Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{2}{-5}\right) -\left(\frac{10}{-8}\right) -\left(\frac{-11}{2}\right)\\= \frac{-2}{5}+ \frac{10}{8}+\frac{11}{2}\\=\frac{-2}{5}+\frac{5}{4}+\frac{11}{2}\\=\frac{-8}{20}+\frac{25}{20}+\frac{110}{20}\\=\frac{-8+25+110}{20}\\=\frac{127}{20}\)
2. \(+\left(\frac{8}{-7}\right) -\left(\frac{7}{-6}\right) -\left(\frac{10}{6}\right)\\= \frac{-8}{7}+ \frac{7}{6}-\frac{10}{6}\\=\frac{-8}{7}+\frac{7}{6}-\frac{5}{3}\\=\frac{-48}{42}+\frac{49}{42}-\frac{70}{42}\\=\frac{-48+49-70}{42}\\=\frac{-69}{42}\\=\frac{-23}{14}\)
3. \(+\left(\frac{-9}{-7}\right) +\left(\frac{-9}{-8}\right) -\left(\frac{7}{-5}\right)\\= \frac{9}{7}+ \frac{9}{8}+\frac{7}{5}\\=\frac{360}{280}+\frac{315}{280}+\frac{392}{280}\\=\frac{360+315+392}{280}\\=\frac{1067}{280}\)
4. \(+\left(\frac{7}{9}\right) -\left(\frac{-3}{-9}\right) -\left(\frac{-4}{-5}\right)\\= \frac{7}{9}- \frac{3}{9}-\frac{4}{5}\\=\frac{7}{9}-\frac{1}{3}-\frac{4}{5}\\=\frac{35}{45}-\frac{15}{45}-\frac{36}{45}\\=\frac{35-15-36}{45}\\=\frac{-16}{45}\)
5. \(+\left(\frac{-10}{-3}\right) +\left(\frac{-6}{6}\right) +\left(\frac{10}{11}\right)\\= \frac{10}{3}- \frac{6}{6}+\frac{10}{11}\\=\frac{10}{3}-\frac{1}{1}+\frac{10}{11}\\=\frac{110}{33}-\frac{33}{33}+\frac{30}{33}\\=\frac{110-33+30}{33}\\=\frac{107}{33}\)
6. \(-\left(\frac{10}{3}\right) -\left(\frac{-8}{8}\right) -\left(\frac{6}{4}\right)\\= \frac{-10}{3}+ \frac{8}{8}-\frac{6}{4}\\=\frac{-10}{3}+\frac{1}{1}-\frac{3}{2}\\=\frac{-20}{6}+\frac{6}{6}-\frac{9}{6}\\=\frac{-20+6-9}{6}\\=\frac{-23}{6}\)
7. \(+\left(\frac{-2}{9}\right) +\left(\frac{8}{-6}\right) +\left(\frac{-9}{8}\right)\\= \frac{-2}{9}- \frac{8}{6}-\frac{9}{8}\\=\frac{-2}{9}-\frac{4}{3}-\frac{9}{8}\\=\frac{-16}{72}-\frac{96}{72}-\frac{81}{72}\\=\frac{-16-96-81}{72}\\=\frac{-193}{72}\)
8. \(+\left(\frac{-9}{-4}\right) -\left(\frac{-10}{10}\right) -\left(\frac{-12}{11}\right)\\= \frac{9}{4}+ \frac{10}{10}+\frac{12}{11}\\=\frac{9}{4}+\frac{1}{1}+\frac{12}{11}\\=\frac{99}{44}+\frac{44}{44}+\frac{48}{44}\\=\frac{99+44+48}{44}\\=\frac{191}{44}\)
9. \(+\left(\frac{8}{7}\right) +\left(\frac{8}{6}\right) +\left(\frac{4}{-8}\right)\\= \frac{8}{7}+ \frac{8}{6}-\frac{4}{8}\\=\frac{8}{7}+\frac{4}{3}-\frac{1}{2}\\=\frac{48}{42}+\frac{56}{42}-\frac{21}{42}\\=\frac{48+56-21}{42}\\=\frac{83}{42}\)
10. \(+\left(\frac{2}{-7}\right) -\left(\frac{-3}{-6}\right) -\left(\frac{-6}{-11}\right)\\= \frac{-2}{7}- \frac{3}{6}-\frac{6}{11}\\=\frac{-2}{7}-\frac{1}{2}-\frac{6}{11}\\=\frac{-44}{154}-\frac{77}{154}-\frac{84}{154}\\=\frac{-44-77-84}{154}\\=\frac{-205}{154}\)
11. \(+\left(\frac{-10}{-3}\right) +\left(\frac{-7}{5}\right) -\left(\frac{-4}{-8}\right)\\= \frac{10}{3}- \frac{7}{5}-\frac{4}{8}\\=\frac{10}{3}-\frac{7}{5}-\frac{1}{2}\\=\frac{100}{30}-\frac{42}{30}-\frac{15}{30}\\=\frac{100-42-15}{30}\\=\frac{43}{30}\)
12. \(+\left(\frac{5}{-8}\right) +\left(\frac{-8}{-9}\right) +\left(\frac{2}{-5}\right)\\= \frac{-5}{8}+ \frac{8}{9}-\frac{2}{5}\\=\frac{-225}{360}+\frac{320}{360}-\frac{144}{360}\\=\frac{-225+320-144}{360}\\=\frac{-49}{360}\)