Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{7}{-2}\right) -\left(\frac{5}{-5}\right) +\left(\frac{8}{-8}\right)\\= \frac{-7}{2}+ \frac{5}{5}-\frac{8}{8}\\=\frac{-7}{2}+\frac{1}{1}-\frac{1}{1}\\=\frac{-7+1-1}{2}\\=\frac{-7}{2}\)
2. \(+\left(\frac{3}{5}\right) -\left(\frac{9}{-6}\right) +\left(\frac{6}{-6}\right)\\= \frac{3}{5}+ \frac{9}{6}-\frac{6}{6}\\=\frac{3}{5}+\frac{3}{2}-\frac{1}{1}\\=\frac{6}{10}+\frac{15}{10}-\frac{10}{10}\\=\frac{6+15-10}{10}\\=\frac{11}{10}\)
3. \(-\left(\frac{3}{5}\right) +\left(\frac{-5}{5}\right) -\left(\frac{11}{4}\right)\\= \frac{-3}{5}- \frac{5}{5}-\frac{11}{4}\\=\frac{-3}{5}-\frac{1}{1}-\frac{11}{4}\\=\frac{-12}{20}-\frac{20}{20}-\frac{55}{20}\\=\frac{-12-20-55}{20}\\=\frac{-87}{20}\)
4. \(+\left(\frac{3}{-7}\right) +\left(\frac{8}{8}\right) +\left(\frac{6}{9}\right)\\= \frac{-3}{7}+ \frac{8}{8}+\frac{6}{9}\\=\frac{-3}{7}+\frac{1}{1}+\frac{2}{3}\\=\frac{-9}{21}+\frac{21}{21}+\frac{14}{21}\\=\frac{-9+21+14}{21}\\=\frac{26}{21}\)
5. \(+\left(\frac{-6}{-5}\right) +\left(\frac{5}{-9}\right) +\left(\frac{-8}{8}\right)\\= \frac{6}{5}- \frac{5}{9}-\frac{8}{8}\\=\frac{6}{5}-\frac{5}{9}-\frac{1}{1}\\=\frac{54}{45}-\frac{25}{45}-\frac{45}{45}\\=\frac{54-25-45}{45}\\=\frac{-16}{45}\)
6. \(+\left(\frac{-7}{-6}\right) +\left(\frac{-8}{-7}\right) -\left(\frac{-12}{-7}\right)\\= \frac{7}{6}+ \frac{8}{7}-\frac{12}{7}\\=\frac{49}{42}+\frac{48}{42}-\frac{72}{42}\\=\frac{49+48-72}{42}\\=\frac{25}{42}\)
7. \(-\left(\frac{3}{4}\right) -\left(\frac{3}{-2}\right) -\left(\frac{-10}{11}\right)\\= \frac{-3}{4}+ \frac{3}{2}+\frac{10}{11}\\=\frac{-33}{44}+\frac{66}{44}+\frac{40}{44}\\=\frac{-33+66+40}{44}\\=\frac{73}{44}\)
8. \(-\left(\frac{-4}{-9}\right) +\left(\frac{-3}{-9}\right) +\left(\frac{5}{10}\right)\\= \frac{-4}{9}+ \frac{3}{9}+\frac{5}{10}\\=\frac{-4}{9}+\frac{1}{3}+\frac{1}{2}\\=\frac{-8}{18}+\frac{6}{18}+\frac{9}{18}\\=\frac{-8+6+9}{18}\\=\frac{7}{18}\)
9. \(-\left(\frac{3}{-2}\right) +\left(\frac{-9}{-2}\right) +\left(\frac{-7}{-12}\right)\\= \frac{3}{2}+ \frac{9}{2}+\frac{7}{12}\\=\frac{18}{12}+\frac{54}{12}+\frac{7}{12}\\=\frac{18+54+7}{12}\\=\frac{79}{12}\)
10. \(-\left(\frac{9}{-2}\right) +\left(\frac{3}{-10}\right) -\left(\frac{-9}{9}\right)\\= \frac{9}{2}- \frac{3}{10}+\frac{9}{9}\\=\frac{9}{2}-\frac{3}{10}+\frac{1}{1}\\=\frac{45}{10}-\frac{3}{10}+\frac{10}{10}\\=\frac{45-3+10}{10}\\=\frac{52}{10}\\=\frac{26}{5}\)
11. \(+\left(\frac{-9}{7}\right) -\left(\frac{8}{10}\right) +\left(\frac{6}{-8}\right)\\= \frac{-9}{7}- \frac{8}{10}-\frac{6}{8}\\=\frac{-9}{7}-\frac{4}{5}-\frac{3}{4}\\=\frac{-180}{140}-\frac{112}{140}-\frac{105}{140}\\=\frac{-180-112-105}{140}\\=\frac{-397}{140}\)
12. \(+\left(\frac{6}{5}\right) +\left(\frac{3}{4}\right) -\left(\frac{9}{-8}\right)\\= \frac{6}{5}+ \frac{3}{4}+\frac{9}{8}\\=\frac{48}{40}+\frac{30}{40}+\frac{45}{40}\\=\frac{48+30+45}{40}\\=\frac{123}{40}\)