Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{4}{3}\right) +\left(\frac{10}{-5}\right) -\left(\frac{10}{-7}\right)\\= \frac{-4}{3}- \frac{10}{5}+\frac{10}{7}\\=\frac{-4}{3}-\frac{2}{1}+\frac{10}{7}\\=\frac{-28}{21}-\frac{42}{21}+\frac{30}{21}\\=\frac{-28-42+30}{21}\\=\frac{-40}{21}\)
2. \(-\left(\frac{6}{7}\right) -\left(\frac{-5}{-5}\right) +\left(\frac{5}{9}\right)\\= \frac{-6}{7}- \frac{5}{5}+\frac{5}{9}\\=\frac{-6}{7}-\frac{1}{1}+\frac{5}{9}\\=\frac{-54}{63}-\frac{63}{63}+\frac{35}{63}\\=\frac{-54-63+35}{63}\\=\frac{-82}{63}\)
3. \(-\left(\frac{-2}{7}\right) +\left(\frac{-4}{-4}\right) +\left(\frac{11}{-7}\right)\\= \frac{2}{7}+ \frac{4}{4}-\frac{11}{7}\\=\frac{2}{7}+\frac{1}{1}-\frac{11}{7}\\=\frac{2+1-11}{7}\\=\frac{-8}{7}\)
4. \(-\left(\frac{9}{-2}\right) -\left(\frac{-6}{3}\right) +\left(\frac{-8}{6}\right)\\= \frac{9}{2}+ \frac{6}{3}-\frac{8}{6}\\=\frac{9}{2}+\frac{2}{1}-\frac{4}{3}\\=\frac{27}{6}+\frac{12}{6}-\frac{8}{6}\\=\frac{27+12-8}{6}\\=\frac{31}{6}\)
5. \(+\left(\frac{10}{-7}\right) +\left(\frac{4}{-10}\right) +\left(\frac{5}{5}\right)\\= \frac{-10}{7}- \frac{4}{10}+\frac{5}{5}\\=\frac{-10}{7}-\frac{2}{5}+\frac{1}{1}\\=\frac{-50}{35}-\frac{14}{35}+\frac{35}{35}\\=\frac{-50-14+35}{35}\\=\frac{-29}{35}\)
6. \(+\left(\frac{5}{-2}\right) +\left(\frac{10}{3}\right) +\left(\frac{2}{-12}\right)\\= \frac{-5}{2}+ \frac{10}{3}-\frac{2}{12}\\=\frac{-5}{2}+\frac{10}{3}-\frac{1}{6}\\=\frac{-15}{6}+\frac{20}{6}-\frac{1}{6}\\=\frac{-15+20-1}{6}\\=\frac{4}{6}\\=\frac{2}{3}\)
7. \(-\left(\frac{8}{3}\right) +\left(\frac{-10}{-4}\right) +\left(\frac{9}{5}\right)\\= \frac{-8}{3}+ \frac{10}{4}+\frac{9}{5}\\=\frac{-8}{3}+\frac{5}{2}+\frac{9}{5}\\=\frac{-80}{30}+\frac{75}{30}+\frac{54}{30}\\=\frac{-80+75+54}{30}\\=\frac{49}{30}\)
8. \(+\left(\frac{-6}{5}\right) -\left(\frac{-2}{-3}\right) +\left(\frac{-2}{11}\right)\\= \frac{-6}{5}- \frac{2}{3}-\frac{2}{11}\\=\frac{-198}{165}-\frac{110}{165}-\frac{30}{165}\\=\frac{-198-110-30}{165}\\=\frac{-338}{165}\)
9. \(+\left(\frac{-7}{-6}\right) -\left(\frac{-4}{8}\right) -\left(\frac{-4}{5}\right)\\= \frac{7}{6}+ \frac{4}{8}+\frac{4}{5}\\=\frac{7}{6}+\frac{1}{2}+\frac{4}{5}\\=\frac{35}{30}+\frac{15}{30}+\frac{24}{30}\\=\frac{35+15+24}{30}\\=\frac{74}{30}\\=\frac{37}{15}\)
10. \(+\left(\frac{-3}{-2}\right) +\left(\frac{3}{6}\right) -\left(\frac{11}{11}\right)\\= \frac{3}{2}+ \frac{3}{6}-\frac{11}{11}\\=\frac{3}{2}+\frac{1}{2}-\frac{1}{1}\\=\frac{3+1-1}{2}\\=\frac{3}{2}\)
11. \(+\left(\frac{-5}{4}\right) +\left(\frac{5}{-8}\right) +\left(\frac{-8}{-9}\right)\\= \frac{-5}{4}- \frac{5}{8}+\frac{8}{9}\\=\frac{-90}{72}-\frac{45}{72}+\frac{64}{72}\\=\frac{-90-45+64}{72}\\=\frac{-71}{72}\)
12. \(+\left(\frac{7}{5}\right) -\left(\frac{-3}{8}\right) +\left(\frac{-3}{-2}\right)\\= \frac{7}{5}+ \frac{3}{8}+\frac{3}{2}\\=\frac{56}{40}+\frac{15}{40}+\frac{60}{40}\\=\frac{56+15+60}{40}\\=\frac{131}{40}\)