Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{-7}\right) -\left(\frac{3}{6}\right) -\left(\frac{-3}{6}\right)\\= \frac{10}{7}- \frac{3}{6}+\frac{3}{6}\\=\frac{10}{7}-\frac{1}{2}+\frac{1}{2}\\=\frac{20}{14}-\frac{7}{14}+\frac{7}{14}\\=\frac{20-7+7}{14}\\=\frac{20}{14}\\=\frac{10}{7}\)
2. \(-\left(\frac{-2}{-5}\right) +\left(\frac{-4}{7}\right) +\left(\frac{6}{-9}\right)\\= \frac{-2}{5}- \frac{4}{7}-\frac{6}{9}\\=\frac{-2}{5}-\frac{4}{7}-\frac{2}{3}\\=\frac{-42}{105}-\frac{60}{105}-\frac{70}{105}\\=\frac{-42-60-70}{105}\\=\frac{-172}{105}\)
3. \(+\left(\frac{8}{5}\right) -\left(\frac{7}{10}\right) +\left(\frac{12}{9}\right)\\= \frac{8}{5}- \frac{7}{10}+\frac{12}{9}\\=\frac{8}{5}-\frac{7}{10}+\frac{4}{3}\\=\frac{48}{30}-\frac{21}{30}+\frac{40}{30}\\=\frac{48-21+40}{30}\\=\frac{67}{30}\)
4. \(-\left(\frac{-6}{5}\right) -\left(\frac{-6}{10}\right) -\left(\frac{4}{-8}\right)\\= \frac{6}{5}+ \frac{6}{10}+\frac{4}{8}\\=\frac{6}{5}+\frac{3}{5}+\frac{1}{2}\\=\frac{12}{10}+\frac{6}{10}+\frac{5}{10}\\=\frac{12+6+5}{10}\\=\frac{23}{10}\)
5. \(+\left(\frac{4}{9}\right) -\left(\frac{-5}{3}\right) +\left(\frac{4}{-10}\right)\\= \frac{4}{9}+ \frac{5}{3}-\frac{4}{10}\\=\frac{4}{9}+\frac{5}{3}-\frac{2}{5}\\=\frac{20}{45}+\frac{75}{45}-\frac{18}{45}\\=\frac{20+75-18}{45}\\=\frac{77}{45}\)
6. \(+\left(\frac{8}{3}\right) -\left(\frac{-10}{-5}\right) -\left(\frac{4}{10}\right)\\= \frac{8}{3}- \frac{10}{5}-\frac{4}{10}\\=\frac{8}{3}-\frac{2}{1}-\frac{2}{5}\\=\frac{40}{15}-\frac{30}{15}-\frac{6}{15}\\=\frac{40-30-6}{15}\\=\frac{4}{15}\)
7. \(-\left(\frac{-3}{4}\right) -\left(\frac{-8}{3}\right) +\left(\frac{-6}{-5}\right)\\= \frac{3}{4}+ \frac{8}{3}+\frac{6}{5}\\=\frac{45}{60}+\frac{160}{60}+\frac{72}{60}\\=\frac{45+160+72}{60}\\=\frac{277}{60}\)
8. \(-\left(\frac{-9}{7}\right) +\left(\frac{-6}{2}\right) +\left(\frac{-9}{12}\right)\\= \frac{9}{7}- \frac{6}{2}-\frac{9}{12}\\=\frac{9}{7}-\frac{3}{1}-\frac{3}{4}\\=\frac{36}{28}-\frac{84}{28}-\frac{21}{28}\\=\frac{36-84-21}{28}\\=\frac{-69}{28}\)
9. \(-\left(\frac{2}{5}\right) -\left(\frac{9}{4}\right) +\left(\frac{6}{-3}\right)\\= \frac{-2}{5}- \frac{9}{4}-\frac{6}{3}\\=\frac{-2}{5}-\frac{9}{4}-\frac{2}{1}\\=\frac{-8}{20}-\frac{45}{20}-\frac{40}{20}\\=\frac{-8-45-40}{20}\\=\frac{-93}{20}\)
10. \(+\left(\frac{3}{7}\right) +\left(\frac{3}{3}\right) -\left(\frac{-6}{-6}\right)\\= \frac{3}{7}+ \frac{3}{3}-\frac{6}{6}\\=\frac{3}{7}+\frac{1}{1}-\frac{1}{1}\\=\frac{3+1-1}{7}\\=\frac{3}{7}\)
11. \(+\left(\frac{-9}{-4}\right) -\left(\frac{5}{10}\right) +\left(\frac{9}{-10}\right)\\= \frac{9}{4}- \frac{5}{10}-\frac{9}{10}\\=\frac{9}{4}-\frac{1}{2}-\frac{9}{10}\\=\frac{45}{20}-\frac{10}{20}-\frac{18}{20}\\=\frac{45-10-18}{20}\\=\frac{17}{20}\)
12. \(-\left(\frac{-3}{2}\right) -\left(\frac{2}{-8}\right) +\left(\frac{9}{9}\right)\\= \frac{3}{2}+ \frac{2}{8}+\frac{9}{9}\\=\frac{3}{2}+\frac{1}{4}+\frac{1}{1}\\=\frac{6}{4}+\frac{1}{4}+\frac{4}{4}\\=\frac{6+1+4}{4}\\=\frac{11}{4}\)