Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{-7}\right) +\left(\frac{6}{-5}\right) +\left(\frac{10}{7}\right)\\= \frac{4}{7}- \frac{6}{5}+\frac{10}{7}\\=\frac{20}{35}-\frac{42}{35}+\frac{50}{35}\\=\frac{20-42+50}{35}\\=\frac{28}{35}\\=\frac{4}{5}\)
2. \(+\left(\frac{3}{-2}\right) -\left(\frac{3}{-4}\right) +\left(\frac{-12}{6}\right)\\= \frac{-3}{2}+ \frac{3}{4}-\frac{12}{6}\\=\frac{-3}{2}+\frac{3}{4}-\frac{2}{1}\\=\frac{-6}{4}+\frac{3}{4}-\frac{8}{4}\\=\frac{-6+3-8}{4}\\=\frac{-11}{4}\)
3. \(-\left(\frac{5}{7}\right) -\left(\frac{-5}{3}\right) +\left(\frac{4}{-11}\right)\\= \frac{-5}{7}+ \frac{5}{3}-\frac{4}{11}\\=\frac{-165}{231}+\frac{385}{231}-\frac{84}{231}\\=\frac{-165+385-84}{231}\\=\frac{136}{231}\)
4. \(+\left(\frac{-5}{2}\right) +\left(\frac{-8}{-4}\right) -\left(\frac{2}{4}\right)\\= \frac{-5}{2}+ \frac{8}{4}-\frac{2}{4}\\=\frac{-5}{2}+\frac{2}{1}-\frac{1}{2}\\=\frac{-5+2-1}{2}\\=\frac{-4}{2}\\=\frac{-2}{1}\)
5. \(+\left(\frac{-9}{-4}\right) -\left(\frac{2}{-8}\right) +\left(\frac{-8}{-9}\right)\\= \frac{9}{4}+ \frac{2}{8}+\frac{8}{9}\\=\frac{9}{4}+\frac{1}{4}+\frac{8}{9}\\=\frac{81}{36}+\frac{9}{36}+\frac{32}{36}\\=\frac{81+9+32}{36}\\=\frac{122}{36}\\=\frac{61}{18}\)
6. \(-\left(\frac{-7}{-2}\right) -\left(\frac{2}{5}\right) +\left(\frac{-5}{-10}\right)\\= \frac{-7}{2}- \frac{2}{5}+\frac{5}{10}\\=\frac{-7}{2}-\frac{2}{5}+\frac{1}{2}\\=\frac{-35}{10}-\frac{4}{10}+\frac{5}{10}\\=\frac{-35-4+5}{10}\\=\frac{-34}{10}\\=\frac{-17}{5}\)
7. \(+\left(\frac{8}{9}\right) -\left(\frac{-10}{-7}\right) -\left(\frac{-2}{3}\right)\\= \frac{8}{9}- \frac{10}{7}+\frac{2}{3}\\=\frac{56}{63}-\frac{90}{63}+\frac{42}{63}\\=\frac{56-90+42}{63}\\=\frac{8}{63}\)
8. \(+\left(\frac{-10}{7}\right) +\left(\frac{5}{4}\right) +\left(\frac{4}{10}\right)\\= \frac{-10}{7}+ \frac{5}{4}+\frac{4}{10}\\=\frac{-10}{7}+\frac{5}{4}+\frac{2}{5}\\=\frac{-200}{140}+\frac{175}{140}+\frac{56}{140}\\=\frac{-200+175+56}{140}\\=\frac{31}{140}\)
9. \(-\left(\frac{-8}{3}\right) +\left(\frac{-5}{5}\right) +\left(\frac{-8}{-5}\right)\\= \frac{8}{3}- \frac{5}{5}+\frac{8}{5}\\=\frac{8}{3}-\frac{1}{1}+\frac{8}{5}\\=\frac{40}{15}-\frac{15}{15}+\frac{24}{15}\\=\frac{40-15+24}{15}\\=\frac{49}{15}\)
10. \(-\left(\frac{-2}{-9}\right) -\left(\frac{3}{8}\right) +\left(\frac{-7}{-8}\right)\\= \frac{-2}{9}- \frac{3}{8}+\frac{7}{8}\\=\frac{-16}{72}-\frac{27}{72}+\frac{63}{72}\\=\frac{-16-27+63}{72}\\=\frac{20}{72}\\=\frac{5}{18}\)
11. \(-\left(\frac{-2}{-5}\right) +\left(\frac{-7}{10}\right) -\left(\frac{10}{12}\right)\\= \frac{-2}{5}- \frac{7}{10}-\frac{10}{12}\\=\frac{-2}{5}-\frac{7}{10}-\frac{5}{6}\\=\frac{-12}{30}-\frac{21}{30}-\frac{25}{30}\\=\frac{-12-21-25}{30}\\=\frac{-58}{30}\\=\frac{-29}{15}\)
12. \(-\left(\frac{3}{-4}\right) +\left(\frac{-6}{2}\right) +\left(\frac{8}{4}\right)\\= \frac{3}{4}- \frac{6}{2}+\frac{8}{4}\\=\frac{3}{4}-\frac{3}{1}+\frac{2}{1}\\=\frac{3-3+2}{4}\\=\frac{2}{4}\\=\frac{1}{2}\)