Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{4}{3}\right) -\left(\frac{-3}{2}\right) -\left(\frac{8}{3}\right)\\= \frac{4}{3}+ \frac{3}{2}-\frac{8}{3}\\=\frac{8}{6}+\frac{9}{6}-\frac{16}{6}\\=\frac{8+9-16}{6}\\=\frac{1}{6}\)
2. \(-\left(\frac{6}{-5}\right) +\left(\frac{3}{3}\right) +\left(\frac{6}{-5}\right)\\= \frac{6}{5}+ \frac{3}{3}-\frac{6}{5}\\=\frac{6}{5}+\frac{1}{1}-\frac{6}{5}\\=\frac{6+1-6}{5}\\=\frac{1}{5}\)
3. \(-\left(\frac{-5}{8}\right) -\left(\frac{7}{-2}\right) +\left(\frac{-8}{-4}\right)\\= \frac{5}{8}+ \frac{7}{2}+\frac{8}{4}\\=\frac{5}{8}+\frac{7}{2}+\frac{2}{1}\\=\frac{5+7+2}{8}\\=\frac{14}{8}\\=\frac{7}{4}\)
4. \(-\left(\frac{9}{7}\right) -\left(\frac{10}{8}\right) +\left(\frac{-11}{3}\right)\\= \frac{-9}{7}- \frac{10}{8}-\frac{11}{3}\\=\frac{-9}{7}-\frac{5}{4}-\frac{11}{3}\\=\frac{-108}{84}-\frac{105}{84}-\frac{308}{84}\\=\frac{-108-105-308}{84}\\=\frac{-521}{84}\)
5. \(+\left(\frac{-3}{7}\right) -\left(\frac{-6}{2}\right) -\left(\frac{-8}{-7}\right)\\= \frac{-3}{7}+ \frac{6}{2}-\frac{8}{7}\\=\frac{-3}{7}+\frac{3}{1}-\frac{8}{7}\\=\frac{-3+3-8}{7}\\=\frac{-8}{7}\)
6. \(-\left(\frac{-8}{7}\right) +\left(\frac{-4}{5}\right) -\left(\frac{-10}{-5}\right)\\= \frac{8}{7}- \frac{4}{5}-\frac{10}{5}\\=\frac{8}{7}-\frac{4}{5}-\frac{2}{1}\\=\frac{40}{35}-\frac{28}{35}-\frac{70}{35}\\=\frac{40-28-70}{35}\\=\frac{-58}{35}\)
7. \(-\left(\frac{-9}{-8}\right) -\left(\frac{9}{-8}\right) +\left(\frac{-2}{10}\right)\\= \frac{-9}{8}+ \frac{9}{8}-\frac{2}{10}\\=\frac{-9}{8}+\frac{9}{8}-\frac{1}{5}\\=\frac{-45}{40}+\frac{45}{40}-\frac{8}{40}\\=\frac{-45+45-8}{40}\\=\frac{-8}{40}\\=\frac{-1}{5}\)
8. \(-\left(\frac{-9}{-2}\right) +\left(\frac{6}{9}\right) -\left(\frac{-11}{-11}\right)\\= \frac{-9}{2}+ \frac{6}{9}-\frac{11}{11}\\=\frac{-9}{2}+\frac{2}{3}-\frac{1}{1}\\=\frac{-27}{6}+\frac{4}{6}-\frac{6}{6}\\=\frac{-27+4-6}{6}\\=\frac{-29}{6}\)
9. \(+\left(\frac{6}{7}\right) +\left(\frac{-4}{-3}\right) -\left(\frac{4}{-6}\right)\\= \frac{6}{7}+ \frac{4}{3}+\frac{4}{6}\\=\frac{6}{7}+\frac{4}{3}+\frac{2}{3}\\=\frac{18}{21}+\frac{28}{21}+\frac{14}{21}\\=\frac{18+28+14}{21}\\=\frac{60}{21}\\=\frac{20}{7}\)
10. \(-\left(\frac{-8}{-3}\right) +\left(\frac{5}{8}\right) -\left(\frac{3}{4}\right)\\= \frac{-8}{3}+ \frac{5}{8}-\frac{3}{4}\\=\frac{-64}{24}+\frac{15}{24}-\frac{18}{24}\\=\frac{-64+15-18}{24}\\=\frac{-67}{24}\)
11. \(+\left(\frac{-9}{2}\right) +\left(\frac{-7}{-7}\right) +\left(\frac{-3}{-4}\right)\\= \frac{-9}{2}+ \frac{7}{7}+\frac{3}{4}\\=\frac{-9}{2}+\frac{1}{1}+\frac{3}{4}\\=\frac{-18}{4}+\frac{4}{4}+\frac{3}{4}\\=\frac{-18+4+3}{4}\\=\frac{-11}{4}\)
12. \(+\left(\frac{-2}{-3}\right) -\left(\frac{8}{-6}\right) -\left(\frac{-2}{-10}\right)\\= \frac{2}{3}+ \frac{8}{6}-\frac{2}{10}\\=\frac{2}{3}+\frac{4}{3}-\frac{1}{5}\\=\frac{10}{15}+\frac{20}{15}-\frac{3}{15}\\=\frac{10+20-3}{15}\\=\frac{27}{15}\\=\frac{9}{5}\)