Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{8}{-9}\right) +\left(\frac{-6}{-5}\right) +\left(\frac{5}{9}\right)\\= \frac{-8}{9}+ \frac{6}{5}+\frac{5}{9}\\=\frac{-40}{45}+\frac{54}{45}+\frac{25}{45}\\=\frac{-40+54+25}{45}\\=\frac{39}{45}\\=\frac{13}{15}\)
2. \(-\left(\frac{-2}{7}\right) -\left(\frac{-8}{-3}\right) +\left(\frac{-3}{9}\right)\\= \frac{2}{7}- \frac{8}{3}-\frac{3}{9}\\=\frac{2}{7}-\frac{8}{3}-\frac{1}{3}\\=\frac{6}{21}-\frac{56}{21}-\frac{7}{21}\\=\frac{6-56-7}{21}\\=\frac{-57}{21}\\=\frac{-19}{7}\)
3. \(-\left(\frac{3}{8}\right) -\left(\frac{9}{-6}\right) -\left(\frac{-9}{-10}\right)\\= \frac{-3}{8}+ \frac{9}{6}-\frac{9}{10}\\=\frac{-3}{8}+\frac{3}{2}-\frac{9}{10}\\=\frac{-15}{40}+\frac{60}{40}-\frac{36}{40}\\=\frac{-15+60-36}{40}\\=\frac{9}{40}\)
4. \(+\left(\frac{3}{8}\right) -\left(\frac{2}{8}\right) +\left(\frac{-6}{11}\right)\\= \frac{3}{8}- \frac{2}{8}-\frac{6}{11}\\=\frac{3}{8}-\frac{1}{4}-\frac{6}{11}\\=\frac{33}{88}-\frac{22}{88}-\frac{48}{88}\\=\frac{33-22-48}{88}\\=\frac{-37}{88}\)
5. \(+\left(\frac{-3}{-7}\right) +\left(\frac{5}{7}\right) -\left(\frac{-3}{-12}\right)\\= \frac{3}{7}+ \frac{5}{7}-\frac{3}{12}\\=\frac{3}{7}+\frac{5}{7}-\frac{1}{4}\\=\frac{12}{28}+\frac{20}{28}-\frac{7}{28}\\=\frac{12+20-7}{28}\\=\frac{25}{28}\)
6. \(+\left(\frac{2}{-9}\right) -\left(\frac{-7}{-6}\right) -\left(\frac{-11}{-10}\right)\\= \frac{-2}{9}- \frac{7}{6}-\frac{11}{10}\\=\frac{-20}{90}-\frac{105}{90}-\frac{99}{90}\\=\frac{-20-105-99}{90}\\=\frac{-224}{90}\\=\frac{-112}{45}\)
7. \(-\left(\frac{-5}{-8}\right) +\left(\frac{-7}{-6}\right) +\left(\frac{-9}{9}\right)\\= \frac{-5}{8}+ \frac{7}{6}-\frac{9}{9}\\=\frac{-5}{8}+\frac{7}{6}-\frac{1}{1}\\=\frac{-15}{24}+\frac{28}{24}-\frac{24}{24}\\=\frac{-15+28-24}{24}\\=\frac{-11}{24}\)
8. \(-\left(\frac{8}{9}\right) +\left(\frac{-3}{7}\right) +\left(\frac{4}{11}\right)\\= \frac{-8}{9}- \frac{3}{7}+\frac{4}{11}\\=\frac{-616}{693}-\frac{297}{693}+\frac{252}{693}\\=\frac{-616-297+252}{693}\\=\frac{-661}{693}\)
9. \(-\left(\frac{8}{3}\right) +\left(\frac{-9}{-3}\right) -\left(\frac{5}{10}\right)\\= \frac{-8}{3}+ \frac{9}{3}-\frac{5}{10}\\=\frac{-8}{3}+\frac{3}{1}-\frac{1}{2}\\=\frac{-16}{6}+\frac{18}{6}-\frac{3}{6}\\=\frac{-16+18-3}{6}\\=\frac{-1}{6}\)
10. \(-\left(\frac{7}{-2}\right) +\left(\frac{7}{10}\right) +\left(\frac{3}{3}\right)\\= \frac{7}{2}+ \frac{7}{10}+\frac{3}{3}\\=\frac{7}{2}+\frac{7}{10}+\frac{1}{1}\\=\frac{35}{10}+\frac{7}{10}+\frac{10}{10}\\=\frac{35+7+10}{10}\\=\frac{52}{10}\\=\frac{26}{5}\)
11. \(+\left(\frac{8}{-3}\right) +\left(\frac{-10}{4}\right) -\left(\frac{7}{-9}\right)\\= \frac{-8}{3}- \frac{10}{4}+\frac{7}{9}\\=\frac{-8}{3}-\frac{5}{2}+\frac{7}{9}\\=\frac{-48}{18}-\frac{45}{18}+\frac{14}{18}\\=\frac{-48-45+14}{18}\\=\frac{-79}{18}\)
12. \(-\left(\frac{3}{-4}\right) +\left(\frac{-3}{-7}\right) -\left(\frac{-10}{8}\right)\\= \frac{3}{4}+ \frac{3}{7}+\frac{10}{8}\\=\frac{3}{4}+\frac{3}{7}+\frac{5}{4}\\=\frac{21}{28}+\frac{12}{28}+\frac{35}{28}\\=\frac{21+12+35}{28}\\=\frac{68}{28}\\=\frac{17}{7}\)