Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{-5}\right) -\left(\frac{-2}{6}\right) +\left(\frac{-6}{3}\right)\\= \frac{2}{5}+ \frac{2}{6}-\frac{6}{3}\\=\frac{2}{5}+\frac{1}{3}-\frac{2}{1}\\=\frac{6}{15}+\frac{5}{15}-\frac{30}{15}\\=\frac{6+5-30}{15}\\=\frac{-19}{15}\)
2. \(+\left(\frac{-4}{-7}\right) -\left(\frac{-3}{3}\right) +\left(\frac{7}{-7}\right)\\= \frac{4}{7}+ \frac{3}{3}-\frac{7}{7}\\=\frac{4}{7}+\frac{1}{1}-\frac{1}{1}\\=\frac{4+1-1}{7}\\=\frac{4}{7}\)
3. \(+\left(\frac{7}{-8}\right) +\left(\frac{2}{-9}\right) +\left(\frac{10}{6}\right)\\= \frac{-7}{8}- \frac{2}{9}+\frac{10}{6}\\=\frac{-7}{8}-\frac{2}{9}+\frac{5}{3}\\=\frac{-63}{72}-\frac{16}{72}+\frac{120}{72}\\=\frac{-63-16+120}{72}\\=\frac{41}{72}\)
4. \(-\left(\frac{4}{7}\right) -\left(\frac{-6}{10}\right) -\left(\frac{9}{-11}\right)\\= \frac{-4}{7}+ \frac{6}{10}+\frac{9}{11}\\=\frac{-4}{7}+\frac{3}{5}+\frac{9}{11}\\=\frac{-220}{385}+\frac{231}{385}+\frac{315}{385}\\=\frac{-220+231+315}{385}\\=\frac{326}{385}\)
5. \(+\left(\frac{-2}{-9}\right) -\left(\frac{-8}{10}\right) +\left(\frac{2}{12}\right)\\= \frac{2}{9}+ \frac{8}{10}+\frac{2}{12}\\=\frac{2}{9}+\frac{4}{5}+\frac{1}{6}\\=\frac{20}{90}+\frac{72}{90}+\frac{15}{90}\\=\frac{20+72+15}{90}\\=\frac{107}{90}\)
6. \(+\left(\frac{-6}{5}\right) -\left(\frac{2}{2}\right) +\left(\frac{-5}{11}\right)\\= \frac{-6}{5}- \frac{2}{2}-\frac{5}{11}\\=\frac{-6}{5}-\frac{1}{1}-\frac{5}{11}\\=\frac{-66}{55}-\frac{55}{55}-\frac{25}{55}\\=\frac{-66-55-25}{55}\\=\frac{-146}{55}\)
7. \(-\left(\frac{-9}{7}\right) +\left(\frac{7}{-2}\right) +\left(\frac{7}{3}\right)\\= \frac{9}{7}- \frac{7}{2}+\frac{7}{3}\\=\frac{54}{42}-\frac{147}{42}+\frac{98}{42}\\=\frac{54-147+98}{42}\\=\frac{5}{42}\)
8. \(+\left(\frac{6}{7}\right) +\left(\frac{3}{-7}\right) +\left(\frac{12}{3}\right)\\= \frac{6}{7}- \frac{3}{7}+\frac{12}{3}\\=\frac{6}{7}-\frac{3}{7}+\frac{4}{1}\\=\frac{6-3+4}{7}\\=\frac{7}{7}\\=\frac{1}{1}\)
9. \(+\left(\frac{6}{-7}\right) -\left(\frac{-9}{4}\right) +\left(\frac{-3}{7}\right)\\= \frac{-6}{7}+ \frac{9}{4}-\frac{3}{7}\\=\frac{-24}{28}+\frac{63}{28}-\frac{12}{28}\\=\frac{-24+63-12}{28}\\=\frac{27}{28}\)
10. \(+\left(\frac{-7}{-9}\right) -\left(\frac{-5}{-7}\right) +\left(\frac{-9}{11}\right)\\= \frac{7}{9}- \frac{5}{7}-\frac{9}{11}\\=\frac{539}{693}-\frac{495}{693}-\frac{567}{693}\\=\frac{539-495-567}{693}\\=\frac{-523}{693}\)
11. \(+\left(\frac{5}{8}\right) +\left(\frac{-7}{3}\right) +\left(\frac{10}{9}\right)\\= \frac{5}{8}- \frac{7}{3}+\frac{10}{9}\\=\frac{45}{72}-\frac{168}{72}+\frac{80}{72}\\=\frac{45-168+80}{72}\\=\frac{-43}{72}\)
12. \(+\left(\frac{-2}{-5}\right) +\left(\frac{9}{-7}\right) +\left(\frac{6}{9}\right)\\= \frac{2}{5}- \frac{9}{7}+\frac{6}{9}\\=\frac{2}{5}-\frac{9}{7}+\frac{2}{3}\\=\frac{42}{105}-\frac{135}{105}+\frac{70}{105}\\=\frac{42-135+70}{105}\\=\frac{-23}{105}\)