Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{-8}\right) +\left(\frac{10}{10}\right) +\left(\frac{5}{-11}\right)\\= \frac{-5}{8}+ \frac{10}{10}-\frac{5}{11}\\=\frac{-5}{8}+\frac{1}{1}-\frac{5}{11}\\=\frac{-55}{88}+\frac{88}{88}-\frac{40}{88}\\=\frac{-55+88-40}{88}\\=\frac{-7}{88}\)
2. \(-\left(\frac{8}{5}\right) -\left(\frac{-10}{9}\right) +\left(\frac{-6}{11}\right)\\= \frac{-8}{5}+ \frac{10}{9}-\frac{6}{11}\\=\frac{-792}{495}+\frac{550}{495}-\frac{270}{495}\\=\frac{-792+550-270}{495}\\=\frac{-512}{495}\)
3. \(+\left(\frac{5}{3}\right) -\left(\frac{-8}{4}\right) -\left(\frac{2}{-9}\right)\\= \frac{5}{3}+ \frac{8}{4}+\frac{2}{9}\\=\frac{5}{3}+\frac{2}{1}+\frac{2}{9}\\=\frac{15}{9}+\frac{18}{9}+\frac{2}{9}\\=\frac{15+18+2}{9}\\=\frac{35}{9}\)
4. \(-\left(\frac{-2}{9}\right) -\left(\frac{6}{-7}\right) -\left(\frac{11}{-7}\right)\\= \frac{2}{9}+ \frac{6}{7}+\frac{11}{7}\\=\frac{14}{63}+\frac{54}{63}+\frac{99}{63}\\=\frac{14+54+99}{63}\\=\frac{167}{63}\)
5. \(+\left(\frac{6}{5}\right) +\left(\frac{9}{2}\right) +\left(\frac{5}{10}\right)\\= \frac{6}{5}+ \frac{9}{2}+\frac{5}{10}\\=\frac{6}{5}+\frac{9}{2}+\frac{1}{2}\\=\frac{12}{10}+\frac{45}{10}+\frac{5}{10}\\=\frac{12+45+5}{10}\\=\frac{62}{10}\\=\frac{31}{5}\)
6. \(-\left(\frac{9}{-4}\right) +\left(\frac{10}{-9}\right) -\left(\frac{-9}{7}\right)\\= \frac{9}{4}- \frac{10}{9}+\frac{9}{7}\\=\frac{567}{252}-\frac{280}{252}+\frac{324}{252}\\=\frac{567-280+324}{252}\\=\frac{611}{252}\)
7. \(-\left(\frac{-7}{-5}\right) -\left(\frac{8}{10}\right) +\left(\frac{-5}{9}\right)\\= \frac{-7}{5}- \frac{8}{10}-\frac{5}{9}\\=\frac{-7}{5}-\frac{4}{5}-\frac{5}{9}\\=\frac{-63}{45}-\frac{36}{45}-\frac{25}{45}\\=\frac{-63-36-25}{45}\\=\frac{-124}{45}\)
8. \(+\left(\frac{7}{-9}\right) +\left(\frac{-10}{9}\right) -\left(\frac{-6}{7}\right)\\= \frac{-7}{9}- \frac{10}{9}+\frac{6}{7}\\=\frac{-49}{63}-\frac{70}{63}+\frac{54}{63}\\=\frac{-49-70+54}{63}\\=\frac{-65}{63}\)
9. \(-\left(\frac{3}{-2}\right) -\left(\frac{9}{3}\right) -\left(\frac{-11}{9}\right)\\= \frac{3}{2}- \frac{9}{3}+\frac{11}{9}\\=\frac{3}{2}-\frac{3}{1}+\frac{11}{9}\\=\frac{27}{18}-\frac{54}{18}+\frac{22}{18}\\=\frac{27-54+22}{18}\\=\frac{-5}{18}\)
10. \(+\left(\frac{5}{2}\right) -\left(\frac{6}{2}\right) -\left(\frac{7}{-12}\right)\\= \frac{5}{2}- \frac{6}{2}+\frac{7}{12}\\=\frac{5}{2}-\frac{3}{1}+\frac{7}{12}\\=\frac{30}{12}-\frac{36}{12}+\frac{7}{12}\\=\frac{30-36+7}{12}\\=\frac{1}{12}\)
11. \(+\left(\frac{3}{-7}\right) -\left(\frac{-10}{7}\right) +\left(\frac{-8}{-9}\right)\\= \frac{-3}{7}+ \frac{10}{7}+\frac{8}{9}\\=\frac{-27}{63}+\frac{90}{63}+\frac{56}{63}\\=\frac{-27+90+56}{63}\\=\frac{119}{63}\\=\frac{17}{9}\)
12. \(+\left(\frac{6}{5}\right) +\left(\frac{-6}{-10}\right) +\left(\frac{7}{3}\right)\\= \frac{6}{5}+ \frac{6}{10}+\frac{7}{3}\\=\frac{6}{5}+\frac{3}{5}+\frac{7}{3}\\=\frac{18}{15}+\frac{9}{15}+\frac{35}{15}\\=\frac{18+9+35}{15}\\=\frac{62}{15}\)