Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{-5}\right) -\left(\frac{-9}{-6}\right) -\left(\frac{-7}{4}\right)\\= \frac{6}{5}- \frac{9}{6}+\frac{7}{4}\\=\frac{6}{5}-\frac{3}{2}+\frac{7}{4}\\=\frac{24}{20}-\frac{30}{20}+\frac{35}{20}\\=\frac{24-30+35}{20}\\=\frac{29}{20}\)
2. \(+\left(\frac{3}{-4}\right) +\left(\frac{5}{-3}\right) +\left(\frac{3}{-8}\right)\\= \frac{-3}{4}- \frac{5}{3}-\frac{3}{8}\\=\frac{-18}{24}-\frac{40}{24}-\frac{9}{24}\\=\frac{-18-40-9}{24}\\=\frac{-67}{24}\)
3. \(+\left(\frac{-7}{5}\right) +\left(\frac{6}{-3}\right) +\left(\frac{3}{8}\right)\\= \frac{-7}{5}- \frac{6}{3}+\frac{3}{8}\\=\frac{-7}{5}-\frac{2}{1}+\frac{3}{8}\\=\frac{-56}{40}-\frac{80}{40}+\frac{15}{40}\\=\frac{-56-80+15}{40}\\=\frac{-121}{40}\)
4. \(+\left(\frac{-6}{5}\right) -\left(\frac{-9}{-5}\right) -\left(\frac{-9}{9}\right)\\= \frac{-6}{5}- \frac{9}{5}+\frac{9}{9}\\=\frac{-6}{5}-\frac{9}{5}+\frac{1}{1}\\=\frac{-6-9+1}{5}\\=\frac{-14}{5}\)
5. \(+\left(\frac{-8}{-3}\right) -\left(\frac{-3}{6}\right) +\left(\frac{-5}{11}\right)\\= \frac{8}{3}+ \frac{3}{6}-\frac{5}{11}\\=\frac{8}{3}+\frac{1}{2}-\frac{5}{11}\\=\frac{176}{66}+\frac{33}{66}-\frac{30}{66}\\=\frac{176+33-30}{66}\\=\frac{179}{66}\)
6. \(+\left(\frac{-6}{5}\right) +\left(\frac{4}{-4}\right) -\left(\frac{4}{-7}\right)\\= \frac{-6}{5}- \frac{4}{4}+\frac{4}{7}\\=\frac{-6}{5}-\frac{1}{1}+\frac{4}{7}\\=\frac{-42}{35}-\frac{35}{35}+\frac{20}{35}\\=\frac{-42-35+20}{35}\\=\frac{-57}{35}\)
7. \(+\left(\frac{-9}{-4}\right) +\left(\frac{-2}{-3}\right) +\left(\frac{6}{-11}\right)\\= \frac{9}{4}+ \frac{2}{3}-\frac{6}{11}\\=\frac{297}{132}+\frac{88}{132}-\frac{72}{132}\\=\frac{297+88-72}{132}\\=\frac{313}{132}\)
8. \(+\left(\frac{-10}{-7}\right) -\left(\frac{9}{3}\right) +\left(\frac{7}{-7}\right)\\= \frac{10}{7}- \frac{9}{3}-\frac{7}{7}\\=\frac{10}{7}-\frac{3}{1}-\frac{1}{1}\\=\frac{10-3-1}{7}\\=\frac{6}{7}\)
9. \(+\left(\frac{-10}{-3}\right) +\left(\frac{10}{2}\right) -\left(\frac{-7}{-3}\right)\\= \frac{10}{3}+ \frac{10}{2}-\frac{7}{3}\\=\frac{10}{3}+\frac{5}{1}-\frac{7}{3}\\=\frac{10+5-7}{3}\\=\frac{8}{3}\)
10. \(-\left(\frac{-6}{5}\right) -\left(\frac{-4}{-6}\right) +\left(\frac{5}{-10}\right)\\= \frac{6}{5}- \frac{4}{6}-\frac{5}{10}\\=\frac{6}{5}-\frac{2}{3}-\frac{1}{2}\\=\frac{36}{30}-\frac{20}{30}-\frac{15}{30}\\=\frac{36-20-15}{30}\\=\frac{1}{30}\)
11. \(+\left(\frac{-5}{-8}\right) -\left(\frac{9}{2}\right) +\left(\frac{-5}{10}\right)\\= \frac{5}{8}- \frac{9}{2}-\frac{5}{10}\\=\frac{5}{8}-\frac{9}{2}-\frac{1}{2}\\=\frac{5-9-1}{8}\\=\frac{-5}{8}\)
12. \(-\left(\frac{-10}{3}\right) -\left(\frac{5}{-3}\right) +\left(\frac{-8}{-7}\right)\\= \frac{10}{3}+ \frac{5}{3}+\frac{8}{7}\\=\frac{70}{21}+\frac{35}{21}+\frac{24}{21}\\=\frac{70+35+24}{21}\\=\frac{129}{21}\\=\frac{43}{7}\)