Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-7}{-2}\right) +\left(\frac{6}{10}\right) +\left(\frac{-12}{7}\right)\\= \frac{-7}{2}+ \frac{6}{10}-\frac{12}{7}\\=\frac{-7}{2}+\frac{3}{5}-\frac{12}{7}\\=\frac{-245}{70}+\frac{42}{70}-\frac{120}{70}\\=\frac{-245+42-120}{70}\\=\frac{-323}{70}\)
2. \(-\left(\frac{-9}{7}\right) +\left(\frac{6}{10}\right) -\left(\frac{-5}{2}\right)\\= \frac{9}{7}+ \frac{6}{10}+\frac{5}{2}\\=\frac{9}{7}+\frac{3}{5}+\frac{5}{2}\\=\frac{90}{70}+\frac{42}{70}+\frac{175}{70}\\=\frac{90+42+175}{70}\\=\frac{307}{70}\)
3. \(-\left(\frac{-3}{-8}\right) +\left(\frac{-6}{-9}\right) +\left(\frac{-6}{5}\right)\\= \frac{-3}{8}+ \frac{6}{9}-\frac{6}{5}\\=\frac{-3}{8}+\frac{2}{3}-\frac{6}{5}\\=\frac{-45}{120}+\frac{80}{120}-\frac{144}{120}\\=\frac{-45+80-144}{120}\\=\frac{-109}{120}\)
4. \(+\left(\frac{7}{5}\right) -\left(\frac{-8}{-10}\right) +\left(\frac{8}{-5}\right)\\= \frac{7}{5}- \frac{8}{10}-\frac{8}{5}\\=\frac{7}{5}-\frac{4}{5}-\frac{8}{5}\\=\frac{7-4-8}{5}\\=\frac{-5}{5}\\=\frac{-1}{1}\)
5. \(-\left(\frac{5}{9}\right) -\left(\frac{9}{-5}\right) +\left(\frac{-8}{9}\right)\\= \frac{-5}{9}+ \frac{9}{5}-\frac{8}{9}\\=\frac{-25}{45}+\frac{81}{45}-\frac{40}{45}\\=\frac{-25+81-40}{45}\\=\frac{16}{45}\)
6. \(+\left(\frac{9}{-2}\right) -\left(\frac{-9}{6}\right) +\left(\frac{-2}{10}\right)\\= \frac{-9}{2}+ \frac{9}{6}-\frac{2}{10}\\=\frac{-9}{2}+\frac{3}{2}-\frac{1}{5}\\=\frac{-45}{10}+\frac{15}{10}-\frac{2}{10}\\=\frac{-45+15-2}{10}\\=\frac{-32}{10}\\=\frac{-16}{5}\)
7. \(-\left(\frac{3}{2}\right) -\left(\frac{-3}{10}\right) -\left(\frac{2}{-10}\right)\\= \frac{-3}{2}+ \frac{3}{10}+\frac{2}{10}\\=\frac{-3}{2}+\frac{3}{10}+\frac{1}{5}\\=\frac{-15}{10}+\frac{3}{10}+\frac{2}{10}\\=\frac{-15+3+2}{10}\\=\frac{-10}{10}\\=\frac{-1}{1}\)
8. \(+\left(\frac{8}{-9}\right) +\left(\frac{-9}{7}\right) -\left(\frac{-7}{6}\right)\\= \frac{-8}{9}- \frac{9}{7}+\frac{7}{6}\\=\frac{-112}{126}-\frac{162}{126}+\frac{147}{126}\\=\frac{-112-162+147}{126}\\=\frac{-127}{126}\)
9. \(-\left(\frac{8}{3}\right) -\left(\frac{-2}{10}\right) +\left(\frac{-12}{-10}\right)\\= \frac{-8}{3}+ \frac{2}{10}+\frac{12}{10}\\=\frac{-8}{3}+\frac{1}{5}+\frac{6}{5}\\=\frac{-40}{15}+\frac{3}{15}+\frac{18}{15}\\=\frac{-40+3+18}{15}\\=\frac{-19}{15}\)
10. \(+\left(\frac{-3}{-7}\right) +\left(\frac{-7}{7}\right) +\left(\frac{-5}{5}\right)\\= \frac{3}{7}- \frac{7}{7}-\frac{5}{5}\\=\frac{3}{7}-\frac{1}{1}-\frac{1}{1}\\=\frac{3-1-1}{7}\\=\frac{1}{7}\)
11. \(-\left(\frac{-2}{-3}\right) +\left(\frac{4}{-4}\right) +\left(\frac{-4}{9}\right)\\= \frac{-2}{3}- \frac{4}{4}-\frac{4}{9}\\=\frac{-2}{3}-\frac{1}{1}-\frac{4}{9}\\=\frac{-6}{9}-\frac{9}{9}-\frac{4}{9}\\=\frac{-6-9-4}{9}\\=\frac{-19}{9}\)
12. \(+\left(\frac{-6}{5}\right) +\left(\frac{6}{-9}\right) +\left(\frac{-5}{-10}\right)\\= \frac{-6}{5}- \frac{6}{9}+\frac{5}{10}\\=\frac{-6}{5}-\frac{2}{3}+\frac{1}{2}\\=\frac{-36}{30}-\frac{20}{30}+\frac{15}{30}\\=\frac{-36-20+15}{30}\\=\frac{-41}{30}\)