Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{7}\right) -\left(\frac{-4}{-6}\right) -\left(\frac{-11}{-7}\right)\\= \frac{-9}{7}- \frac{4}{6}-\frac{11}{7}\\=\frac{-9}{7}-\frac{2}{3}-\frac{11}{7}\\=\frac{-27}{21}-\frac{14}{21}-\frac{33}{21}\\=\frac{-27-14-33}{21}\\=\frac{-74}{21}\)
2. \(-\left(\frac{-2}{-5}\right) +\left(\frac{-5}{9}\right) -\left(\frac{-3}{3}\right)\\= \frac{-2}{5}- \frac{5}{9}+\frac{3}{3}\\=\frac{-2}{5}-\frac{5}{9}+\frac{1}{1}\\=\frac{-18}{45}-\frac{25}{45}+\frac{45}{45}\\=\frac{-18-25+45}{45}\\=\frac{2}{45}\)
3. \(-\left(\frac{-2}{3}\right) +\left(\frac{-3}{-7}\right) -\left(\frac{6}{-11}\right)\\= \frac{2}{3}+ \frac{3}{7}+\frac{6}{11}\\=\frac{154}{231}+\frac{99}{231}+\frac{126}{231}\\=\frac{154+99+126}{231}\\=\frac{379}{231}\)
4. \(-\left(\frac{-4}{9}\right) -\left(\frac{-10}{3}\right) -\left(\frac{4}{-6}\right)\\= \frac{4}{9}+ \frac{10}{3}+\frac{4}{6}\\=\frac{4}{9}+\frac{10}{3}+\frac{2}{3}\\=\frac{4+10+2}{9}\\=\frac{16}{9}\)
5. \(+\left(\frac{8}{-9}\right) +\left(\frac{10}{3}\right) +\left(\frac{2}{-10}\right)\\= \frac{-8}{9}+ \frac{10}{3}-\frac{2}{10}\\=\frac{-8}{9}+\frac{10}{3}-\frac{1}{5}\\=\frac{-40}{45}+\frac{150}{45}-\frac{9}{45}\\=\frac{-40+150-9}{45}\\=\frac{101}{45}\)
6. \(-\left(\frac{-5}{-6}\right) +\left(\frac{5}{-6}\right) +\left(\frac{12}{9}\right)\\= \frac{-5}{6}- \frac{5}{6}+\frac{12}{9}\\=\frac{-5}{6}-\frac{5}{6}+\frac{4}{3}\\=\frac{-5-5+4}{6}\\=\frac{-6}{6}\\=\frac{-1}{1}\)
7. \(+\left(\frac{-9}{-2}\right) -\left(\frac{-5}{-9}\right) +\left(\frac{11}{11}\right)\\= \frac{9}{2}- \frac{5}{9}+\frac{11}{11}\\=\frac{9}{2}-\frac{5}{9}+\frac{1}{1}\\=\frac{81}{18}-\frac{10}{18}+\frac{18}{18}\\=\frac{81-10+18}{18}\\=\frac{89}{18}\)
8. \(+\left(\frac{8}{3}\right) +\left(\frac{-6}{-2}\right) +\left(\frac{-10}{10}\right)\\= \frac{8}{3}+ \frac{6}{2}-\frac{10}{10}\\=\frac{8}{3}+\frac{3}{1}-\frac{1}{1}\\=\frac{8+3-1}{3}\\=\frac{10}{3}\)
9. \(-\left(\frac{9}{7}\right) +\left(\frac{-6}{3}\right) +\left(\frac{11}{-5}\right)\\= \frac{-9}{7}- \frac{6}{3}-\frac{11}{5}\\=\frac{-9}{7}-\frac{2}{1}-\frac{11}{5}\\=\frac{-45}{35}-\frac{70}{35}-\frac{77}{35}\\=\frac{-45-70-77}{35}\\=\frac{-192}{35}\)
10. \(+\left(\frac{3}{-7}\right) +\left(\frac{6}{10}\right) -\left(\frac{10}{-4}\right)\\= \frac{-3}{7}+ \frac{6}{10}+\frac{10}{4}\\=\frac{-3}{7}+\frac{3}{5}+\frac{5}{2}\\=\frac{-30}{70}+\frac{42}{70}+\frac{175}{70}\\=\frac{-30+42+175}{70}\\=\frac{187}{70}\)
11. \(-\left(\frac{-9}{-4}\right) -\left(\frac{7}{8}\right) +\left(\frac{-12}{12}\right)\\= \frac{-9}{4}- \frac{7}{8}-\frac{12}{12}\\=\frac{-9}{4}-\frac{7}{8}-\frac{1}{1}\\=\frac{-18}{8}-\frac{7}{8}-\frac{8}{8}\\=\frac{-18-7-8}{8}\\=\frac{-33}{8}\)
12. \(+\left(\frac{-6}{5}\right) -\left(\frac{-10}{7}\right) +\left(\frac{3}{-6}\right)\\= \frac{-6}{5}+ \frac{10}{7}-\frac{3}{6}\\=\frac{-6}{5}+\frac{10}{7}-\frac{1}{2}\\=\frac{-84}{70}+\frac{100}{70}-\frac{35}{70}\\=\frac{-84+100-35}{70}\\=\frac{-19}{70}\)