Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-7}{-6}\right) +\left(\frac{4}{-6}\right) +\left(\frac{-9}{9}\right)\\= \frac{-7}{6}- \frac{4}{6}-\frac{9}{9}\\=\frac{-7}{6}-\frac{2}{3}-\frac{1}{1}\\=\frac{-7-2-1}{6}\\=\frac{-10}{6}\\=\frac{-5}{3}\)
2. \(+\left(\frac{6}{-7}\right) +\left(\frac{-4}{6}\right) -\left(\frac{2}{10}\right)\\= \frac{-6}{7}- \frac{4}{6}-\frac{2}{10}\\=\frac{-6}{7}-\frac{2}{3}-\frac{1}{5}\\=\frac{-90}{105}-\frac{70}{105}-\frac{21}{105}\\=\frac{-90-70-21}{105}\\=\frac{-181}{105}\)
3. \(+\left(\frac{2}{-9}\right) +\left(\frac{4}{-2}\right) -\left(\frac{-7}{-6}\right)\\= \frac{-2}{9}- \frac{4}{2}-\frac{7}{6}\\=\frac{-2}{9}-\frac{2}{1}-\frac{7}{6}\\=\frac{-4}{18}-\frac{36}{18}-\frac{21}{18}\\=\frac{-4-36-21}{18}\\=\frac{-61}{18}\)
4. \(+\left(\frac{-3}{2}\right) -\left(\frac{7}{5}\right) -\left(\frac{-11}{-10}\right)\\= \frac{-3}{2}- \frac{7}{5}-\frac{11}{10}\\=\frac{-15}{10}-\frac{14}{10}-\frac{11}{10}\\=\frac{-15-14-11}{10}\\=\frac{-40}{10}\\=\frac{-4}{1}\)
5. \(-\left(\frac{-4}{-9}\right) +\left(\frac{-10}{-2}\right) +\left(\frac{-12}{11}\right)\\= \frac{-4}{9}+ \frac{10}{2}-\frac{12}{11}\\=\frac{-4}{9}+\frac{5}{1}-\frac{12}{11}\\=\frac{-44}{99}+\frac{495}{99}-\frac{108}{99}\\=\frac{-44+495-108}{99}\\=\frac{343}{99}\)
6. \(+\left(\frac{6}{5}\right) +\left(\frac{-10}{-6}\right) -\left(\frac{6}{8}\right)\\= \frac{6}{5}+ \frac{10}{6}-\frac{6}{8}\\=\frac{6}{5}+\frac{5}{3}-\frac{3}{4}\\=\frac{72}{60}+\frac{100}{60}-\frac{45}{60}\\=\frac{72+100-45}{60}\\=\frac{127}{60}\)
7. \(+\left(\frac{-8}{3}\right) -\left(\frac{-6}{-3}\right) +\left(\frac{10}{4}\right)\\= \frac{-8}{3}- \frac{6}{3}+\frac{10}{4}\\=\frac{-8}{3}-\frac{2}{1}+\frac{5}{2}\\=\frac{-16}{6}-\frac{12}{6}+\frac{15}{6}\\=\frac{-16-12+15}{6}\\=\frac{-13}{6}\)
8. \(+\left(\frac{-6}{5}\right) -\left(\frac{-6}{6}\right) -\left(\frac{-7}{-3}\right)\\= \frac{-6}{5}+ \frac{6}{6}-\frac{7}{3}\\=\frac{-6}{5}+\frac{1}{1}-\frac{7}{3}\\=\frac{-18}{15}+\frac{15}{15}-\frac{35}{15}\\=\frac{-18+15-35}{15}\\=\frac{-38}{15}\)
9. \(-\left(\frac{-10}{3}\right) +\left(\frac{6}{6}\right) -\left(\frac{12}{-7}\right)\\= \frac{10}{3}+ \frac{6}{6}+\frac{12}{7}\\=\frac{10}{3}+\frac{1}{1}+\frac{12}{7}\\=\frac{70}{21}+\frac{21}{21}+\frac{36}{21}\\=\frac{70+21+36}{21}\\=\frac{127}{21}\)
10. \(+\left(\frac{10}{-7}\right) -\left(\frac{5}{-2}\right) -\left(\frac{-11}{4}\right)\\= \frac{-10}{7}+ \frac{5}{2}+\frac{11}{4}\\=\frac{-40}{28}+\frac{70}{28}+\frac{77}{28}\\=\frac{-40+70+77}{28}\\=\frac{107}{28}\)
11. \(+\left(\frac{6}{-5}\right) +\left(\frac{-8}{3}\right) +\left(\frac{10}{-10}\right)\\= \frac{-6}{5}- \frac{8}{3}-\frac{10}{10}\\=\frac{-6}{5}-\frac{8}{3}-\frac{1}{1}\\=\frac{-18}{15}-\frac{40}{15}-\frac{15}{15}\\=\frac{-18-40-15}{15}\\=\frac{-73}{15}\)
12. \(+\left(\frac{4}{5}\right) +\left(\frac{10}{2}\right) -\left(\frac{-4}{-6}\right)\\= \frac{4}{5}+ \frac{10}{2}-\frac{4}{6}\\=\frac{4}{5}+\frac{5}{1}-\frac{2}{3}\\=\frac{12}{15}+\frac{75}{15}-\frac{10}{15}\\=\frac{12+75-10}{15}\\=\frac{77}{15}\)