Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{9}\right) +\left(\frac{-5}{-10}\right) +\left(\frac{7}{-4}\right)\\= \frac{-2}{9}+ \frac{5}{10}-\frac{7}{4}\\=\frac{-2}{9}+\frac{1}{2}-\frac{7}{4}\\=\frac{-8}{36}+\frac{18}{36}-\frac{63}{36}\\=\frac{-8+18-63}{36}\\=\frac{-53}{36}\)
2. \(-\left(\frac{-10}{3}\right) -\left(\frac{-3}{-9}\right) +\left(\frac{-2}{6}\right)\\= \frac{10}{3}- \frac{3}{9}-\frac{2}{6}\\=\frac{10}{3}-\frac{1}{3}-\frac{1}{3}\\=\frac{10-1-1}{3}\\=\frac{8}{3}\)
3. \(-\left(\frac{2}{9}\right) -\left(\frac{5}{2}\right) -\left(\frac{-2}{-9}\right)\\= \frac{-2}{9}- \frac{5}{2}-\frac{2}{9}\\=\frac{-4}{18}-\frac{45}{18}-\frac{4}{18}\\=\frac{-4-45-4}{18}\\=\frac{-53}{18}\)
4. \(+\left(\frac{-5}{-9}\right) +\left(\frac{-9}{-8}\right) +\left(\frac{-2}{-12}\right)\\= \frac{5}{9}+ \frac{9}{8}+\frac{2}{12}\\=\frac{5}{9}+\frac{9}{8}+\frac{1}{6}\\=\frac{40}{72}+\frac{81}{72}+\frac{12}{72}\\=\frac{40+81+12}{72}\\=\frac{133}{72}\)
5. \(-\left(\frac{-2}{9}\right) +\left(\frac{4}{-3}\right) -\left(\frac{5}{6}\right)\\= \frac{2}{9}- \frac{4}{3}-\frac{5}{6}\\=\frac{4}{18}-\frac{24}{18}-\frac{15}{18}\\=\frac{4-24-15}{18}\\=\frac{-35}{18}\)
6. \(-\left(\frac{-4}{-7}\right) -\left(\frac{-10}{-4}\right) +\left(\frac{-3}{-12}\right)\\= \frac{-4}{7}- \frac{10}{4}+\frac{3}{12}\\=\frac{-4}{7}-\frac{5}{2}+\frac{1}{4}\\=\frac{-16}{28}-\frac{70}{28}+\frac{7}{28}\\=\frac{-16-70+7}{28}\\=\frac{-79}{28}\)
7. \(-\left(\frac{8}{5}\right) +\left(\frac{9}{-5}\right) -\left(\frac{6}{9}\right)\\= \frac{-8}{5}- \frac{9}{5}-\frac{6}{9}\\=\frac{-8}{5}-\frac{9}{5}-\frac{2}{3}\\=\frac{-24}{15}-\frac{27}{15}-\frac{10}{15}\\=\frac{-24-27-10}{15}\\=\frac{-61}{15}\)
8. \(+\left(\frac{-9}{8}\right) -\left(\frac{-7}{-5}\right) -\left(\frac{11}{-4}\right)\\= \frac{-9}{8}- \frac{7}{5}+\frac{11}{4}\\=\frac{-45}{40}-\frac{56}{40}+\frac{110}{40}\\=\frac{-45-56+110}{40}\\=\frac{9}{40}\)
9. \(+\left(\frac{6}{-5}\right) +\left(\frac{9}{-10}\right) +\left(\frac{7}{-5}\right)\\= \frac{-6}{5}- \frac{9}{10}-\frac{7}{5}\\=\frac{-12}{10}-\frac{9}{10}-\frac{14}{10}\\=\frac{-12-9-14}{10}\\=\frac{-35}{10}\\=\frac{-7}{2}\)
10. \(-\left(\frac{7}{-8}\right) -\left(\frac{7}{-8}\right) +\left(\frac{-7}{11}\right)\\= \frac{7}{8}+ \frac{7}{8}-\frac{7}{11}\\=\frac{77}{88}+\frac{77}{88}-\frac{56}{88}\\=\frac{77+77-56}{88}\\=\frac{98}{88}\\=\frac{49}{44}\)
11. \(-\left(\frac{-8}{3}\right) +\left(\frac{5}{-5}\right) -\left(\frac{-5}{-7}\right)\\= \frac{8}{3}- \frac{5}{5}-\frac{5}{7}\\=\frac{8}{3}-\frac{1}{1}-\frac{5}{7}\\=\frac{56}{21}-\frac{21}{21}-\frac{15}{21}\\=\frac{56-21-15}{21}\\=\frac{20}{21}\)
12. \(-\left(\frac{9}{-2}\right) -\left(\frac{-7}{2}\right) +\left(\frac{4}{4}\right)\\= \frac{9}{2}+ \frac{7}{2}+\frac{4}{4}\\=\frac{9}{2}+\frac{7}{2}+\frac{1}{1}\\=\frac{9+7+1}{2}\\=\frac{17}{2}\)