Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{9}\right) -\left(\frac{-4}{8}\right) -\left(\frac{3}{10}\right)\\= \frac{-5}{9}+ \frac{4}{8}-\frac{3}{10}\\=\frac{-5}{9}+\frac{1}{2}-\frac{3}{10}\\=\frac{-50}{90}+\frac{45}{90}-\frac{27}{90}\\=\frac{-50+45-27}{90}\\=\frac{-32}{90}\\=\frac{-16}{45}\)
2. \(+\left(\frac{-2}{7}\right) -\left(\frac{5}{-5}\right) -\left(\frac{-2}{3}\right)\\= \frac{-2}{7}+ \frac{5}{5}+\frac{2}{3}\\=\frac{-2}{7}+\frac{1}{1}+\frac{2}{3}\\=\frac{-6}{21}+\frac{21}{21}+\frac{14}{21}\\=\frac{-6+21+14}{21}\\=\frac{29}{21}\)
3. \(-\left(\frac{7}{3}\right) -\left(\frac{-6}{3}\right) -\left(\frac{-9}{9}\right)\\= \frac{-7}{3}+ \frac{6}{3}+\frac{9}{9}\\=\frac{-7}{3}+\frac{2}{1}+\frac{1}{1}\\=\frac{-7+2+1}{3}\\=\frac{-4}{3}\)
4. \(+\left(\frac{6}{-5}\right) -\left(\frac{-6}{-5}\right) -\left(\frac{-7}{-11}\right)\\= \frac{-6}{5}- \frac{6}{5}-\frac{7}{11}\\=\frac{-66}{55}-\frac{66}{55}-\frac{35}{55}\\=\frac{-66-66-35}{55}\\=\frac{-167}{55}\)
5. \(-\left(\frac{6}{5}\right) +\left(\frac{-3}{-10}\right) -\left(\frac{11}{5}\right)\\= \frac{-6}{5}+ \frac{3}{10}-\frac{11}{5}\\=\frac{-12}{10}+\frac{3}{10}-\frac{22}{10}\\=\frac{-12+3-22}{10}\\=\frac{-31}{10}\)
6. \(-\left(\frac{2}{9}\right) +\left(\frac{-8}{6}\right) -\left(\frac{-10}{-10}\right)\\= \frac{-2}{9}- \frac{8}{6}-\frac{10}{10}\\=\frac{-2}{9}-\frac{4}{3}-\frac{1}{1}\\=\frac{-2-4-1}{9}\\=\frac{-7}{9}\)
7. \(-\left(\frac{2}{9}\right) +\left(\frac{-7}{-5}\right) +\left(\frac{-10}{6}\right)\\= \frac{-2}{9}+ \frac{7}{5}-\frac{10}{6}\\=\frac{-2}{9}+\frac{7}{5}-\frac{5}{3}\\=\frac{-10}{45}+\frac{63}{45}-\frac{75}{45}\\=\frac{-10+63-75}{45}\\=\frac{-22}{45}\)
8. \(-\left(\frac{6}{-5}\right) +\left(\frac{-8}{7}\right) -\left(\frac{-11}{-11}\right)\\= \frac{6}{5}- \frac{8}{7}-\frac{11}{11}\\=\frac{6}{5}-\frac{8}{7}-\frac{1}{1}\\=\frac{42}{35}-\frac{40}{35}-\frac{35}{35}\\=\frac{42-40-35}{35}\\=\frac{-33}{35}\)
9. \(+\left(\frac{-3}{-7}\right) +\left(\frac{2}{6}\right) +\left(\frac{-2}{6}\right)\\= \frac{3}{7}+ \frac{2}{6}-\frac{2}{6}\\=\frac{3}{7}+\frac{1}{3}-\frac{1}{3}\\=\frac{9}{21}+\frac{7}{21}-\frac{7}{21}\\=\frac{9+7-7}{21}\\=\frac{9}{21}\\=\frac{3}{7}\)
10. \(-\left(\frac{5}{-9}\right) -\left(\frac{-10}{7}\right) +\left(\frac{-5}{-10}\right)\\= \frac{5}{9}+ \frac{10}{7}+\frac{5}{10}\\=\frac{5}{9}+\frac{10}{7}+\frac{1}{2}\\=\frac{70}{126}+\frac{180}{126}+\frac{63}{126}\\=\frac{70+180+63}{126}\\=\frac{313}{126}\)
11. \(-\left(\frac{7}{3}\right) +\left(\frac{-10}{-5}\right) -\left(\frac{-12}{10}\right)\\= \frac{-7}{3}+ \frac{10}{5}+\frac{12}{10}\\=\frac{-7}{3}+\frac{2}{1}+\frac{6}{5}\\=\frac{-35}{15}+\frac{30}{15}+\frac{18}{15}\\=\frac{-35+30+18}{15}\\=\frac{13}{15}\)
12. \(+\left(\frac{5}{-9}\right) +\left(\frac{10}{2}\right) -\left(\frac{-4}{3}\right)\\= \frac{-5}{9}+ \frac{10}{2}+\frac{4}{3}\\=\frac{-5}{9}+\frac{5}{1}+\frac{4}{3}\\=\frac{-5+5+4}{9}\\=\frac{4}{9}\)