Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-8}{-3}\right) -\left(\frac{10}{8}\right) -\left(\frac{8}{-5}\right)\\= \frac{-8}{3}- \frac{10}{8}+\frac{8}{5}\\=\frac{-8}{3}-\frac{5}{4}+\frac{8}{5}\\=\frac{-160}{60}-\frac{75}{60}+\frac{96}{60}\\=\frac{-160-75+96}{60}\\=\frac{-139}{60}\)
2. \(+\left(\frac{2}{-5}\right) +\left(\frac{8}{2}\right) -\left(\frac{-8}{2}\right)\\= \frac{-2}{5}+ \frac{8}{2}+\frac{8}{2}\\=\frac{-2}{5}+\frac{4}{1}+\frac{4}{1}\\=\frac{-2+4+4}{5}\\=\frac{6}{5}\)
3. \(+\left(\frac{-9}{-4}\right) +\left(\frac{-5}{4}\right) +\left(\frac{9}{-5}\right)\\= \frac{9}{4}- \frac{5}{4}-\frac{9}{5}\\=\frac{45}{20}-\frac{25}{20}-\frac{36}{20}\\=\frac{45-25-36}{20}\\=\frac{-16}{20}\\=\frac{-4}{5}\)
4. \(+\left(\frac{3}{-8}\right) +\left(\frac{-9}{-7}\right) +\left(\frac{3}{12}\right)\\= \frac{-3}{8}+ \frac{9}{7}+\frac{3}{12}\\=\frac{-3}{8}+\frac{9}{7}+\frac{1}{4}\\=\frac{-21}{56}+\frac{72}{56}+\frac{14}{56}\\=\frac{-21+72+14}{56}\\=\frac{65}{56}\)
5. \(-\left(\frac{-2}{-7}\right) +\left(\frac{-6}{8}\right) -\left(\frac{-10}{-10}\right)\\= \frac{-2}{7}- \frac{6}{8}-\frac{10}{10}\\=\frac{-2}{7}-\frac{3}{4}-\frac{1}{1}\\=\frac{-8}{28}-\frac{21}{28}-\frac{28}{28}\\=\frac{-8-21-28}{28}\\=\frac{-57}{28}\)
6. \(+\left(\frac{-7}{-2}\right) -\left(\frac{-9}{7}\right) -\left(\frac{4}{10}\right)\\= \frac{7}{2}+ \frac{9}{7}-\frac{4}{10}\\=\frac{7}{2}+\frac{9}{7}-\frac{2}{5}\\=\frac{245}{70}+\frac{90}{70}-\frac{28}{70}\\=\frac{245+90-28}{70}\\=\frac{307}{70}\)
7. \(-\left(\frac{8}{-7}\right) +\left(\frac{8}{10}\right) +\left(\frac{3}{5}\right)\\= \frac{8}{7}+ \frac{8}{10}+\frac{3}{5}\\=\frac{8}{7}+\frac{4}{5}+\frac{3}{5}\\=\frac{40}{35}+\frac{28}{35}+\frac{21}{35}\\=\frac{40+28+21}{35}\\=\frac{89}{35}\)
8. \(-\left(\frac{4}{-3}\right) +\left(\frac{-8}{8}\right) -\left(\frac{9}{-12}\right)\\= \frac{4}{3}- \frac{8}{8}+\frac{9}{12}\\=\frac{4}{3}-\frac{1}{1}+\frac{3}{4}\\=\frac{16}{12}-\frac{12}{12}+\frac{9}{12}\\=\frac{16-12+9}{12}\\=\frac{13}{12}\)
9. \(-\left(\frac{5}{-6}\right) -\left(\frac{-7}{6}\right) +\left(\frac{-5}{-8}\right)\\= \frac{5}{6}+ \frac{7}{6}+\frac{5}{8}\\=\frac{20}{24}+\frac{28}{24}+\frac{15}{24}\\=\frac{20+28+15}{24}\\=\frac{63}{24}\\=\frac{21}{8}\)
10. \(+\left(\frac{8}{5}\right) +\left(\frac{-9}{8}\right) -\left(\frac{5}{9}\right)\\= \frac{8}{5}- \frac{9}{8}-\frac{5}{9}\\=\frac{576}{360}-\frac{405}{360}-\frac{200}{360}\\=\frac{576-405-200}{360}\\=\frac{-29}{360}\)
11. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-3}{-6}\right) -\left(\frac{7}{-3}\right)\\= \frac{6}{5}+ \frac{3}{6}+\frac{7}{3}\\=\frac{6}{5}+\frac{1}{2}+\frac{7}{3}\\=\frac{36}{30}+\frac{15}{30}+\frac{70}{30}\\=\frac{36+15+70}{30}\\=\frac{121}{30}\)
12. \(-\left(\frac{-9}{8}\right) +\left(\frac{2}{-10}\right) -\left(\frac{-3}{-6}\right)\\= \frac{9}{8}- \frac{2}{10}-\frac{3}{6}\\=\frac{9}{8}-\frac{1}{5}-\frac{1}{2}\\=\frac{45}{40}-\frac{8}{40}-\frac{20}{40}\\=\frac{45-8-20}{40}\\=\frac{17}{40}\)