Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-3}{5}\right) -\left(\frac{-10}{-9}\right) +\left(\frac{-8}{-5}\right)\\= \frac{-3}{5}- \frac{10}{9}+\frac{8}{5}\\=\frac{-27}{45}-\frac{50}{45}+\frac{72}{45}\\=\frac{-27-50+72}{45}\\=\frac{-5}{45}\\=\frac{-1}{9}\)
2. \(-\left(\frac{9}{-2}\right) +\left(\frac{5}{5}\right) -\left(\frac{12}{-2}\right)\\= \frac{9}{2}+ \frac{5}{5}+\frac{12}{2}\\=\frac{9}{2}+\frac{1}{1}+\frac{6}{1}\\=\frac{9+1+6}{2}\\=\frac{16}{2}\\=\frac{8}{1}\)
3. \(+\left(\frac{-3}{-4}\right) +\left(\frac{5}{-8}\right) -\left(\frac{-3}{8}\right)\\= \frac{3}{4}- \frac{5}{8}+\frac{3}{8}\\=\frac{6}{8}-\frac{5}{8}+\frac{3}{8}\\=\frac{6-5+3}{8}\\=\frac{4}{8}\\=\frac{1}{2}\)
4. \(-\left(\frac{-6}{-7}\right) +\left(\frac{-9}{-9}\right) +\left(\frac{12}{-9}\right)\\= \frac{-6}{7}+ \frac{9}{9}-\frac{12}{9}\\=\frac{-6}{7}+\frac{1}{1}-\frac{4}{3}\\=\frac{-18}{21}+\frac{21}{21}-\frac{28}{21}\\=\frac{-18+21-28}{21}\\=\frac{-25}{21}\)
5. \(-\left(\frac{3}{-2}\right) -\left(\frac{2}{-7}\right) -\left(\frac{4}{7}\right)\\= \frac{3}{2}+ \frac{2}{7}-\frac{4}{7}\\=\frac{21}{14}+\frac{4}{14}-\frac{8}{14}\\=\frac{21+4-8}{14}\\=\frac{17}{14}\)
6. \(-\left(\frac{-5}{-4}\right) +\left(\frac{7}{10}\right) -\left(\frac{6}{6}\right)\\= \frac{-5}{4}+ \frac{7}{10}-\frac{6}{6}\\=\frac{-5}{4}+\frac{7}{10}-\frac{1}{1}\\=\frac{-25}{20}+\frac{14}{20}-\frac{20}{20}\\=\frac{-25+14-20}{20}\\=\frac{-31}{20}\)
7. \(-\left(\frac{-9}{4}\right) -\left(\frac{-7}{7}\right) -\left(\frac{-11}{-6}\right)\\= \frac{9}{4}+ \frac{7}{7}-\frac{11}{6}\\=\frac{9}{4}+\frac{1}{1}-\frac{11}{6}\\=\frac{27}{12}+\frac{12}{12}-\frac{22}{12}\\=\frac{27+12-22}{12}\\=\frac{17}{12}\)
8. \(+\left(\frac{5}{-6}\right) +\left(\frac{5}{3}\right) +\left(\frac{-12}{-10}\right)\\= \frac{-5}{6}+ \frac{5}{3}+\frac{12}{10}\\=\frac{-5}{6}+\frac{5}{3}+\frac{6}{5}\\=\frac{-25}{30}+\frac{50}{30}+\frac{36}{30}\\=\frac{-25+50+36}{30}\\=\frac{61}{30}\)
9. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-10}{-10}\right) -\left(\frac{5}{-6}\right)\\= \frac{6}{5}+ \frac{10}{10}+\frac{5}{6}\\=\frac{6}{5}+\frac{1}{1}+\frac{5}{6}\\=\frac{36}{30}+\frac{30}{30}+\frac{25}{30}\\=\frac{36+30+25}{30}\\=\frac{91}{30}\)
10. \(-\left(\frac{10}{-7}\right) +\left(\frac{-4}{10}\right) +\left(\frac{12}{12}\right)\\= \frac{10}{7}- \frac{4}{10}+\frac{12}{12}\\=\frac{10}{7}-\frac{2}{5}+\frac{1}{1}\\=\frac{50}{35}-\frac{14}{35}+\frac{35}{35}\\=\frac{50-14+35}{35}\\=\frac{71}{35}\)
11. \(-\left(\frac{7}{8}\right) -\left(\frac{-9}{9}\right) +\left(\frac{6}{6}\right)\\= \frac{-7}{8}+ \frac{9}{9}+\frac{6}{6}\\=\frac{-7}{8}+\frac{1}{1}+\frac{1}{1}\\=\frac{-7+1+1}{8}\\=\frac{-5}{8}\)
12. \(-\left(\frac{-9}{-7}\right) -\left(\frac{-7}{-5}\right) -\left(\frac{-3}{10}\right)\\= \frac{-9}{7}- \frac{7}{5}+\frac{3}{10}\\=\frac{-90}{70}-\frac{98}{70}+\frac{21}{70}\\=\frac{-90-98+21}{70}\\=\frac{-167}{70}\)