Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{9}{-7}\right) -\left(\frac{-2}{9}\right) -\left(\frac{5}{2}\right)\\= \frac{9}{7}+ \frac{2}{9}-\frac{5}{2}\\=\frac{162}{126}+\frac{28}{126}-\frac{315}{126}\\=\frac{162+28-315}{126}\\=\frac{-125}{126}\)
2. \(-\left(\frac{-10}{9}\right) +\left(\frac{-7}{9}\right) +\left(\frac{-3}{-4}\right)\\= \frac{10}{9}- \frac{7}{9}+\frac{3}{4}\\=\frac{40}{36}-\frac{28}{36}+\frac{27}{36}\\=\frac{40-28+27}{36}\\=\frac{39}{36}\\=\frac{13}{12}\)
3. \(+\left(\frac{-2}{3}\right) -\left(\frac{4}{4}\right) +\left(\frac{6}{10}\right)\\= \frac{-2}{3}- \frac{4}{4}+\frac{6}{10}\\=\frac{-2}{3}-\frac{1}{1}+\frac{3}{5}\\=\frac{-10}{15}-\frac{15}{15}+\frac{9}{15}\\=\frac{-10-15+9}{15}\\=\frac{-16}{15}\)
4. \(+\left(\frac{9}{5}\right) +\left(\frac{2}{-9}\right) -\left(\frac{-8}{10}\right)\\= \frac{9}{5}- \frac{2}{9}+\frac{8}{10}\\=\frac{9}{5}-\frac{2}{9}+\frac{4}{5}\\=\frac{81}{45}-\frac{10}{45}+\frac{36}{45}\\=\frac{81-10+36}{45}\\=\frac{107}{45}\)
5. \(-\left(\frac{-10}{7}\right) +\left(\frac{4}{-6}\right) +\left(\frac{-3}{11}\right)\\= \frac{10}{7}- \frac{4}{6}-\frac{3}{11}\\=\frac{10}{7}-\frac{2}{3}-\frac{3}{11}\\=\frac{330}{231}-\frac{154}{231}-\frac{63}{231}\\=\frac{330-154-63}{231}\\=\frac{113}{231}\)
6. \(+\left(\frac{9}{-5}\right) +\left(\frac{-6}{5}\right) -\left(\frac{10}{-12}\right)\\= \frac{-9}{5}- \frac{6}{5}+\frac{10}{12}\\=\frac{-9}{5}-\frac{6}{5}+\frac{5}{6}\\=\frac{-54}{30}-\frac{36}{30}+\frac{25}{30}\\=\frac{-54-36+25}{30}\\=\frac{-65}{30}\\=\frac{-13}{6}\)
7. \(-\left(\frac{8}{-3}\right) -\left(\frac{5}{10}\right) +\left(\frac{-3}{8}\right)\\= \frac{8}{3}- \frac{5}{10}-\frac{3}{8}\\=\frac{8}{3}-\frac{1}{2}-\frac{3}{8}\\=\frac{64}{24}-\frac{12}{24}-\frac{9}{24}\\=\frac{64-12-9}{24}\\=\frac{43}{24}\)
8. \(-\left(\frac{6}{7}\right) -\left(\frac{-2}{-5}\right) -\left(\frac{6}{12}\right)\\= \frac{-6}{7}- \frac{2}{5}-\frac{6}{12}\\=\frac{-6}{7}-\frac{2}{5}-\frac{1}{2}\\=\frac{-60}{70}-\frac{28}{70}-\frac{35}{70}\\=\frac{-60-28-35}{70}\\=\frac{-123}{70}\)
9. \(-\left(\frac{-9}{-5}\right) +\left(\frac{-7}{-4}\right) -\left(\frac{7}{-10}\right)\\= \frac{-9}{5}+ \frac{7}{4}+\frac{7}{10}\\=\frac{-36}{20}+\frac{35}{20}+\frac{14}{20}\\=\frac{-36+35+14}{20}\\=\frac{13}{20}\)
10. \(+\left(\frac{9}{-4}\right) -\left(\frac{8}{9}\right) -\left(\frac{-12}{-9}\right)\\= \frac{-9}{4}- \frac{8}{9}-\frac{12}{9}\\=\frac{-9}{4}-\frac{8}{9}-\frac{4}{3}\\=\frac{-81}{36}-\frac{32}{36}-\frac{48}{36}\\=\frac{-81-32-48}{36}\\=\frac{-161}{36}\)
11. \(+\left(\frac{-9}{2}\right) +\left(\frac{-10}{6}\right) -\left(\frac{-10}{-9}\right)\\= \frac{-9}{2}- \frac{10}{6}-\frac{10}{9}\\=\frac{-9}{2}-\frac{5}{3}-\frac{10}{9}\\=\frac{-81}{18}-\frac{30}{18}-\frac{20}{18}\\=\frac{-81-30-20}{18}\\=\frac{-131}{18}\)
12. \(-\left(\frac{-4}{7}\right) +\left(\frac{7}{-5}\right) -\left(\frac{2}{9}\right)\\= \frac{4}{7}- \frac{7}{5}-\frac{2}{9}\\=\frac{180}{315}-\frac{441}{315}-\frac{70}{315}\\=\frac{180-441-70}{315}\\=\frac{-331}{315}\)