Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{3}{7}\right) -\left(\frac{-3}{9}\right) +\left(\frac{-8}{8}\right)\\= \frac{-3}{7}+ \frac{3}{9}-\frac{8}{8}\\=\frac{-3}{7}+\frac{1}{3}-\frac{1}{1}\\=\frac{-9}{21}+\frac{7}{21}-\frac{21}{21}\\=\frac{-9+7-21}{21}\\=\frac{-23}{21}\)
2. \(-\left(\frac{-10}{3}\right) +\left(\frac{5}{-5}\right) -\left(\frac{4}{-7}\right)\\= \frac{10}{3}- \frac{5}{5}+\frac{4}{7}\\=\frac{10}{3}-\frac{1}{1}+\frac{4}{7}\\=\frac{70}{21}-\frac{21}{21}+\frac{12}{21}\\=\frac{70-21+12}{21}\\=\frac{61}{21}\)
3. \(-\left(\frac{2}{3}\right) -\left(\frac{5}{4}\right) +\left(\frac{-2}{8}\right)\\= \frac{-2}{3}- \frac{5}{4}-\frac{2}{8}\\=\frac{-2}{3}-\frac{5}{4}-\frac{1}{4}\\=\frac{-8}{12}-\frac{15}{12}-\frac{3}{12}\\=\frac{-8-15-3}{12}\\=\frac{-26}{12}\\=\frac{-13}{6}\)
4. \(+\left(\frac{-3}{-2}\right) +\left(\frac{6}{10}\right) -\left(\frac{-12}{3}\right)\\= \frac{3}{2}+ \frac{6}{10}+\frac{12}{3}\\=\frac{3}{2}+\frac{3}{5}+\frac{4}{1}\\=\frac{15}{10}+\frac{6}{10}+\frac{40}{10}\\=\frac{15+6+40}{10}\\=\frac{61}{10}\)
5. \(+\left(\frac{3}{-7}\right) -\left(\frac{5}{-5}\right) -\left(\frac{-3}{2}\right)\\= \frac{-3}{7}+ \frac{5}{5}+\frac{3}{2}\\=\frac{-3}{7}+\frac{1}{1}+\frac{3}{2}\\=\frac{-6}{14}+\frac{14}{14}+\frac{21}{14}\\=\frac{-6+14+21}{14}\\=\frac{29}{14}\)
6. \(-\left(\frac{7}{-8}\right) -\left(\frac{-9}{-3}\right) +\left(\frac{-3}{12}\right)\\= \frac{7}{8}- \frac{9}{3}-\frac{3}{12}\\=\frac{7}{8}-\frac{3}{1}-\frac{1}{4}\\=\frac{7-3-1}{8}\\=\frac{3}{8}\)
7. \(+\left(\frac{3}{-7}\right) -\left(\frac{-9}{-3}\right) +\left(\frac{6}{4}\right)\\= \frac{-3}{7}- \frac{9}{3}+\frac{6}{4}\\=\frac{-3}{7}-\frac{3}{1}+\frac{3}{2}\\=\frac{-6}{14}-\frac{42}{14}+\frac{21}{14}\\=\frac{-6-42+21}{14}\\=\frac{-27}{14}\)
8. \(-\left(\frac{-8}{-9}\right) +\left(\frac{-2}{-4}\right) +\left(\frac{8}{-2}\right)\\= \frac{-8}{9}+ \frac{2}{4}-\frac{8}{2}\\=\frac{-8}{9}+\frac{1}{2}-\frac{4}{1}\\=\frac{-16}{18}+\frac{9}{18}-\frac{72}{18}\\=\frac{-16+9-72}{18}\\=\frac{-79}{18}\)
9. \(-\left(\frac{7}{-3}\right) +\left(\frac{4}{-4}\right) -\left(\frac{-2}{-2}\right)\\= \frac{7}{3}- \frac{4}{4}-\frac{2}{2}\\=\frac{7}{3}-\frac{1}{1}-\frac{1}{1}\\=\frac{7-1-1}{3}\\=\frac{5}{3}\)
10. \(+\left(\frac{5}{-2}\right) +\left(\frac{-3}{-3}\right) +\left(\frac{-9}{5}\right)\\= \frac{-5}{2}+ \frac{3}{3}-\frac{9}{5}\\=\frac{-5}{2}+\frac{1}{1}-\frac{9}{5}\\=\frac{-25}{10}+\frac{10}{10}-\frac{18}{10}\\=\frac{-25+10-18}{10}\\=\frac{-33}{10}\)
11. \(-\left(\frac{7}{5}\right) +\left(\frac{7}{10}\right) -\left(\frac{10}{-8}\right)\\= \frac{-7}{5}+ \frac{7}{10}+\frac{10}{8}\\=\frac{-7}{5}+\frac{7}{10}+\frac{5}{4}\\=\frac{-28}{20}+\frac{14}{20}+\frac{25}{20}\\=\frac{-28+14+25}{20}\\=\frac{11}{20}\)
12. \(-\left(\frac{10}{7}\right) -\left(\frac{9}{7}\right) -\left(\frac{-2}{-10}\right)\\= \frac{-10}{7}- \frac{9}{7}-\frac{2}{10}\\=\frac{-10}{7}-\frac{9}{7}-\frac{1}{5}\\=\frac{-50}{35}-\frac{45}{35}-\frac{7}{35}\\=\frac{-50-45-7}{35}\\=\frac{-102}{35}\)