Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{-3}\right) -\left(\frac{-6}{9}\right) -\left(\frac{-4}{-2}\right)\\= \frac{-2}{3}+ \frac{6}{9}-\frac{4}{2}\\=\frac{-2}{3}+\frac{2}{3}-\frac{2}{1}\\=\frac{-2+2-2}{3}\\=\frac{-2}{3}\)
2. \(-\left(\frac{-10}{3}\right) +\left(\frac{7}{-10}\right) +\left(\frac{2}{6}\right)\\= \frac{10}{3}- \frac{7}{10}+\frac{2}{6}\\=\frac{10}{3}-\frac{7}{10}+\frac{1}{3}\\=\frac{100}{30}-\frac{21}{30}+\frac{10}{30}\\=\frac{100-21+10}{30}\\=\frac{89}{30}\)
3. \(+\left(\frac{-8}{-9}\right) -\left(\frac{10}{10}\right) -\left(\frac{4}{-5}\right)\\= \frac{8}{9}- \frac{10}{10}+\frac{4}{5}\\=\frac{8}{9}-\frac{1}{1}+\frac{4}{5}\\=\frac{40}{45}-\frac{45}{45}+\frac{36}{45}\\=\frac{40-45+36}{45}\\=\frac{31}{45}\)
4. \(-\left(\frac{9}{4}\right) +\left(\frac{-4}{-4}\right) -\left(\frac{6}{-4}\right)\\= \frac{-9}{4}+ \frac{4}{4}+\frac{6}{4}\\=\frac{-9}{4}+\frac{1}{1}+\frac{3}{2}\\=\frac{-9+1+3}{4}\\=\frac{-5}{4}\)
5. \(-\left(\frac{5}{6}\right) +\left(\frac{-7}{4}\right) -\left(\frac{-5}{4}\right)\\= \frac{-5}{6}- \frac{7}{4}+\frac{5}{4}\\=\frac{-10}{12}-\frac{21}{12}+\frac{15}{12}\\=\frac{-10-21+15}{12}\\=\frac{-16}{12}\\=\frac{-4}{3}\)
6. \(-\left(\frac{-10}{-9}\right) -\left(\frac{-7}{-10}\right) +\left(\frac{9}{-3}\right)\\= \frac{-10}{9}- \frac{7}{10}-\frac{9}{3}\\=\frac{-10}{9}-\frac{7}{10}-\frac{3}{1}\\=\frac{-100}{90}-\frac{63}{90}-\frac{270}{90}\\=\frac{-100-63-270}{90}\\=\frac{-433}{90}\)
7. \(-\left(\frac{6}{-5}\right) -\left(\frac{-3}{-9}\right) -\left(\frac{-9}{12}\right)\\= \frac{6}{5}- \frac{3}{9}+\frac{9}{12}\\=\frac{6}{5}-\frac{1}{3}+\frac{3}{4}\\=\frac{72}{60}-\frac{20}{60}+\frac{45}{60}\\=\frac{72-20+45}{60}\\=\frac{97}{60}\)
8. \(-\left(\frac{10}{9}\right) +\left(\frac{-7}{5}\right) -\left(\frac{-3}{-5}\right)\\= \frac{-10}{9}- \frac{7}{5}-\frac{3}{5}\\=\frac{-50}{45}-\frac{63}{45}-\frac{27}{45}\\=\frac{-50-63-27}{45}\\=\frac{-140}{45}\\=\frac{-28}{9}\)
9. \(+\left(\frac{-7}{2}\right) -\left(\frac{9}{-7}\right) +\left(\frac{12}{11}\right)\\= \frac{-7}{2}+ \frac{9}{7}+\frac{12}{11}\\=\frac{-539}{154}+\frac{198}{154}+\frac{168}{154}\\=\frac{-539+198+168}{154}\\=\frac{-173}{154}\)
10. \(+\left(\frac{5}{6}\right) -\left(\frac{6}{-3}\right) -\left(\frac{-11}{-10}\right)\\= \frac{5}{6}+ \frac{6}{3}-\frac{11}{10}\\=\frac{5}{6}+\frac{2}{1}-\frac{11}{10}\\=\frac{25}{30}+\frac{60}{30}-\frac{33}{30}\\=\frac{25+60-33}{30}\\=\frac{52}{30}\\=\frac{26}{15}\)
11. \(+\left(\frac{8}{-5}\right) -\left(\frac{-8}{-10}\right) +\left(\frac{6}{-12}\right)\\= \frac{-8}{5}- \frac{8}{10}-\frac{6}{12}\\=\frac{-8}{5}-\frac{4}{5}-\frac{1}{2}\\=\frac{-16}{10}-\frac{8}{10}-\frac{5}{10}\\=\frac{-16-8-5}{10}\\=\frac{-29}{10}\)
12. \(-\left(\frac{-6}{7}\right) -\left(\frac{3}{-8}\right) +\left(\frac{9}{11}\right)\\= \frac{6}{7}+ \frac{3}{8}+\frac{9}{11}\\=\frac{528}{616}+\frac{231}{616}+\frac{504}{616}\\=\frac{528+231+504}{616}\\=\frac{1263}{616}\)