Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{6}{-5}\right) +\left(\frac{-4}{10}\right) +\left(\frac{5}{5}\right)\\= \frac{-6}{5}- \frac{4}{10}+\frac{5}{5}\\=\frac{-6}{5}-\frac{2}{5}+\frac{1}{1}\\=\frac{-6-2+1}{5}\\=\frac{-7}{5}\)
2. \(+\left(\frac{3}{-5}\right) +\left(\frac{-9}{-4}\right) +\left(\frac{-9}{-2}\right)\\= \frac{-3}{5}+ \frac{9}{4}+\frac{9}{2}\\=\frac{-12}{20}+\frac{45}{20}+\frac{90}{20}\\=\frac{-12+45+90}{20}\\=\frac{123}{20}\)
3. \(-\left(\frac{-5}{-2}\right) -\left(\frac{-10}{-5}\right) +\left(\frac{-10}{-6}\right)\\= \frac{-5}{2}- \frac{10}{5}+\frac{10}{6}\\=\frac{-5}{2}-\frac{2}{1}+\frac{5}{3}\\=\frac{-15}{6}-\frac{12}{6}+\frac{10}{6}\\=\frac{-15-12+10}{6}\\=\frac{-17}{6}\)
4. \(-\left(\frac{-6}{5}\right) +\left(\frac{-2}{-5}\right) -\left(\frac{8}{9}\right)\\= \frac{6}{5}+ \frac{2}{5}-\frac{8}{9}\\=\frac{54}{45}+\frac{18}{45}-\frac{40}{45}\\=\frac{54+18-40}{45}\\=\frac{32}{45}\)
5. \(+\left(\frac{-9}{-7}\right) -\left(\frac{-4}{-10}\right) -\left(\frac{10}{2}\right)\\= \frac{9}{7}- \frac{4}{10}-\frac{10}{2}\\=\frac{9}{7}-\frac{2}{5}-\frac{5}{1}\\=\frac{45}{35}-\frac{14}{35}-\frac{175}{35}\\=\frac{45-14-175}{35}\\=\frac{-144}{35}\)
6. \(-\left(\frac{-3}{7}\right) -\left(\frac{-9}{5}\right) -\left(\frac{-5}{2}\right)\\= \frac{3}{7}+ \frac{9}{5}+\frac{5}{2}\\=\frac{30}{70}+\frac{126}{70}+\frac{175}{70}\\=\frac{30+126+175}{70}\\=\frac{331}{70}\)
7. \(+\left(\frac{-2}{3}\right) +\left(\frac{2}{-4}\right) +\left(\frac{-12}{8}\right)\\= \frac{-2}{3}- \frac{2}{4}-\frac{12}{8}\\=\frac{-2}{3}-\frac{1}{2}-\frac{3}{2}\\=\frac{-4}{6}-\frac{3}{6}-\frac{9}{6}\\=\frac{-4-3-9}{6}\\=\frac{-16}{6}\\=\frac{-8}{3}\)
8. \(+\left(\frac{8}{3}\right) -\left(\frac{8}{-8}\right) +\left(\frac{-8}{-9}\right)\\= \frac{8}{3}+ \frac{8}{8}+\frac{8}{9}\\=\frac{8}{3}+\frac{1}{1}+\frac{8}{9}\\=\frac{24}{9}+\frac{9}{9}+\frac{8}{9}\\=\frac{24+9+8}{9}\\=\frac{41}{9}\)
9. \(-\left(\frac{2}{-5}\right) +\left(\frac{10}{-3}\right) -\left(\frac{-9}{-2}\right)\\= \frac{2}{5}- \frac{10}{3}-\frac{9}{2}\\=\frac{12}{30}-\frac{100}{30}-\frac{135}{30}\\=\frac{12-100-135}{30}\\=\frac{-223}{30}\)
10. \(-\left(\frac{-5}{-4}\right) -\left(\frac{-6}{-6}\right) +\left(\frac{5}{2}\right)\\= \frac{-5}{4}- \frac{6}{6}+\frac{5}{2}\\=\frac{-5}{4}-\frac{1}{1}+\frac{5}{2}\\=\frac{-5-1+5}{4}\\=\frac{-1}{4}\)
11. \(+\left(\frac{-7}{9}\right) -\left(\frac{-6}{-3}\right) +\left(\frac{-6}{3}\right)\\= \frac{-7}{9}- \frac{6}{3}-\frac{6}{3}\\=\frac{-7}{9}-\frac{2}{1}-\frac{2}{1}\\=\frac{-7-2-2}{9}\\=\frac{-11}{9}\)
12. \(+\left(\frac{-9}{4}\right) +\left(\frac{-10}{-8}\right) -\left(\frac{-6}{-3}\right)\\= \frac{-9}{4}+ \frac{10}{8}-\frac{6}{3}\\=\frac{-9}{4}+\frac{5}{4}-\frac{2}{1}\\=\frac{-9+5-2}{4}\\=\frac{-6}{4}\\=\frac{-3}{2}\)