Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{9}\right) +\left(\frac{-2}{5}\right) +\left(\frac{5}{10}\right)\\= \frac{-8}{9}- \frac{2}{5}+\frac{5}{10}\\=\frac{-8}{9}-\frac{2}{5}+\frac{1}{2}\\=\frac{-80}{90}-\frac{36}{90}+\frac{45}{90}\\=\frac{-80-36+45}{90}\\=\frac{-71}{90}\)
2. \(+\left(\frac{4}{-7}\right) +\left(\frac{-6}{6}\right) +\left(\frac{9}{12}\right)\\= \frac{-4}{7}- \frac{6}{6}+\frac{9}{12}\\=\frac{-4}{7}-\frac{1}{1}+\frac{3}{4}\\=\frac{-16}{28}-\frac{28}{28}+\frac{21}{28}\\=\frac{-16-28+21}{28}\\=\frac{-23}{28}\)
3. \(+\left(\frac{-5}{-6}\right) +\left(\frac{-7}{4}\right) -\left(\frac{10}{5}\right)\\= \frac{5}{6}- \frac{7}{4}-\frac{10}{5}\\=\frac{5}{6}-\frac{7}{4}-\frac{2}{1}\\=\frac{10}{12}-\frac{21}{12}-\frac{24}{12}\\=\frac{10-21-24}{12}\\=\frac{-35}{12}\)
4. \(-\left(\frac{-4}{9}\right) +\left(\frac{-8}{-8}\right) -\left(\frac{-8}{-6}\right)\\= \frac{4}{9}+ \frac{8}{8}-\frac{8}{6}\\=\frac{4}{9}+\frac{1}{1}-\frac{4}{3}\\=\frac{4+1-4}{9}\\=\frac{1}{9}\)
5. \(-\left(\frac{10}{-3}\right) -\left(\frac{-4}{3}\right) +\left(\frac{-7}{-3}\right)\\= \frac{10}{3}+ \frac{4}{3}+\frac{7}{3}\\=\frac{10+4+7}{3}\\=\frac{21}{3}\\=\frac{7}{1}\)
6. \(-\left(\frac{6}{5}\right) -\left(\frac{4}{-6}\right) +\left(\frac{7}{-9}\right)\\= \frac{-6}{5}+ \frac{4}{6}-\frac{7}{9}\\=\frac{-6}{5}+\frac{2}{3}-\frac{7}{9}\\=\frac{-54}{45}+\frac{30}{45}-\frac{35}{45}\\=\frac{-54+30-35}{45}\\=\frac{-59}{45}\)
7. \(-\left(\frac{4}{7}\right) +\left(\frac{-2}{-3}\right) -\left(\frac{-12}{-6}\right)\\= \frac{-4}{7}+ \frac{2}{3}-\frac{12}{6}\\=\frac{-4}{7}+\frac{2}{3}-\frac{2}{1}\\=\frac{-12}{21}+\frac{14}{21}-\frac{42}{21}\\=\frac{-12+14-42}{21}\\=\frac{-40}{21}\)
8. \(-\left(\frac{-5}{4}\right) +\left(\frac{9}{-2}\right) -\left(\frac{-11}{10}\right)\\= \frac{5}{4}- \frac{9}{2}+\frac{11}{10}\\=\frac{25}{20}-\frac{90}{20}+\frac{22}{20}\\=\frac{25-90+22}{20}\\=\frac{-43}{20}\)
9. \(+\left(\frac{-7}{-6}\right) +\left(\frac{-5}{-2}\right) -\left(\frac{12}{10}\right)\\= \frac{7}{6}+ \frac{5}{2}-\frac{12}{10}\\=\frac{7}{6}+\frac{5}{2}-\frac{6}{5}\\=\frac{35}{30}+\frac{75}{30}-\frac{36}{30}\\=\frac{35+75-36}{30}\\=\frac{74}{30}\\=\frac{37}{15}\)
10. \(-\left(\frac{6}{5}\right) +\left(\frac{5}{2}\right) +\left(\frac{6}{9}\right)\\= \frac{-6}{5}+ \frac{5}{2}+\frac{6}{9}\\=\frac{-6}{5}+\frac{5}{2}+\frac{2}{3}\\=\frac{-36}{30}+\frac{75}{30}+\frac{20}{30}\\=\frac{-36+75+20}{30}\\=\frac{59}{30}\)
11. \(+\left(\frac{-3}{7}\right) -\left(\frac{-9}{-8}\right) +\left(\frac{7}{-3}\right)\\= \frac{-3}{7}- \frac{9}{8}-\frac{7}{3}\\=\frac{-72}{168}-\frac{189}{168}-\frac{392}{168}\\=\frac{-72-189-392}{168}\\=\frac{-653}{168}\)
12. \(+\left(\frac{-8}{-5}\right) -\left(\frac{-9}{-9}\right) +\left(\frac{-9}{5}\right)\\= \frac{8}{5}- \frac{9}{9}-\frac{9}{5}\\=\frac{8}{5}-\frac{1}{1}-\frac{9}{5}\\=\frac{8-1-9}{5}\\=\frac{-2}{5}\)