Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{-2}\right) +\left(\frac{-10}{4}\right) +\left(\frac{-9}{11}\right)\\= \frac{-3}{2}- \frac{10}{4}-\frac{9}{11}\\=\frac{-3}{2}-\frac{5}{2}-\frac{9}{11}\\=\frac{-33}{22}-\frac{55}{22}-\frac{18}{22}\\=\frac{-33-55-18}{22}\\=\frac{-106}{22}\\=\frac{-53}{11}\)
2. \(+\left(\frac{7}{-8}\right) +\left(\frac{-3}{4}\right) -\left(\frac{-12}{-5}\right)\\= \frac{-7}{8}- \frac{3}{4}-\frac{12}{5}\\=\frac{-35}{40}-\frac{30}{40}-\frac{96}{40}\\=\frac{-35-30-96}{40}\\=\frac{-161}{40}\)
3. \(-\left(\frac{-5}{-3}\right) -\left(\frac{-4}{-6}\right) +\left(\frac{4}{10}\right)\\= \frac{-5}{3}- \frac{4}{6}+\frac{4}{10}\\=\frac{-5}{3}-\frac{2}{3}+\frac{2}{5}\\=\frac{-25}{15}-\frac{10}{15}+\frac{6}{15}\\=\frac{-25-10+6}{15}\\=\frac{-29}{15}\)
4. \(+\left(\frac{4}{-3}\right) +\left(\frac{5}{4}\right) +\left(\frac{3}{-5}\right)\\= \frac{-4}{3}+ \frac{5}{4}-\frac{3}{5}\\=\frac{-80}{60}+\frac{75}{60}-\frac{36}{60}\\=\frac{-80+75-36}{60}\\=\frac{-41}{60}\)
5. \(-\left(\frac{-9}{-7}\right) +\left(\frac{-6}{-7}\right) +\left(\frac{-6}{7}\right)\\= \frac{-9}{7}+ \frac{6}{7}-\frac{6}{7}\\=\frac{-9+6-6}{7}\\=\frac{-9}{7}\)
6. \(+\left(\frac{-8}{-5}\right) -\left(\frac{-8}{7}\right) +\left(\frac{2}{-5}\right)\\= \frac{8}{5}+ \frac{8}{7}-\frac{2}{5}\\=\frac{56}{35}+\frac{40}{35}-\frac{14}{35}\\=\frac{56+40-14}{35}\\=\frac{82}{35}\)
7. \(+\left(\frac{2}{3}\right) +\left(\frac{-8}{-3}\right) -\left(\frac{7}{5}\right)\\= \frac{2}{3}+ \frac{8}{3}-\frac{7}{5}\\=\frac{10}{15}+\frac{40}{15}-\frac{21}{15}\\=\frac{10+40-21}{15}\\=\frac{29}{15}\)
8. \(-\left(\frac{-7}{9}\right) -\left(\frac{8}{9}\right) -\left(\frac{5}{-5}\right)\\= \frac{7}{9}- \frac{8}{9}+\frac{5}{5}\\=\frac{7}{9}-\frac{8}{9}+\frac{1}{1}\\=\frac{7-8+1}{9}\\=\frac{0}{9}\\=\frac{0}{1}\)
9. \(+\left(\frac{6}{-5}\right) -\left(\frac{4}{6}\right) +\left(\frac{12}{6}\right)\\= \frac{-6}{5}- \frac{4}{6}+\frac{12}{6}\\=\frac{-6}{5}-\frac{2}{3}+\frac{2}{1}\\=\frac{-18}{15}-\frac{10}{15}+\frac{30}{15}\\=\frac{-18-10+30}{15}\\=\frac{2}{15}\)
10. \(+\left(\frac{10}{7}\right) +\left(\frac{5}{5}\right) -\left(\frac{-8}{-10}\right)\\= \frac{10}{7}+ \frac{5}{5}-\frac{8}{10}\\=\frac{10}{7}+\frac{1}{1}-\frac{4}{5}\\=\frac{50}{35}+\frac{35}{35}-\frac{28}{35}\\=\frac{50+35-28}{35}\\=\frac{57}{35}\)
11. \(+\left(\frac{4}{7}\right) +\left(\frac{-2}{-5}\right) -\left(\frac{-9}{-12}\right)\\= \frac{4}{7}+ \frac{2}{5}-\frac{9}{12}\\=\frac{4}{7}+\frac{2}{5}-\frac{3}{4}\\=\frac{80}{140}+\frac{56}{140}-\frac{105}{140}\\=\frac{80+56-105}{140}\\=\frac{31}{140}\)
12. \(-\left(\frac{-3}{-8}\right) +\left(\frac{6}{-6}\right) -\left(\frac{9}{2}\right)\\= \frac{-3}{8}- \frac{6}{6}-\frac{9}{2}\\=\frac{-3}{8}-\frac{1}{1}-\frac{9}{2}\\=\frac{-3-1-9}{8}\\=\frac{-13}{8}\)