Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{6}\right) +\left(\frac{-2}{-10}\right) -\left(\frac{10}{6}\right)\\= \frac{-5}{6}+ \frac{2}{10}-\frac{10}{6}\\=\frac{-5}{6}+\frac{1}{5}-\frac{5}{3}\\=\frac{-25}{30}+\frac{6}{30}-\frac{50}{30}\\=\frac{-25+6-50}{30}\\=\frac{-69}{30}\\=\frac{-23}{10}\)
2. \(+\left(\frac{4}{-7}\right) +\left(\frac{8}{-8}\right) +\left(\frac{11}{11}\right)\\= \frac{-4}{7}- \frac{8}{8}+\frac{11}{11}\\=\frac{-4}{7}-\frac{1}{1}+\frac{1}{1}\\=\frac{-4-1+1}{7}\\=\frac{-4}{7}\)
3. \(+\left(\frac{-3}{2}\right) +\left(\frac{9}{-6}\right) -\left(\frac{7}{4}\right)\\= \frac{-3}{2}- \frac{9}{6}-\frac{7}{4}\\=\frac{-3}{2}-\frac{3}{2}-\frac{7}{4}\\=\frac{-6}{4}-\frac{6}{4}-\frac{7}{4}\\=\frac{-6-6-7}{4}\\=\frac{-19}{4}\)
4. \(-\left(\frac{7}{2}\right) +\left(\frac{10}{-6}\right) -\left(\frac{7}{-3}\right)\\= \frac{-7}{2}- \frac{10}{6}+\frac{7}{3}\\=\frac{-7}{2}-\frac{5}{3}+\frac{7}{3}\\=\frac{-21}{6}-\frac{10}{6}+\frac{14}{6}\\=\frac{-21-10+14}{6}\\=\frac{-17}{6}\)
5. \(-\left(\frac{-5}{2}\right) -\left(\frac{-8}{-4}\right) -\left(\frac{-10}{-11}\right)\\= \frac{5}{2}- \frac{8}{4}-\frac{10}{11}\\=\frac{5}{2}-\frac{2}{1}-\frac{10}{11}\\=\frac{55}{22}-\frac{44}{22}-\frac{20}{22}\\=\frac{55-44-20}{22}\\=\frac{-9}{22}\)
6. \(-\left(\frac{7}{-8}\right) -\left(\frac{8}{7}\right) +\left(\frac{6}{5}\right)\\= \frac{7}{8}- \frac{8}{7}+\frac{6}{5}\\=\frac{245}{280}-\frac{320}{280}+\frac{336}{280}\\=\frac{245-320+336}{280}\\=\frac{261}{280}\)
7. \(-\left(\frac{-2}{-9}\right) -\left(\frac{-5}{4}\right) +\left(\frac{4}{-4}\right)\\= \frac{-2}{9}+ \frac{5}{4}-\frac{4}{4}\\=\frac{-2}{9}+\frac{5}{4}-\frac{1}{1}\\=\frac{-8}{36}+\frac{45}{36}-\frac{36}{36}\\=\frac{-8+45-36}{36}\\=\frac{1}{36}\)
8. \(+\left(\frac{8}{3}\right) +\left(\frac{-4}{10}\right) +\left(\frac{3}{3}\right)\\= \frac{8}{3}- \frac{4}{10}+\frac{3}{3}\\=\frac{8}{3}-\frac{2}{5}+\frac{1}{1}\\=\frac{40}{15}-\frac{6}{15}+\frac{15}{15}\\=\frac{40-6+15}{15}\\=\frac{49}{15}\)
9. \(+\left(\frac{2}{-3}\right) +\left(\frac{-8}{-4}\right) -\left(\frac{-6}{-10}\right)\\= \frac{-2}{3}+ \frac{8}{4}-\frac{6}{10}\\=\frac{-2}{3}+\frac{2}{1}-\frac{3}{5}\\=\frac{-10}{15}+\frac{30}{15}-\frac{9}{15}\\=\frac{-10+30-9}{15}\\=\frac{11}{15}\)
10. \(-\left(\frac{-7}{-5}\right) +\left(\frac{3}{8}\right) +\left(\frac{4}{-4}\right)\\= \frac{-7}{5}+ \frac{3}{8}-\frac{4}{4}\\=\frac{-7}{5}+\frac{3}{8}-\frac{1}{1}\\=\frac{-56}{40}+\frac{15}{40}-\frac{40}{40}\\=\frac{-56+15-40}{40}\\=\frac{-81}{40}\)
11. \(+\left(\frac{-8}{-3}\right) -\left(\frac{8}{5}\right) -\left(\frac{5}{-5}\right)\\= \frac{8}{3}- \frac{8}{5}+\frac{5}{5}\\=\frac{8}{3}-\frac{8}{5}+\frac{1}{1}\\=\frac{40}{15}-\frac{24}{15}+\frac{15}{15}\\=\frac{40-24+15}{15}\\=\frac{31}{15}\)
12. \(-\left(\frac{10}{-7}\right) -\left(\frac{9}{3}\right) +\left(\frac{2}{7}\right)\\= \frac{10}{7}- \frac{9}{3}+\frac{2}{7}\\=\frac{10}{7}-\frac{3}{1}+\frac{2}{7}\\=\frac{10-3+2}{7}\\=\frac{9}{7}\)