=\frac{137}{42}\)
9. \(-\left(\frac{5}{-7}\right) +\left(\frac{7}{-4}\right) -\left(\frac{3}{-11}\right)\\= \frac{5}{7}- \frac{7}{4}+\frac{3}{11}\\=\frac{220}{308}-\frac{539}{308}+\frac{84}{308}\\=\frac{220-539+84}{308}\\=\frac{-235}{308}\)
10. \(-\left(\frac{8}{-7}\right) +\left(\frac{-10}{5}\right) -\left(\frac{-2}{8}\right)\\= \frac{8}{7}- \frac{10}{5}+\frac{2}{8}\\=\frac{8}{7}-\frac{2}{1}+\frac{1}{4}\\=\frac{32}{28}-\frac{56}{28}+\frac{7}{28}\\=\frac{32-56+7}{28}\\=\frac{-17}{28}\)
11. \(+\left(\frac{3}{-5}\right) -\left(\frac{-7}{-2}\right) +\left(\frac{-12}{5}\right)\\= \frac{-3}{5}- \frac{7}{2}-\frac{12}{5}\\=\frac{-6}{10}-\frac{35}{10}-\frac{24}{10}\\=\frac{-6-35-24}{10}\\=\frac{-65}{10}\\=\frac{-13}{2}\)
12. \(+\left(\frac{2}{5}\right) +\left(\frac{-3}{-2}\right) -\left(\frac{-12}{-10}\right)\\= \frac{2}{5}+ \frac{3}{2}-\frac{12}{10}\\=\frac{2}{5}+\frac{3}{2}-\frac{6}{5}\\=\frac{4}{10}+\frac{15}{10}-\frac{12}{10}\\=\frac{4+15-12}{10}\\=\frac{7}{10}\)