Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{-6}\right) +\left(\frac{-10}{-3}\right) -\left(\frac{11}{-3}\right)\\= \frac{-5}{6}+ \frac{10}{3}+\frac{11}{3}\\=\frac{-5+10+11}{6}\\=\frac{16}{6}\\=\frac{8}{3}\)
2. \(+\left(\frac{-8}{3}\right) -\left(\frac{4}{-8}\right) +\left(\frac{8}{10}\right)\\= \frac{-8}{3}+ \frac{4}{8}+\frac{8}{10}\\=\frac{-8}{3}+\frac{1}{2}+\frac{4}{5}\\=\frac{-80}{30}+\frac{15}{30}+\frac{24}{30}\\=\frac{-80+15+24}{30}\\=\frac{-41}{30}\)
3. \(-\left(\frac{8}{-5}\right) -\left(\frac{7}{4}\right) +\left(\frac{2}{9}\right)\\= \frac{8}{5}- \frac{7}{4}+\frac{2}{9}\\=\frac{288}{180}-\frac{315}{180}+\frac{40}{180}\\=\frac{288-315+40}{180}\\=\frac{13}{180}\)
4. \(-\left(\frac{5}{6}\right) -\left(\frac{-8}{6}\right) -\left(\frac{11}{12}\right)\\= \frac{-5}{6}+ \frac{8}{6}-\frac{11}{12}\\=\frac{-5}{6}+\frac{4}{3}-\frac{11}{12}\\=\frac{-10}{12}+\frac{16}{12}-\frac{11}{12}\\=\frac{-10+16-11}{12}\\=\frac{-5}{12}\)
5. \(+\left(\frac{9}{-2}\right) -\left(\frac{-7}{-4}\right) +\left(\frac{-9}{-8}\right)\\= \frac{-9}{2}- \frac{7}{4}+\frac{9}{8}\\=\frac{-36}{8}-\frac{14}{8}+\frac{9}{8}\\=\frac{-36-14+9}{8}\\=\frac{-41}{8}\)
6. \(+\left(\frac{7}{-5}\right) -\left(\frac{-9}{9}\right) +\left(\frac{7}{3}\right)\\= \frac{-7}{5}+ \frac{9}{9}+\frac{7}{3}\\=\frac{-7}{5}+\frac{1}{1}+\frac{7}{3}\\=\frac{-21}{15}+\frac{15}{15}+\frac{35}{15}\\=\frac{-21+15+35}{15}\\=\frac{29}{15}\)
7. \(+\left(\frac{4}{5}\right) -\left(\frac{2}{-5}\right) -\left(\frac{-9}{-5}\right)\\= \frac{4}{5}+ \frac{2}{5}-\frac{9}{5}\\=\frac{4+2-9}{5}\\=\frac{-3}{5}\)
8. \(+\left(\frac{-7}{-4}\right) -\left(\frac{8}{10}\right) +\left(\frac{-6}{2}\right)\\= \frac{7}{4}- \frac{8}{10}-\frac{6}{2}\\=\frac{7}{4}-\frac{4}{5}-\frac{3}{1}\\=\frac{35}{20}-\frac{16}{20}-\frac{60}{20}\\=\frac{35-16-60}{20}\\=\frac{-41}{20}\)
9. \(-\left(\frac{-6}{7}\right) -\left(\frac{2}{-8}\right) +\left(\frac{2}{-7}\right)\\= \frac{6}{7}+ \frac{2}{8}-\frac{2}{7}\\=\frac{6}{7}+\frac{1}{4}-\frac{2}{7}\\=\frac{24}{28}+\frac{7}{28}-\frac{8}{28}\\=\frac{24+7-8}{28}\\=\frac{23}{28}\)
10. \(+\left(\frac{9}{4}\right) +\left(\frac{-3}{5}\right) -\left(\frac{11}{8}\right)\\= \frac{9}{4}- \frac{3}{5}-\frac{11}{8}\\=\frac{90}{40}-\frac{24}{40}-\frac{55}{40}\\=\frac{90-24-55}{40}\\=\frac{11}{40}\)
11. \(-\left(\frac{-8}{5}\right) +\left(\frac{4}{10}\right) +\left(\frac{3}{-6}\right)\\= \frac{8}{5}+ \frac{4}{10}-\frac{3}{6}\\=\frac{8}{5}+\frac{2}{5}-\frac{1}{2}\\=\frac{16}{10}+\frac{4}{10}-\frac{5}{10}\\=\frac{16+4-5}{10}\\=\frac{15}{10}\\=\frac{3}{2}\)
12. \(+\left(\frac{-2}{7}\right) -\left(\frac{-6}{-2}\right) +\left(\frac{11}{-6}\right)\\= \frac{-2}{7}- \frac{6}{2}-\frac{11}{6}\\=\frac{-2}{7}-\frac{3}{1}-\frac{11}{6}\\=\frac{-12}{42}-\frac{126}{42}-\frac{77}{42}\\=\frac{-12-126-77}{42}\\=\frac{-215}{42}\)