Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{6}{7}\right) +\left(\frac{-4}{10}\right) +\left(\frac{3}{-4}\right)\\= \frac{-6}{7}- \frac{4}{10}-\frac{3}{4}\\=\frac{-6}{7}-\frac{2}{5}-\frac{3}{4}\\=\frac{-120}{140}-\frac{56}{140}-\frac{105}{140}\\=\frac{-120-56-105}{140}\\=\frac{-281}{140}\)
2. \(-\left(\frac{3}{-7}\right) +\left(\frac{5}{-10}\right) +\left(\frac{-4}{-2}\right)\\= \frac{3}{7}- \frac{5}{10}+\frac{4}{2}\\=\frac{3}{7}-\frac{1}{2}+\frac{2}{1}\\=\frac{6}{14}-\frac{7}{14}+\frac{28}{14}\\=\frac{6-7+28}{14}\\=\frac{27}{14}\)
3. \(+\left(\frac{6}{-5}\right) +\left(\frac{-7}{-9}\right) +\left(\frac{-2}{-4}\right)\\= \frac{-6}{5}+ \frac{7}{9}+\frac{2}{4}\\=\frac{-6}{5}+\frac{7}{9}+\frac{1}{2}\\=\frac{-108}{90}+\frac{70}{90}+\frac{45}{90}\\=\frac{-108+70+45}{90}\\=\frac{7}{90}\)
4. \(+\left(\frac{5}{2}\right) +\left(\frac{-7}{7}\right) -\left(\frac{10}{-9}\right)\\= \frac{5}{2}- \frac{7}{7}+\frac{10}{9}\\=\frac{5}{2}-\frac{1}{1}+\frac{10}{9}\\=\frac{45}{18}-\frac{18}{18}+\frac{20}{18}\\=\frac{45-18+20}{18}\\=\frac{47}{18}\)
5. \(+\left(\frac{4}{5}\right) -\left(\frac{6}{2}\right) -\left(\frac{4}{-10}\right)\\= \frac{4}{5}- \frac{6}{2}+\frac{4}{10}\\=\frac{4}{5}-\frac{3}{1}+\frac{2}{5}\\=\frac{4-3+2}{5}\\=\frac{3}{5}\)
6. \(+\left(\frac{-3}{-2}\right) +\left(\frac{-5}{5}\right) +\left(\frac{11}{-8}\right)\\= \frac{3}{2}- \frac{5}{5}-\frac{11}{8}\\=\frac{3}{2}-\frac{1}{1}-\frac{11}{8}\\=\frac{12}{8}-\frac{8}{8}-\frac{11}{8}\\=\frac{12-8-11}{8}\\=\frac{-7}{8}\)
7. \(-\left(\frac{7}{4}\right) -\left(\frac{-4}{9}\right) -\left(\frac{12}{5}\right)\\= \frac{-7}{4}+ \frac{4}{9}-\frac{12}{5}\\=\frac{-315}{180}+\frac{80}{180}-\frac{432}{180}\\=\frac{-315+80-432}{180}\\=\frac{-667}{180}\)
8. \(-\left(\frac{7}{2}\right) +\left(\frac{-9}{2}\right) +\left(\frac{-7}{-8}\right)\\= \frac{-7}{2}- \frac{9}{2}+\frac{7}{8}\\=\frac{-28}{8}-\frac{36}{8}+\frac{7}{8}\\=\frac{-28-36+7}{8}\\=\frac{-57}{8}\)
9. \(+\left(\frac{2}{-9}\right) +\left(\frac{4}{-4}\right) +\left(\frac{2}{10}\right)\\= \frac{-2}{9}- \frac{4}{4}+\frac{2}{10}\\=\frac{-2}{9}-\frac{1}{1}+\frac{1}{5}\\=\frac{-10}{45}-\frac{45}{45}+\frac{9}{45}\\=\frac{-10-45+9}{45}\\=\frac{-46}{45}\)
10. \(-\left(\frac{-10}{-7}\right) -\left(\frac{5}{-7}\right) -\left(\frac{3}{5}\right)\\= \frac{-10}{7}+ \frac{5}{7}-\frac{3}{5}\\=\frac{-50}{35}+\frac{25}{35}-\frac{21}{35}\\=\frac{-50+25-21}{35}\\=\frac{-46}{35}\)
11. \(+\left(\frac{-2}{5}\right) +\left(\frac{6}{-6}\right) -\left(\frac{6}{-4}\right)\\= \frac{-2}{5}- \frac{6}{6}+\frac{6}{4}\\=\frac{-2}{5}-\frac{1}{1}+\frac{3}{2}\\=\frac{-4}{10}-\frac{10}{10}+\frac{15}{10}\\=\frac{-4-10+15}{10}\\=\frac{1}{10}\)
12. \(-\left(\frac{9}{2}\right) -\left(\frac{2}{-4}\right) -\left(\frac{-10}{-4}\right)\\= \frac{-9}{2}+ \frac{2}{4}-\frac{10}{4}\\=\frac{-9}{2}+\frac{1}{2}-\frac{5}{2}\\=\frac{-9+1-5}{2}\\=\frac{-13}{2}\)