Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{9}\right) +\left(\frac{-8}{-4}\right) -\left(\frac{-6}{-11}\right)\\= \frac{-4}{9}+ \frac{8}{4}-\frac{6}{11}\\=\frac{-4}{9}+\frac{2}{1}-\frac{6}{11}\\=\frac{-44}{99}+\frac{198}{99}-\frac{54}{99}\\=\frac{-44+198-54}{99}\\=\frac{100}{99}\)
2. \(+\left(\frac{-9}{-2}\right) +\left(\frac{-6}{8}\right) -\left(\frac{-10}{10}\right)\\= \frac{9}{2}- \frac{6}{8}+\frac{10}{10}\\=\frac{9}{2}-\frac{3}{4}+\frac{1}{1}\\=\frac{18}{4}-\frac{3}{4}+\frac{4}{4}\\=\frac{18-3+4}{4}\\=\frac{19}{4}\)
3. \(-\left(\frac{-9}{2}\right) -\left(\frac{-10}{4}\right) -\left(\frac{7}{-5}\right)\\= \frac{9}{2}+ \frac{10}{4}+\frac{7}{5}\\=\frac{9}{2}+\frac{5}{2}+\frac{7}{5}\\=\frac{45}{10}+\frac{25}{10}+\frac{14}{10}\\=\frac{45+25+14}{10}\\=\frac{84}{10}\\=\frac{42}{5}\)
4. \(-\left(\frac{-8}{5}\right) -\left(\frac{-2}{-5}\right) -\left(\frac{-6}{9}\right)\\= \frac{8}{5}- \frac{2}{5}+\frac{6}{9}\\=\frac{8}{5}-\frac{2}{5}+\frac{2}{3}\\=\frac{24}{15}-\frac{6}{15}+\frac{10}{15}\\=\frac{24-6+10}{15}\\=\frac{28}{15}\)
5. \(+\left(\frac{6}{5}\right) -\left(\frac{4}{6}\right) -\left(\frac{10}{10}\right)\\= \frac{6}{5}- \frac{4}{6}-\frac{10}{10}\\=\frac{6}{5}-\frac{2}{3}-\frac{1}{1}\\=\frac{18}{15}-\frac{10}{15}-\frac{15}{15}\\=\frac{18-10-15}{15}\\=\frac{-7}{15}\)
6. \(+\left(\frac{-5}{-9}\right) +\left(\frac{9}{2}\right) +\left(\frac{-10}{-2}\right)\\= \frac{5}{9}+ \frac{9}{2}+\frac{10}{2}\\=\frac{5}{9}+\frac{9}{2}+\frac{5}{1}\\=\frac{10}{18}+\frac{81}{18}+\frac{90}{18}\\=\frac{10+81+90}{18}\\=\frac{181}{18}\)
7. \(+\left(\frac{-3}{-4}\right) +\left(\frac{8}{2}\right) -\left(\frac{2}{12}\right)\\= \frac{3}{4}+ \frac{8}{2}-\frac{2}{12}\\=\frac{3}{4}+\frac{4}{1}-\frac{1}{6}\\=\frac{9}{12}+\frac{48}{12}-\frac{2}{12}\\=\frac{9+48-2}{12}\\=\frac{55}{12}\)
8. \(-\left(\frac{-8}{-7}\right) -\left(\frac{-6}{-5}\right) -\left(\frac{-7}{-11}\right)\\= \frac{-8}{7}- \frac{6}{5}-\frac{7}{11}\\=\frac{-440}{385}-\frac{462}{385}-\frac{245}{385}\\=\frac{-440-462-245}{385}\\=\frac{-1147}{385}\)
9. \(+\left(\frac{-6}{-5}\right) +\left(\frac{8}{3}\right) +\left(\frac{-11}{7}\right)\\= \frac{6}{5}+ \frac{8}{3}-\frac{11}{7}\\=\frac{126}{105}+\frac{280}{105}-\frac{165}{105}\\=\frac{126+280-165}{105}\\=\frac{241}{105}\)
10. \(+\left(\frac{10}{-9}\right) +\left(\frac{-9}{-10}\right) -\left(\frac{-10}{-12}\right)\\= \frac{-10}{9}+ \frac{9}{10}-\frac{10}{12}\\=\frac{-10}{9}+\frac{9}{10}-\frac{5}{6}\\=\frac{-100}{90}+\frac{81}{90}-\frac{75}{90}\\=\frac{-100+81-75}{90}\\=\frac{-94}{90}\\=\frac{-47}{45}\)
11. \(+\left(\frac{2}{-3}\right) -\left(\frac{-9}{-10}\right) -\left(\frac{-8}{-4}\right)\\= \frac{-2}{3}- \frac{9}{10}-\frac{8}{4}\\=\frac{-2}{3}-\frac{9}{10}-\frac{2}{1}\\=\frac{-20}{30}-\frac{27}{30}-\frac{60}{30}\\=\frac{-20-27-60}{30}\\=\frac{-107}{30}\)
12. \(-\left(\frac{-10}{3}\right) -\left(\frac{-5}{-6}\right) -\left(\frac{-8}{-3}\right)\\= \frac{10}{3}- \frac{5}{6}-\frac{8}{3}\\=\frac{20}{6}-\frac{5}{6}-\frac{16}{6}\\=\frac{20-5-16}{6}\\=\frac{-1}{6}\)