Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{-8}\right) -\left(\frac{-4}{-10}\right) -\left(\frac{8}{6}\right)\\= \frac{3}{8}- \frac{4}{10}-\frac{8}{6}\\=\frac{3}{8}-\frac{2}{5}-\frac{4}{3}\\=\frac{45}{120}-\frac{48}{120}-\frac{160}{120}\\=\frac{45-48-160}{120}\\=\frac{-163}{120}\)
2. \(+\left(\frac{6}{-5}\right) -\left(\frac{6}{8}\right) -\left(\frac{11}{8}\right)\\= \frac{-6}{5}- \frac{6}{8}-\frac{11}{8}\\=\frac{-6}{5}-\frac{3}{4}-\frac{11}{8}\\=\frac{-48}{40}-\frac{30}{40}-\frac{55}{40}\\=\frac{-48-30-55}{40}\\=\frac{-133}{40}\)
3. \(+\left(\frac{-4}{-7}\right) +\left(\frac{5}{5}\right) +\left(\frac{2}{-6}\right)\\= \frac{4}{7}+ \frac{5}{5}-\frac{2}{6}\\=\frac{4}{7}+\frac{1}{1}-\frac{1}{3}\\=\frac{12}{21}+\frac{21}{21}-\frac{7}{21}\\=\frac{12+21-7}{21}\\=\frac{26}{21}\)
4. \(+\left(\frac{9}{-2}\right) +\left(\frac{9}{-7}\right) +\left(\frac{-5}{-12}\right)\\= \frac{-9}{2}- \frac{9}{7}+\frac{5}{12}\\=\frac{-378}{84}-\frac{108}{84}+\frac{35}{84}\\=\frac{-378-108+35}{84}\\=\frac{-451}{84}\)
5. \(+\left(\frac{6}{-5}\right) -\left(\frac{10}{-9}\right) +\left(\frac{12}{-5}\right)\\= \frac{-6}{5}+ \frac{10}{9}-\frac{12}{5}\\=\frac{-54}{45}+\frac{50}{45}-\frac{108}{45}\\=\frac{-54+50-108}{45}\\=\frac{-112}{45}\)
6. \(+\left(\frac{-6}{-7}\right) -\left(\frac{4}{-7}\right) +\left(\frac{12}{11}\right)\\= \frac{6}{7}+ \frac{4}{7}+\frac{12}{11}\\=\frac{66}{77}+\frac{44}{77}+\frac{84}{77}\\=\frac{66+44+84}{77}\\=\frac{194}{77}\)
7. \(+\left(\frac{-7}{6}\right) -\left(\frac{4}{-3}\right) -\left(\frac{-4}{8}\right)\\= \frac{-7}{6}+ \frac{4}{3}+\frac{4}{8}\\=\frac{-7}{6}+\frac{4}{3}+\frac{1}{2}\\=\frac{-7+4+1}{6}\\=\frac{-2}{6}\\=\frac{-1}{3}\)
8. \(-\left(\frac{6}{5}\right) -\left(\frac{7}{-4}\right) +\left(\frac{-5}{4}\right)\\= \frac{-6}{5}+ \frac{7}{4}-\frac{5}{4}\\=\frac{-24}{20}+\frac{35}{20}-\frac{25}{20}\\=\frac{-24+35-25}{20}\\=\frac{-14}{20}\\=\frac{-7}{10}\)
9. \(+\left(\frac{-9}{4}\right) -\left(\frac{8}{-10}\right) -\left(\frac{-3}{-2}\right)\\= \frac{-9}{4}+ \frac{8}{10}-\frac{3}{2}\\=\frac{-9}{4}+\frac{4}{5}-\frac{3}{2}\\=\frac{-45}{20}+\frac{16}{20}-\frac{30}{20}\\=\frac{-45+16-30}{20}\\=\frac{-59}{20}\)
10. \(+\left(\frac{-6}{5}\right) +\left(\frac{-9}{-8}\right) +\left(\frac{11}{-9}\right)\\= \frac{-6}{5}+ \frac{9}{8}-\frac{11}{9}\\=\frac{-432}{360}+\frac{405}{360}-\frac{440}{360}\\=\frac{-432+405-440}{360}\\=\frac{-467}{360}\)
11. \(+\left(\frac{9}{-7}\right) +\left(\frac{-6}{-10}\right) -\left(\frac{-9}{5}\right)\\= \frac{-9}{7}+ \frac{6}{10}+\frac{9}{5}\\=\frac{-9}{7}+\frac{3}{5}+\frac{9}{5}\\=\frac{-45}{35}+\frac{21}{35}+\frac{63}{35}\\=\frac{-45+21+63}{35}\\=\frac{39}{35}\)
12. \(-\left(\frac{-10}{-3}\right) -\left(\frac{-10}{3}\right) -\left(\frac{-8}{8}\right)\\= \frac{-10}{3}+ \frac{10}{3}+\frac{8}{8}\\=\frac{-10}{3}+\frac{10}{3}+\frac{1}{1}\\=\frac{-10+10+1}{3}\\=\frac{1}{3}\)