Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{5}\right) -\left(\frac{10}{10}\right) -\left(\frac{-3}{3}\right)\\= \frac{3}{5}- \frac{10}{10}+\frac{3}{3}\\=\frac{3}{5}-\frac{1}{1}+\frac{1}{1}\\=\frac{3-1+1}{5}\\=\frac{3}{5}\)
2. \(-\left(\frac{10}{-7}\right) -\left(\frac{-7}{6}\right) -\left(\frac{12}{-8}\right)\\= \frac{10}{7}+ \frac{7}{6}+\frac{12}{8}\\=\frac{10}{7}+\frac{7}{6}+\frac{3}{2}\\=\frac{60}{42}+\frac{49}{42}+\frac{63}{42}\\=\frac{60+49+63}{42}\\=\frac{172}{42}\\=\frac{86}{21}\)
3. \(-\left(\frac{-9}{-7}\right) +\left(\frac{2}{3}\right) +\left(\frac{-2}{2}\right)\\= \frac{-9}{7}+ \frac{2}{3}-\frac{2}{2}\\=\frac{-9}{7}+\frac{2}{3}-\frac{1}{1}\\=\frac{-27}{21}+\frac{14}{21}-\frac{21}{21}\\=\frac{-27+14-21}{21}\\=\frac{-34}{21}\)
4. \(-\left(\frac{7}{-8}\right) -\left(\frac{-3}{-5}\right) +\left(\frac{-5}{8}\right)\\= \frac{7}{8}- \frac{3}{5}-\frac{5}{8}\\=\frac{35}{40}-\frac{24}{40}-\frac{25}{40}\\=\frac{35-24-25}{40}\\=\frac{-14}{40}\\=\frac{-7}{20}\)
5. \(-\left(\frac{7}{-5}\right) +\left(\frac{-2}{-4}\right) -\left(\frac{-11}{7}\right)\\= \frac{7}{5}+ \frac{2}{4}+\frac{11}{7}\\=\frac{7}{5}+\frac{1}{2}+\frac{11}{7}\\=\frac{98}{70}+\frac{35}{70}+\frac{110}{70}\\=\frac{98+35+110}{70}\\=\frac{243}{70}\)
6. \(-\left(\frac{10}{-9}\right) -\left(\frac{7}{7}\right) -\left(\frac{10}{5}\right)\\= \frac{10}{9}- \frac{7}{7}-\frac{10}{5}\\=\frac{10}{9}-\frac{1}{1}-\frac{2}{1}\\=\frac{10-1-2}{9}\\=\frac{7}{9}\)
7. \(+\left(\frac{-7}{2}\right) -\left(\frac{8}{-2}\right) +\left(\frac{-7}{-6}\right)\\= \frac{-7}{2}+ \frac{8}{2}+\frac{7}{6}\\=\frac{-7}{2}+\frac{4}{1}+\frac{7}{6}\\=\frac{-21}{6}+\frac{24}{6}+\frac{7}{6}\\=\frac{-21+24+7}{6}\\=\frac{10}{6}\\=\frac{5}{3}\)
8. \(-\left(\frac{8}{-7}\right) -\left(\frac{5}{-3}\right) +\left(\frac{8}{8}\right)\\= \frac{8}{7}+ \frac{5}{3}+\frac{8}{8}\\=\frac{8}{7}+\frac{5}{3}+\frac{1}{1}\\=\frac{24}{21}+\frac{35}{21}+\frac{21}{21}\\=\frac{24+35+21}{21}\\=\frac{80}{21}\)
9. \(+\left(\frac{-6}{-7}\right) -\left(\frac{-9}{-9}\right) -\left(\frac{9}{-2}\right)\\= \frac{6}{7}- \frac{9}{9}+\frac{9}{2}\\=\frac{6}{7}-\frac{1}{1}+\frac{9}{2}\\=\frac{12}{14}-\frac{14}{14}+\frac{63}{14}\\=\frac{12-14+63}{14}\\=\frac{61}{14}\)
10. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-10}{-4}\right) -\left(\frac{9}{-2}\right)\\= \frac{-6}{5}- \frac{10}{4}+\frac{9}{2}\\=\frac{-6}{5}-\frac{5}{2}+\frac{9}{2}\\=\frac{-12}{10}-\frac{25}{10}+\frac{45}{10}\\=\frac{-12-25+45}{10}\\=\frac{8}{10}\\=\frac{4}{5}\)
11. \(-\left(\frac{-10}{9}\right) -\left(\frac{-2}{9}\right) -\left(\frac{3}{6}\right)\\= \frac{10}{9}+ \frac{2}{9}-\frac{3}{6}\\=\frac{10}{9}+\frac{2}{9}-\frac{1}{2}\\=\frac{20}{18}+\frac{4}{18}-\frac{9}{18}\\=\frac{20+4-9}{18}\\=\frac{15}{18}\\=\frac{5}{6}\)
12. \(+\left(\frac{-10}{-9}\right) -\left(\frac{-4}{-2}\right) -\left(\frac{-11}{-2}\right)\\= \frac{10}{9}- \frac{4}{2}-\frac{11}{2}\\=\frac{10}{9}-\frac{2}{1}-\frac{11}{2}\\=\frac{20}{18}-\frac{36}{18}-\frac{99}{18}\\=\frac{20-36-99}{18}\\=\frac{-115}{18}\)