Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{7}{-9}\right) -\left(\frac{-2}{-6}\right) +\left(\frac{-6}{-5}\right)\\= \frac{7}{9}- \frac{2}{6}+\frac{6}{5}\\=\frac{7}{9}-\frac{1}{3}+\frac{6}{5}\\=\frac{35}{45}-\frac{15}{45}+\frac{54}{45}\\=\frac{35-15+54}{45}\\=\frac{74}{45}\)
2. \(-\left(\frac{-10}{7}\right) +\left(\frac{2}{-9}\right) -\left(\frac{-10}{-11}\right)\\= \frac{10}{7}- \frac{2}{9}-\frac{10}{11}\\=\frac{990}{693}-\frac{154}{693}-\frac{630}{693}\\=\frac{990-154-630}{693}\\=\frac{206}{693}\)
3. \(+\left(\frac{9}{-2}\right) +\left(\frac{-7}{-6}\right) -\left(\frac{5}{4}\right)\\= \frac{-9}{2}+ \frac{7}{6}-\frac{5}{4}\\=\frac{-54}{12}+\frac{14}{12}-\frac{15}{12}\\=\frac{-54+14-15}{12}\\=\frac{-55}{12}\)
4. \(-\left(\frac{4}{-5}\right) -\left(\frac{-2}{-4}\right) -\left(\frac{-6}{4}\right)\\= \frac{4}{5}- \frac{2}{4}+\frac{6}{4}\\=\frac{4}{5}-\frac{1}{2}+\frac{3}{2}\\=\frac{8}{10}-\frac{5}{10}+\frac{15}{10}\\=\frac{8-5+15}{10}\\=\frac{18}{10}\\=\frac{9}{5}\)
5. \(-\left(\frac{4}{-3}\right) -\left(\frac{-8}{-5}\right) +\left(\frac{-11}{-11}\right)\\= \frac{4}{3}- \frac{8}{5}+\frac{11}{11}\\=\frac{4}{3}-\frac{8}{5}+\frac{1}{1}\\=\frac{20}{15}-\frac{24}{15}+\frac{15}{15}\\=\frac{20-24+15}{15}\\=\frac{11}{15}\)
6. \(+\left(\frac{10}{9}\right) +\left(\frac{3}{-6}\right) +\left(\frac{-7}{10}\right)\\= \frac{10}{9}- \frac{3}{6}-\frac{7}{10}\\=\frac{10}{9}-\frac{1}{2}-\frac{7}{10}\\=\frac{100}{90}-\frac{45}{90}-\frac{63}{90}\\=\frac{100-45-63}{90}\\=\frac{-8}{90}\\=\frac{-4}{45}\)
7. \(+\left(\frac{7}{-4}\right) +\left(\frac{-6}{-4}\right) -\left(\frac{-2}{11}\right)\\= \frac{-7}{4}+ \frac{6}{4}+\frac{2}{11}\\=\frac{-7}{4}+\frac{3}{2}+\frac{2}{11}\\=\frac{-77}{44}+\frac{66}{44}+\frac{8}{44}\\=\frac{-77+66+8}{44}\\=\frac{-3}{44}\)
8. \(-\left(\frac{4}{-5}\right) -\left(\frac{5}{10}\right) -\left(\frac{2}{-12}\right)\\= \frac{4}{5}- \frac{5}{10}+\frac{2}{12}\\=\frac{4}{5}-\frac{1}{2}+\frac{1}{6}\\=\frac{24}{30}-\frac{15}{30}+\frac{5}{30}\\=\frac{24-15+5}{30}\\=\frac{14}{30}\\=\frac{7}{15}\)
9. \(+\left(\frac{6}{-5}\right) +\left(\frac{2}{2}\right) +\left(\frac{9}{2}\right)\\= \frac{-6}{5}+ \frac{2}{2}+\frac{9}{2}\\=\frac{-6}{5}+\frac{1}{1}+\frac{9}{2}\\=\frac{-12}{10}+\frac{10}{10}+\frac{45}{10}\\=\frac{-12+10+45}{10}\\=\frac{43}{10}\)
10. \(-\left(\frac{-2}{-7}\right) +\left(\frac{5}{-10}\right) +\left(\frac{12}{-11}\right)\\= \frac{-2}{7}- \frac{5}{10}-\frac{12}{11}\\=\frac{-2}{7}-\frac{1}{2}-\frac{12}{11}\\=\frac{-44}{154}-\frac{77}{154}-\frac{168}{154}\\=\frac{-44-77-168}{154}\\=\frac{-289}{154}\)
11. \(+\left(\frac{3}{2}\right) -\left(\frac{-9}{10}\right) +\left(\frac{-5}{-5}\right)\\= \frac{3}{2}+ \frac{9}{10}+\frac{5}{5}\\=\frac{3}{2}+\frac{9}{10}+\frac{1}{1}\\=\frac{15}{10}+\frac{9}{10}+\frac{10}{10}\\=\frac{15+9+10}{10}\\=\frac{34}{10}\\=\frac{17}{5}\)
12. \(+\left(\frac{-6}{-5}\right) -\left(\frac{8}{3}\right) +\left(\frac{-10}{2}\right)\\= \frac{6}{5}- \frac{8}{3}-\frac{10}{2}\\=\frac{6}{5}-\frac{8}{3}-\frac{5}{1}\\=\frac{18}{15}-\frac{40}{15}-\frac{75}{15}\\=\frac{18-40-75}{15}\\=\frac{-97}{15}\)