Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{-6}\right) +\left(\frac{-9}{3}\right) -\left(\frac{9}{5}\right)\\= \frac{-5}{6}- \frac{9}{3}-\frac{9}{5}\\=\frac{-5}{6}-\frac{3}{1}-\frac{9}{5}\\=\frac{-25}{30}-\frac{90}{30}-\frac{54}{30}\\=\frac{-25-90-54}{30}\\=\frac{-169}{30}\)
2. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-10}{7}\right) -\left(\frac{-9}{-3}\right)\\= \frac{6}{5}- \frac{10}{7}-\frac{9}{3}\\=\frac{6}{5}-\frac{10}{7}-\frac{3}{1}\\=\frac{42}{35}-\frac{50}{35}-\frac{105}{35}\\=\frac{42-50-105}{35}\\=\frac{-113}{35}\)
3. \(+\left(\frac{2}{3}\right) +\left(\frac{9}{2}\right) +\left(\frac{-6}{7}\right)\\= \frac{2}{3}+ \frac{9}{2}-\frac{6}{7}\\=\frac{28}{42}+\frac{189}{42}-\frac{36}{42}\\=\frac{28+189-36}{42}\\=\frac{181}{42}\)
4. \(+\left(\frac{-6}{5}\right) +\left(\frac{4}{5}\right) +\left(\frac{10}{7}\right)\\= \frac{-6}{5}+ \frac{4}{5}+\frac{10}{7}\\=\frac{-42}{35}+\frac{28}{35}+\frac{50}{35}\\=\frac{-42+28+50}{35}\\=\frac{36}{35}\)
5. \(+\left(\frac{2}{3}\right) -\left(\frac{3}{10}\right) +\left(\frac{6}{-6}\right)\\= \frac{2}{3}- \frac{3}{10}-\frac{6}{6}\\=\frac{2}{3}-\frac{3}{10}-\frac{1}{1}\\=\frac{20}{30}-\frac{9}{30}-\frac{30}{30}\\=\frac{20-9-30}{30}\\=\frac{-19}{30}\)
6. \(-\left(\frac{-7}{-8}\right) +\left(\frac{5}{-4}\right) -\left(\frac{5}{3}\right)\\= \frac{-7}{8}- \frac{5}{4}-\frac{5}{3}\\=\frac{-21}{24}-\frac{30}{24}-\frac{40}{24}\\=\frac{-21-30-40}{24}\\=\frac{-91}{24}\)
7. \(+\left(\frac{3}{-2}\right) +\left(\frac{-8}{8}\right) -\left(\frac{12}{2}\right)\\= \frac{-3}{2}- \frac{8}{8}-\frac{12}{2}\\=\frac{-3}{2}-\frac{1}{1}-\frac{6}{1}\\=\frac{-3-1-6}{2}\\=\frac{-10}{2}\\=\frac{-5}{1}\)
8. \(+\left(\frac{-7}{4}\right) -\left(\frac{2}{-4}\right) -\left(\frac{-9}{7}\right)\\= \frac{-7}{4}+ \frac{2}{4}+\frac{9}{7}\\=\frac{-7}{4}+\frac{1}{2}+\frac{9}{7}\\=\frac{-49}{28}+\frac{14}{28}+\frac{36}{28}\\=\frac{-49+14+36}{28}\\=\frac{1}{28}\)
9. \(-\left(\frac{8}{9}\right) +\left(\frac{-3}{-4}\right) +\left(\frac{-9}{-7}\right)\\= \frac{-8}{9}+ \frac{3}{4}+\frac{9}{7}\\=\frac{-224}{252}+\frac{189}{252}+\frac{324}{252}\\=\frac{-224+189+324}{252}\\=\frac{289}{252}\)
10. \(-\left(\frac{6}{5}\right) +\left(\frac{-6}{7}\right) -\left(\frac{-5}{-2}\right)\\= \frac{-6}{5}- \frac{6}{7}-\frac{5}{2}\\=\frac{-84}{70}-\frac{60}{70}-\frac{175}{70}\\=\frac{-84-60-175}{70}\\=\frac{-319}{70}\)
11. \(+\left(\frac{10}{3}\right) +\left(\frac{-6}{-7}\right) -\left(\frac{11}{9}\right)\\= \frac{10}{3}+ \frac{6}{7}-\frac{11}{9}\\=\frac{210}{63}+\frac{54}{63}-\frac{77}{63}\\=\frac{210+54-77}{63}\\=\frac{187}{63}\)
12. \(-\left(\frac{9}{2}\right) +\left(\frac{-10}{-10}\right) -\left(\frac{7}{-4}\right)\\= \frac{-9}{2}+ \frac{10}{10}+\frac{7}{4}\\=\frac{-9}{2}+\frac{1}{1}+\frac{7}{4}\\=\frac{-18}{4}+\frac{4}{4}+\frac{7}{4}\\=\frac{-18+4+7}{4}\\=\frac{-7}{4}\)