Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{10}{3}\right) -\left(\frac{8}{6}\right) -\left(\frac{-7}{-10}\right)\\= \frac{-10}{3}- \frac{8}{6}-\frac{7}{10}\\=\frac{-10}{3}-\frac{4}{3}-\frac{7}{10}\\=\frac{-100}{30}-\frac{40}{30}-\frac{21}{30}\\=\frac{-100-40-21}{30}\\=\frac{-161}{30}\)
2. \(+\left(\frac{6}{-5}\right) -\left(\frac{-7}{-10}\right) +\left(\frac{7}{-8}\right)\\= \frac{-6}{5}- \frac{7}{10}-\frac{7}{8}\\=\frac{-48}{40}-\frac{28}{40}-\frac{35}{40}\\=\frac{-48-28-35}{40}\\=\frac{-111}{40}\)
3. \(+\left(\frac{-3}{2}\right) +\left(\frac{4}{-7}\right) -\left(\frac{3}{-2}\right)\\= \frac{-3}{2}- \frac{4}{7}+\frac{3}{2}\\=\frac{-21}{14}-\frac{8}{14}+\frac{21}{14}\\=\frac{-21-8+21}{14}\\=\frac{-8}{14}\\=\frac{-4}{7}\)
4. \(+\left(\frac{8}{9}\right) +\left(\frac{-7}{5}\right) +\left(\frac{-9}{4}\right)\\= \frac{8}{9}- \frac{7}{5}-\frac{9}{4}\\=\frac{160}{180}-\frac{252}{180}-\frac{405}{180}\\=\frac{160-252-405}{180}\\=\frac{-497}{180}\)
5. \(+\left(\frac{-9}{7}\right) -\left(\frac{-9}{-3}\right) +\left(\frac{10}{4}\right)\\= \frac{-9}{7}- \frac{9}{3}+\frac{10}{4}\\=\frac{-9}{7}-\frac{3}{1}+\frac{5}{2}\\=\frac{-18}{14}-\frac{42}{14}+\frac{35}{14}\\=\frac{-18-42+35}{14}\\=\frac{-25}{14}\)
6. \(-\left(\frac{7}{-6}\right) +\left(\frac{-8}{2}\right) -\left(\frac{-8}{-9}\right)\\= \frac{7}{6}- \frac{8}{2}-\frac{8}{9}\\=\frac{7}{6}-\frac{4}{1}-\frac{8}{9}\\=\frac{21}{18}-\frac{72}{18}-\frac{16}{18}\\=\frac{21-72-16}{18}\\=\frac{-67}{18}\)
7. \(-\left(\frac{-2}{-5}\right) -\left(\frac{10}{7}\right) -\left(\frac{-5}{-11}\right)\\= \frac{-2}{5}- \frac{10}{7}-\frac{5}{11}\\=\frac{-154}{385}-\frac{550}{385}-\frac{175}{385}\\=\frac{-154-550-175}{385}\\=\frac{-879}{385}\)
8. \(-\left(\frac{-7}{8}\right) +\left(\frac{-8}{8}\right) -\left(\frac{11}{6}\right)\\= \frac{7}{8}- \frac{8}{8}-\frac{11}{6}\\=\frac{7}{8}-\frac{1}{1}-\frac{11}{6}\\=\frac{21}{24}-\frac{24}{24}-\frac{44}{24}\\=\frac{21-24-44}{24}\\=\frac{-47}{24}\)
9. \(-\left(\frac{3}{8}\right) +\left(\frac{9}{-3}\right) +\left(\frac{-3}{-9}\right)\\= \frac{-3}{8}- \frac{9}{3}+\frac{3}{9}\\=\frac{-3}{8}-\frac{3}{1}+\frac{1}{3}\\=\frac{-9}{24}-\frac{72}{24}+\frac{8}{24}\\=\frac{-9-72+8}{24}\\=\frac{-73}{24}\)
10. \(+\left(\frac{-3}{-4}\right) +\left(\frac{3}{-3}\right) +\left(\frac{5}{5}\right)\\= \frac{3}{4}- \frac{3}{3}+\frac{5}{5}\\=\frac{3}{4}-\frac{1}{1}+\frac{1}{1}\\=\frac{3-1+1}{4}\\=\frac{3}{4}\)
11. \(-\left(\frac{-4}{-5}\right) -\left(\frac{-5}{-3}\right) -\left(\frac{-7}{5}\right)\\= \frac{-4}{5}- \frac{5}{3}+\frac{7}{5}\\=\frac{-12}{15}-\frac{25}{15}+\frac{21}{15}\\=\frac{-12-25+21}{15}\\=\frac{-16}{15}\)
12. \(-\left(\frac{9}{-5}\right) +\left(\frac{-5}{-8}\right) -\left(\frac{-8}{6}\right)\\= \frac{9}{5}+ \frac{5}{8}+\frac{8}{6}\\=\frac{9}{5}+\frac{5}{8}+\frac{4}{3}\\=\frac{216}{120}+\frac{75}{120}+\frac{160}{120}\\=\frac{216+75+160}{120}\\=\frac{451}{120}\)