Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-10}{3}\right) +\left(\frac{6}{9}\right) +\left(\frac{2}{6}\right)\\= \frac{-10}{3}+ \frac{6}{9}+\frac{2}{6}\\=\frac{-10}{3}+\frac{2}{3}+\frac{1}{3}\\=\frac{-10+2+1}{3}\\=\frac{-7}{3}\)
2. \(-\left(\frac{-7}{-9}\right) +\left(\frac{-3}{5}\right) +\left(\frac{-3}{-4}\right)\\= \frac{-7}{9}- \frac{3}{5}+\frac{3}{4}\\=\frac{-140}{180}-\frac{108}{180}+\frac{135}{180}\\=\frac{-140-108+135}{180}\\=\frac{-113}{180}\)
3. \(+\left(\frac{-10}{-9}\right) -\left(\frac{9}{7}\right) -\left(\frac{-5}{-9}\right)\\= \frac{10}{9}- \frac{9}{7}-\frac{5}{9}\\=\frac{70}{63}-\frac{81}{63}-\frac{35}{63}\\=\frac{70-81-35}{63}\\=\frac{-46}{63}\)
4. \(+\left(\frac{-9}{-2}\right) +\left(\frac{2}{-9}\right) +\left(\frac{-6}{2}\right)\\= \frac{9}{2}- \frac{2}{9}-\frac{6}{2}\\=\frac{9}{2}-\frac{2}{9}-\frac{3}{1}\\=\frac{81}{18}-\frac{4}{18}-\frac{54}{18}\\=\frac{81-4-54}{18}\\=\frac{23}{18}\)
5. \(-\left(\frac{-8}{-3}\right) +\left(\frac{3}{7}\right) -\left(\frac{10}{-7}\right)\\= \frac{-8}{3}+ \frac{3}{7}+\frac{10}{7}\\=\frac{-56}{21}+\frac{9}{21}+\frac{30}{21}\\=\frac{-56+9+30}{21}\\=\frac{-17}{21}\)
6. \(+\left(\frac{10}{9}\right) +\left(\frac{-2}{2}\right) +\left(\frac{-7}{-5}\right)\\= \frac{10}{9}- \frac{2}{2}+\frac{7}{5}\\=\frac{10}{9}-\frac{1}{1}+\frac{7}{5}\\=\frac{50}{45}-\frac{45}{45}+\frac{63}{45}\\=\frac{50-45+63}{45}\\=\frac{68}{45}\)
7. \(-\left(\frac{2}{-9}\right) -\left(\frac{-4}{8}\right) -\left(\frac{11}{11}\right)\\= \frac{2}{9}+ \frac{4}{8}-\frac{11}{11}\\=\frac{2}{9}+\frac{1}{2}-\frac{1}{1}\\=\frac{4}{18}+\frac{9}{18}-\frac{18}{18}\\=\frac{4+9-18}{18}\\=\frac{-5}{18}\)
8. \(+\left(\frac{-4}{-3}\right) +\left(\frac{-4}{5}\right) -\left(\frac{3}{10}\right)\\= \frac{4}{3}- \frac{4}{5}-\frac{3}{10}\\=\frac{40}{30}-\frac{24}{30}-\frac{9}{30}\\=\frac{40-24-9}{30}\\=\frac{7}{30}\)
9. \(-\left(\frac{-7}{8}\right) -\left(\frac{8}{-8}\right) -\left(\frac{-9}{-4}\right)\\= \frac{7}{8}+ \frac{8}{8}-\frac{9}{4}\\=\frac{7}{8}+\frac{1}{1}-\frac{9}{4}\\=\frac{7+1-9}{8}\\=\frac{-1}{8}\)
10. \(-\left(\frac{-6}{5}\right) +\left(\frac{-9}{-3}\right) -\left(\frac{5}{10}\right)\\= \frac{6}{5}+ \frac{9}{3}-\frac{5}{10}\\=\frac{6}{5}+\frac{3}{1}-\frac{1}{2}\\=\frac{12}{10}+\frac{30}{10}-\frac{5}{10}\\=\frac{12+30-5}{10}\\=\frac{37}{10}\)
11. \(-\left(\frac{-5}{-2}\right) -\left(\frac{-7}{9}\right) +\left(\frac{-9}{5}\right)\\= \frac{-5}{2}+ \frac{7}{9}-\frac{9}{5}\\=\frac{-225}{90}+\frac{70}{90}-\frac{162}{90}\\=\frac{-225+70-162}{90}\\=\frac{-317}{90}\)
12. \(-\left(\frac{-9}{5}\right) -\left(\frac{-5}{6}\right) +\left(\frac{7}{-10}\right)\\= \frac{9}{5}+ \frac{5}{6}-\frac{7}{10}\\=\frac{54}{30}+\frac{25}{30}-\frac{21}{30}\\=\frac{54+25-21}{30}\\=\frac{58}{30}\\=\frac{29}{15}\)