Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{-7}\right) +\left(\frac{6}{4}\right) +\left(\frac{-5}{9}\right)\\= \frac{9}{7}+ \frac{6}{4}-\frac{5}{9}\\=\frac{9}{7}+\frac{3}{2}-\frac{5}{9}\\=\frac{162}{126}+\frac{189}{126}-\frac{70}{126}\\=\frac{162+189-70}{126}\\=\frac{281}{126}\)
2. \(-\left(\frac{-6}{5}\right) +\left(\frac{9}{-5}\right) -\left(\frac{-4}{-7}\right)\\= \frac{6}{5}- \frac{9}{5}-\frac{4}{7}\\=\frac{42}{35}-\frac{63}{35}-\frac{20}{35}\\=\frac{42-63-20}{35}\\=\frac{-41}{35}\)
3. \(+\left(\frac{-3}{-7}\right) -\left(\frac{6}{-9}\right) -\left(\frac{-2}{-8}\right)\\= \frac{3}{7}+ \frac{6}{9}-\frac{2}{8}\\=\frac{3}{7}+\frac{2}{3}-\frac{1}{4}\\=\frac{36}{84}+\frac{56}{84}-\frac{21}{84}\\=\frac{36+56-21}{84}\\=\frac{71}{84}\)
4. \(-\left(\frac{-2}{3}\right) +\left(\frac{-10}{3}\right) -\left(\frac{2}{4}\right)\\= \frac{2}{3}- \frac{10}{3}-\frac{2}{4}\\=\frac{2}{3}-\frac{10}{3}-\frac{1}{2}\\=\frac{4}{6}-\frac{20}{6}-\frac{3}{6}\\=\frac{4-20-3}{6}\\=\frac{-19}{6}\)
5. \(+\left(\frac{9}{2}\right) +\left(\frac{-6}{-5}\right) -\left(\frac{-6}{12}\right)\\= \frac{9}{2}+ \frac{6}{5}+\frac{6}{12}\\=\frac{9}{2}+\frac{6}{5}+\frac{1}{2}\\=\frac{45}{10}+\frac{12}{10}+\frac{5}{10}\\=\frac{45+12+5}{10}\\=\frac{62}{10}\\=\frac{31}{5}\)
6. \(+\left(\frac{3}{4}\right) -\left(\frac{8}{-8}\right) +\left(\frac{-9}{-10}\right)\\= \frac{3}{4}+ \frac{8}{8}+\frac{9}{10}\\=\frac{3}{4}+\frac{1}{1}+\frac{9}{10}\\=\frac{15}{20}+\frac{20}{20}+\frac{18}{20}\\=\frac{15+20+18}{20}\\=\frac{53}{20}\)
7. \(+\left(\frac{-6}{-5}\right) -\left(\frac{2}{-3}\right) +\left(\frac{-7}{-7}\right)\\= \frac{6}{5}+ \frac{2}{3}+\frac{7}{7}\\=\frac{6}{5}+\frac{2}{3}+\frac{1}{1}\\=\frac{18}{15}+\frac{10}{15}+\frac{15}{15}\\=\frac{18+10+15}{15}\\=\frac{43}{15}\)
8. \(-\left(\frac{-4}{-7}\right) +\left(\frac{7}{3}\right) +\left(\frac{4}{12}\right)\\= \frac{-4}{7}+ \frac{7}{3}+\frac{4}{12}\\=\frac{-4}{7}+\frac{7}{3}+\frac{1}{3}\\=\frac{-12}{21}+\frac{49}{21}+\frac{7}{21}\\=\frac{-12+49+7}{21}\\=\frac{44}{21}\)
9. \(-\left(\frac{2}{-7}\right) +\left(\frac{-4}{-7}\right) -\left(\frac{-8}{12}\right)\\= \frac{2}{7}+ \frac{4}{7}+\frac{8}{12}\\=\frac{2}{7}+\frac{4}{7}+\frac{2}{3}\\=\frac{6}{21}+\frac{12}{21}+\frac{14}{21}\\=\frac{6+12+14}{21}\\=\frac{32}{21}\)
10. \(+\left(\frac{9}{-4}\right) -\left(\frac{-10}{9}\right) +\left(\frac{10}{-11}\right)\\= \frac{-9}{4}+ \frac{10}{9}-\frac{10}{11}\\=\frac{-891}{396}+\frac{440}{396}-\frac{360}{396}\\=\frac{-891+440-360}{396}\\=\frac{-811}{396}\)
11. \(+\left(\frac{5}{7}\right) +\left(\frac{-2}{-6}\right) -\left(\frac{6}{8}\right)\\= \frac{5}{7}+ \frac{2}{6}-\frac{6}{8}\\=\frac{5}{7}+\frac{1}{3}-\frac{3}{4}\\=\frac{60}{84}+\frac{28}{84}-\frac{63}{84}\\=\frac{60+28-63}{84}\\=\frac{25}{84}\)
12. \(+\left(\frac{5}{-8}\right) -\left(\frac{6}{4}\right) -\left(\frac{-3}{12}\right)\\= \frac{-5}{8}- \frac{6}{4}+\frac{3}{12}\\=\frac{-5}{8}-\frac{3}{2}+\frac{1}{4}\\=\frac{-5-3+1}{8}\\=\frac{-7}{8}\)