Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-9}{-7}\right) -\left(\frac{-12}{6}\right)\\= \frac{-10}{7}+ \frac{9}{7}+\frac{12}{6}\\=\frac{-10}{7}+\frac{9}{7}+\frac{2}{1}\\=\frac{-10+9+2}{7}\\=\frac{1}{7}\)
2. \(-\left(\frac{-3}{2}\right) -\left(\frac{8}{-4}\right) +\left(\frac{4}{-8}\right)\\= \frac{3}{2}+ \frac{8}{4}-\frac{4}{8}\\=\frac{3}{2}+\frac{2}{1}-\frac{1}{2}\\=\frac{3+2-1}{2}\\=\frac{4}{2}\\=\frac{2}{1}\)
3. \(-\left(\frac{3}{-8}\right) -\left(\frac{4}{6}\right) -\left(\frac{-5}{-8}\right)\\= \frac{3}{8}- \frac{4}{6}-\frac{5}{8}\\=\frac{3}{8}-\frac{2}{3}-\frac{5}{8}\\=\frac{9}{24}-\frac{16}{24}-\frac{15}{24}\\=\frac{9-16-15}{24}\\=\frac{-22}{24}\\=\frac{-11}{12}\)
4. \(-\left(\frac{-2}{5}\right) +\left(\frac{10}{7}\right) +\left(\frac{-10}{6}\right)\\= \frac{2}{5}+ \frac{10}{7}-\frac{10}{6}\\=\frac{2}{5}+\frac{10}{7}-\frac{5}{3}\\=\frac{42}{105}+\frac{150}{105}-\frac{175}{105}\\=\frac{42+150-175}{105}\\=\frac{17}{105}\)
5. \(-\left(\frac{10}{3}\right) +\left(\frac{-5}{-10}\right) +\left(\frac{12}{10}\right)\\= \frac{-10}{3}+ \frac{5}{10}+\frac{12}{10}\\=\frac{-10}{3}+\frac{1}{2}+\frac{6}{5}\\=\frac{-100}{30}+\frac{15}{30}+\frac{36}{30}\\=\frac{-100+15+36}{30}\\=\frac{-49}{30}\)
6. \(-\left(\frac{-3}{4}\right) -\left(\frac{-6}{-3}\right) +\left(\frac{-7}{3}\right)\\= \frac{3}{4}- \frac{6}{3}-\frac{7}{3}\\=\frac{3}{4}-\frac{2}{1}-\frac{7}{3}\\=\frac{9}{12}-\frac{24}{12}-\frac{28}{12}\\=\frac{9-24-28}{12}\\=\frac{-43}{12}\)
7. \(-\left(\frac{2}{-9}\right) -\left(\frac{9}{10}\right) -\left(\frac{-7}{-11}\right)\\= \frac{2}{9}- \frac{9}{10}-\frac{7}{11}\\=\frac{220}{990}-\frac{891}{990}-\frac{630}{990}\\=\frac{220-891-630}{990}\\=\frac{-1301}{990}\)
8. \(-\left(\frac{5}{-2}\right) +\left(\frac{-2}{-5}\right) +\left(\frac{12}{-4}\right)\\= \frac{5}{2}+ \frac{2}{5}-\frac{12}{4}\\=\frac{5}{2}+\frac{2}{5}-\frac{3}{1}\\=\frac{25}{10}+\frac{4}{10}-\frac{30}{10}\\=\frac{25+4-30}{10}\\=\frac{-1}{10}\)
9. \(+\left(\frac{-4}{3}\right) -\left(\frac{-6}{-10}\right) -\left(\frac{12}{-6}\right)\\= \frac{-4}{3}- \frac{6}{10}+\frac{12}{6}\\=\frac{-4}{3}-\frac{3}{5}+\frac{2}{1}\\=\frac{-20}{15}-\frac{9}{15}+\frac{30}{15}\\=\frac{-20-9+30}{15}\\=\frac{1}{15}\)
10. \(-\left(\frac{-4}{-9}\right) +\left(\frac{-10}{4}\right) -\left(\frac{-3}{8}\right)\\= \frac{-4}{9}- \frac{10}{4}+\frac{3}{8}\\=\frac{-4}{9}-\frac{5}{2}+\frac{3}{8}\\=\frac{-32}{72}-\frac{180}{72}+\frac{27}{72}\\=\frac{-32-180+27}{72}\\=\frac{-185}{72}\)
11. \(+\left(\frac{2}{9}\right) +\left(\frac{3}{-7}\right) -\left(\frac{9}{-6}\right)\\= \frac{2}{9}- \frac{3}{7}+\frac{9}{6}\\=\frac{2}{9}-\frac{3}{7}+\frac{3}{2}\\=\frac{28}{126}-\frac{54}{126}+\frac{189}{126}\\=\frac{28-54+189}{126}\\=\frac{163}{126}\)
12. \(+\left(\frac{-5}{4}\right) -\left(\frac{-9}{-10}\right) -\left(\frac{5}{9}\right)\\= \frac{-5}{4}- \frac{9}{10}-\frac{5}{9}\\=\frac{-225}{180}-\frac{162}{180}-\frac{100}{180}\\=\frac{-225-162-100}{180}\\=\frac{-487}{180}\)