Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{5}{4}\right) -\left(\frac{8}{-9}\right) -\left(\frac{7}{-5}\right)\\= \frac{5}{4}+ \frac{8}{9}+\frac{7}{5}\\=\frac{225}{180}+\frac{160}{180}+\frac{252}{180}\\=\frac{225+160+252}{180}\\=\frac{637}{180}\)
2. \(-\left(\frac{-8}{-5}\right) +\left(\frac{9}{-3}\right) -\left(\frac{-8}{-6}\right)\\= \frac{-8}{5}- \frac{9}{3}-\frac{8}{6}\\=\frac{-8}{5}-\frac{3}{1}-\frac{4}{3}\\=\frac{-24}{15}-\frac{45}{15}-\frac{20}{15}\\=\frac{-24-45-20}{15}\\=\frac{-89}{15}\)
3. \(+\left(\frac{8}{-3}\right) +\left(\frac{-6}{2}\right) +\left(\frac{-9}{-9}\right)\\= \frac{-8}{3}- \frac{6}{2}+\frac{9}{9}\\=\frac{-8}{3}-\frac{3}{1}+\frac{1}{1}\\=\frac{-8-3+1}{3}\\=\frac{-10}{3}\)
4. \(+\left(\frac{-9}{-7}\right) +\left(\frac{-6}{10}\right) -\left(\frac{-7}{-5}\right)\\= \frac{9}{7}- \frac{6}{10}-\frac{7}{5}\\=\frac{9}{7}-\frac{3}{5}-\frac{7}{5}\\=\frac{45}{35}-\frac{21}{35}-\frac{49}{35}\\=\frac{45-21-49}{35}\\=\frac{-25}{35}\\=\frac{-5}{7}\)
5. \(-\left(\frac{-9}{2}\right) -\left(\frac{7}{3}\right) -\left(\frac{-12}{-6}\right)\\= \frac{9}{2}- \frac{7}{3}-\frac{12}{6}\\=\frac{9}{2}-\frac{7}{3}-\frac{2}{1}\\=\frac{27}{6}-\frac{14}{6}-\frac{12}{6}\\=\frac{27-14-12}{6}\\=\frac{1}{6}\)
6. \(-\left(\frac{-7}{2}\right) -\left(\frac{-4}{-2}\right) -\left(\frac{-10}{8}\right)\\= \frac{7}{2}- \frac{4}{2}+\frac{10}{8}\\=\frac{7}{2}-\frac{2}{1}+\frac{5}{4}\\=\frac{14}{4}-\frac{8}{4}+\frac{5}{4}\\=\frac{14-8+5}{4}\\=\frac{11}{4}\)
7. \(+\left(\frac{-6}{5}\right) -\left(\frac{8}{-4}\right) -\left(\frac{-11}{4}\right)\\= \frac{-6}{5}+ \frac{8}{4}+\frac{11}{4}\\=\frac{-6}{5}+\frac{2}{1}+\frac{11}{4}\\=\frac{-24}{20}+\frac{40}{20}+\frac{55}{20}\\=\frac{-24+40+55}{20}\\=\frac{71}{20}\)
8. \(-\left(\frac{-4}{-9}\right) +\left(\frac{6}{5}\right) -\left(\frac{8}{-12}\right)\\= \frac{-4}{9}+ \frac{6}{5}+\frac{8}{12}\\=\frac{-4}{9}+\frac{6}{5}+\frac{2}{3}\\=\frac{-20}{45}+\frac{54}{45}+\frac{30}{45}\\=\frac{-20+54+30}{45}\\=\frac{64}{45}\)
9. \(-\left(\frac{-3}{4}\right) +\left(\frac{5}{10}\right) +\left(\frac{-9}{5}\right)\\= \frac{3}{4}+ \frac{5}{10}-\frac{9}{5}\\=\frac{3}{4}+\frac{1}{2}-\frac{9}{5}\\=\frac{15}{20}+\frac{10}{20}-\frac{36}{20}\\=\frac{15+10-36}{20}\\=\frac{-11}{20}\)
10. \(-\left(\frac{-9}{2}\right) +\left(\frac{2}{8}\right) +\left(\frac{6}{-2}\right)\\= \frac{9}{2}+ \frac{2}{8}-\frac{6}{2}\\=\frac{9}{2}+\frac{1}{4}-\frac{3}{1}\\=\frac{18}{4}+\frac{1}{4}-\frac{12}{4}\\=\frac{18+1-12}{4}\\=\frac{7}{4}\)
11. \(-\left(\frac{4}{7}\right) -\left(\frac{8}{-4}\right) +\left(\frac{-3}{6}\right)\\= \frac{-4}{7}+ \frac{8}{4}-\frac{3}{6}\\=\frac{-4}{7}+\frac{2}{1}-\frac{1}{2}\\=\frac{-8}{14}+\frac{28}{14}-\frac{7}{14}\\=\frac{-8+28-7}{14}\\=\frac{13}{14}\)
12. \(+\left(\frac{-7}{6}\right) +\left(\frac{-7}{-4}\right) -\left(\frac{-10}{3}\right)\\= \frac{-7}{6}+ \frac{7}{4}+\frac{10}{3}\\=\frac{-14}{12}+\frac{21}{12}+\frac{40}{12}\\=\frac{-14+21+40}{12}\\=\frac{47}{12}\)