Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{-3}\right) +\left(\frac{5}{9}\right) -\left(\frac{12}{-12}\right)\\= \frac{4}{3}+ \frac{5}{9}+\frac{12}{12}\\=\frac{4}{3}+\frac{5}{9}+\frac{1}{1}\\=\frac{12}{9}+\frac{5}{9}+\frac{9}{9}\\=\frac{12+5+9}{9}\\=\frac{26}{9}\)
2. \(-\left(\frac{-8}{9}\right) +\left(\frac{10}{-10}\right) +\left(\frac{4}{10}\right)\\= \frac{8}{9}- \frac{10}{10}+\frac{4}{10}\\=\frac{8}{9}-\frac{1}{1}+\frac{2}{5}\\=\frac{40}{45}-\frac{45}{45}+\frac{18}{45}\\=\frac{40-45+18}{45}\\=\frac{13}{45}\)
3. \(-\left(\frac{-8}{-7}\right) -\left(\frac{-5}{-3}\right) -\left(\frac{-11}{6}\right)\\= \frac{-8}{7}- \frac{5}{3}+\frac{11}{6}\\=\frac{-48}{42}-\frac{70}{42}+\frac{77}{42}\\=\frac{-48-70+77}{42}\\=\frac{-41}{42}\)
4. \(-\left(\frac{-8}{-3}\right) -\left(\frac{-9}{7}\right) +\left(\frac{5}{-8}\right)\\= \frac{-8}{3}+ \frac{9}{7}-\frac{5}{8}\\=\frac{-448}{168}+\frac{216}{168}-\frac{105}{168}\\=\frac{-448+216-105}{168}\\=\frac{-337}{168}\)
5. \(+\left(\frac{-5}{-2}\right) -\left(\frac{3}{-6}\right) +\left(\frac{8}{-10}\right)\\= \frac{5}{2}+ \frac{3}{6}-\frac{8}{10}\\=\frac{5}{2}+\frac{1}{2}-\frac{4}{5}\\=\frac{25}{10}+\frac{5}{10}-\frac{8}{10}\\=\frac{25+5-8}{10}\\=\frac{22}{10}\\=\frac{11}{5}\)
6. \(+\left(\frac{-10}{3}\right) -\left(\frac{7}{-5}\right) -\left(\frac{2}{-11}\right)\\= \frac{-10}{3}+ \frac{7}{5}+\frac{2}{11}\\=\frac{-550}{165}+\frac{231}{165}+\frac{30}{165}\\=\frac{-550+231+30}{165}\\=\frac{-289}{165}\)
7. \(+\left(\frac{9}{5}\right) +\left(\frac{-2}{-5}\right) -\left(\frac{9}{10}\right)\\= \frac{9}{5}+ \frac{2}{5}-\frac{9}{10}\\=\frac{18}{10}+\frac{4}{10}-\frac{9}{10}\\=\frac{18+4-9}{10}\\=\frac{13}{10}\)
8. \(+\left(\frac{7}{-2}\right) -\left(\frac{7}{-3}\right) +\left(\frac{12}{2}\right)\\= \frac{-7}{2}+ \frac{7}{3}+\frac{12}{2}\\=\frac{-7}{2}+\frac{7}{3}+\frac{6}{1}\\=\frac{-21}{6}+\frac{14}{6}+\frac{36}{6}\\=\frac{-21+14+36}{6}\\=\frac{29}{6}\)
9. \(+\left(\frac{-3}{7}\right) +\left(\frac{7}{-3}\right) +\left(\frac{-4}{-12}\right)\\= \frac{-3}{7}- \frac{7}{3}+\frac{4}{12}\\=\frac{-3}{7}-\frac{7}{3}+\frac{1}{3}\\=\frac{-9}{21}-\frac{49}{21}+\frac{7}{21}\\=\frac{-9-49+7}{21}\\=\frac{-51}{21}\\=\frac{-17}{7}\)
10. \(+\left(\frac{6}{7}\right) -\left(\frac{-5}{9}\right) +\left(\frac{-10}{6}\right)\\= \frac{6}{7}+ \frac{5}{9}-\frac{10}{6}\\=\frac{6}{7}+\frac{5}{9}-\frac{5}{3}\\=\frac{54}{63}+\frac{35}{63}-\frac{105}{63}\\=\frac{54+35-105}{63}\\=\frac{-16}{63}\)
11. \(-\left(\frac{6}{5}\right) -\left(\frac{-10}{10}\right) +\left(\frac{-8}{7}\right)\\= \frac{-6}{5}+ \frac{10}{10}-\frac{8}{7}\\=\frac{-6}{5}+\frac{1}{1}-\frac{8}{7}\\=\frac{-42}{35}+\frac{35}{35}-\frac{40}{35}\\=\frac{-42+35-40}{35}\\=\frac{-47}{35}\)
12. \(+\left(\frac{5}{6}\right) -\left(\frac{-7}{2}\right) -\left(\frac{-9}{-12}\right)\\= \frac{5}{6}+ \frac{7}{2}-\frac{9}{12}\\=\frac{5}{6}+\frac{7}{2}-\frac{3}{4}\\=\frac{10}{12}+\frac{42}{12}-\frac{9}{12}\\=\frac{10+42-9}{12}\\=\frac{43}{12}\)