Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-7}{9}\right) -\left(\frac{-9}{7}\right) +\left(\frac{-12}{-4}\right)\\= \frac{-7}{9}+ \frac{9}{7}+\frac{12}{4}\\=\frac{-7}{9}+\frac{9}{7}+\frac{3}{1}\\=\frac{-49}{63}+\frac{81}{63}+\frac{189}{63}\\=\frac{-49+81+189}{63}\\=\frac{221}{63}\)
2. \(+\left(\frac{2}{7}\right) +\left(\frac{-9}{2}\right) -\left(\frac{6}{8}\right)\\= \frac{2}{7}- \frac{9}{2}-\frac{6}{8}\\=\frac{2}{7}-\frac{9}{2}-\frac{3}{4}\\=\frac{8}{28}-\frac{126}{28}-\frac{21}{28}\\=\frac{8-126-21}{28}\\=\frac{-139}{28}\)
3. \(+\left(\frac{-4}{-9}\right) +\left(\frac{6}{-7}\right) -\left(\frac{4}{11}\right)\\= \frac{4}{9}- \frac{6}{7}-\frac{4}{11}\\=\frac{308}{693}-\frac{594}{693}-\frac{252}{693}\\=\frac{308-594-252}{693}\\=\frac{-538}{693}\)
4. \(+\left(\frac{-4}{3}\right) -\left(\frac{6}{-10}\right) +\left(\frac{-3}{8}\right)\\= \frac{-4}{3}+ \frac{6}{10}-\frac{3}{8}\\=\frac{-4}{3}+\frac{3}{5}-\frac{3}{8}\\=\frac{-160}{120}+\frac{72}{120}-\frac{45}{120}\\=\frac{-160+72-45}{120}\\=\frac{-133}{120}\)
5. \(-\left(\frac{-7}{-2}\right) +\left(\frac{6}{-9}\right) +\left(\frac{8}{-6}\right)\\= \frac{-7}{2}- \frac{6}{9}-\frac{8}{6}\\=\frac{-7}{2}-\frac{2}{3}-\frac{4}{3}\\=\frac{-21}{6}-\frac{4}{6}-\frac{8}{6}\\=\frac{-21-4-8}{6}\\=\frac{-33}{6}\\=\frac{-11}{2}\)
6. \(-\left(\frac{2}{3}\right) -\left(\frac{6}{-2}\right) -\left(\frac{-8}{-9}\right)\\= \frac{-2}{3}+ \frac{6}{2}-\frac{8}{9}\\=\frac{-2}{3}+\frac{3}{1}-\frac{8}{9}\\=\frac{-6}{9}+\frac{27}{9}-\frac{8}{9}\\=\frac{-6+27-8}{9}\\=\frac{13}{9}\)
7. \(-\left(\frac{-9}{4}\right) +\left(\frac{2}{-9}\right) +\left(\frac{12}{-9}\right)\\= \frac{9}{4}- \frac{2}{9}-\frac{12}{9}\\=\frac{9}{4}-\frac{2}{9}-\frac{4}{3}\\=\frac{81}{36}-\frac{8}{36}-\frac{48}{36}\\=\frac{81-8-48}{36}\\=\frac{25}{36}\)
8. \(+\left(\frac{8}{9}\right) +\left(\frac{4}{-7}\right) +\left(\frac{-3}{12}\right)\\= \frac{8}{9}- \frac{4}{7}-\frac{3}{12}\\=\frac{8}{9}-\frac{4}{7}-\frac{1}{4}\\=\frac{224}{252}-\frac{144}{252}-\frac{63}{252}\\=\frac{224-144-63}{252}\\=\frac{17}{252}\)
9. \(-\left(\frac{7}{8}\right) +\left(\frac{7}{-4}\right) -\left(\frac{-12}{11}\right)\\= \frac{-7}{8}- \frac{7}{4}+\frac{12}{11}\\=\frac{-77}{88}-\frac{154}{88}+\frac{96}{88}\\=\frac{-77-154+96}{88}\\=\frac{-135}{88}\)
10. \(-\left(\frac{9}{-2}\right) -\left(\frac{-2}{-8}\right) +\left(\frac{-12}{-8}\right)\\= \frac{9}{2}- \frac{2}{8}+\frac{12}{8}\\=\frac{9}{2}-\frac{1}{4}+\frac{3}{2}\\=\frac{18}{4}-\frac{1}{4}+\frac{6}{4}\\=\frac{18-1+6}{4}\\=\frac{23}{4}\)
11. \(+\left(\frac{-9}{4}\right) -\left(\frac{8}{4}\right) -\left(\frac{9}{3}\right)\\= \frac{-9}{4}- \frac{8}{4}-\frac{9}{3}\\=\frac{-9}{4}-\frac{2}{1}-\frac{3}{1}\\=\frac{-9-2-3}{4}\\=\frac{-14}{4}\\=\frac{-7}{2}\)
12. \(-\left(\frac{-10}{-9}\right) -\left(\frac{-7}{-6}\right) +\left(\frac{2}{-5}\right)\\= \frac{-10}{9}- \frac{7}{6}-\frac{2}{5}\\=\frac{-100}{90}-\frac{105}{90}-\frac{36}{90}\\=\frac{-100-105-36}{90}\\=\frac{-241}{90}\)