Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-3}{2}\right) +\left(\frac{8}{-5}\right) +\left(\frac{5}{-4}\right)\\= \frac{3}{2}- \frac{8}{5}-\frac{5}{4}\\=\frac{30}{20}-\frac{32}{20}-\frac{25}{20}\\=\frac{30-32-25}{20}\\=\frac{-27}{20}\)
2. \(-\left(\frac{-3}{-4}\right) -\left(\frac{-9}{10}\right) +\left(\frac{-3}{4}\right)\\= \frac{-3}{4}+ \frac{9}{10}-\frac{3}{4}\\=\frac{-15}{20}+\frac{18}{20}-\frac{15}{20}\\=\frac{-15+18-15}{20}\\=\frac{-12}{20}\\=\frac{-3}{5}\)
3. \(-\left(\frac{7}{6}\right) +\left(\frac{-3}{-9}\right) -\left(\frac{-5}{-10}\right)\\= \frac{-7}{6}+ \frac{3}{9}-\frac{5}{10}\\=\frac{-7}{6}+\frac{1}{3}-\frac{1}{2}\\=\frac{-7+1-1}{6}\\=\frac{-7}{6}\)
4. \(+\left(\frac{-4}{3}\right) +\left(\frac{-6}{6}\right) -\left(\frac{4}{-7}\right)\\= \frac{-4}{3}- \frac{6}{6}+\frac{4}{7}\\=\frac{-4}{3}-\frac{1}{1}+\frac{4}{7}\\=\frac{-28}{21}-\frac{21}{21}+\frac{12}{21}\\=\frac{-28-21+12}{21}\\=\frac{-37}{21}\)
5. \(-\left(\frac{5}{-7}\right) -\left(\frac{5}{-10}\right) -\left(\frac{-10}{12}\right)\\= \frac{5}{7}+ \frac{5}{10}+\frac{10}{12}\\=\frac{5}{7}+\frac{1}{2}+\frac{5}{6}\\=\frac{30}{42}+\frac{21}{42}+\frac{35}{42}\\=\frac{30+21+35}{42}\\=\frac{86}{42}\\=\frac{43}{21}\)
6. \(-\left(\frac{8}{9}\right) +\left(\frac{3}{-7}\right) -\left(\frac{12}{-11}\right)\\= \frac{-8}{9}- \frac{3}{7}+\frac{12}{11}\\=\frac{-616}{693}-\frac{297}{693}+\frac{756}{693}\\=\frac{-616-297+756}{693}\\=\frac{-157}{693}\)
7. \(+\left(\frac{2}{5}\right) +\left(\frac{-5}{-3}\right) -\left(\frac{8}{5}\right)\\= \frac{2}{5}+ \frac{5}{3}-\frac{8}{5}\\=\frac{6}{15}+\frac{25}{15}-\frac{24}{15}\\=\frac{6+25-24}{15}\\=\frac{7}{15}\)
8. \(+\left(\frac{2}{-3}\right) -\left(\frac{2}{-5}\right) +\left(\frac{-8}{6}\right)\\= \frac{-2}{3}+ \frac{2}{5}-\frac{8}{6}\\=\frac{-2}{3}+\frac{2}{5}-\frac{4}{3}\\=\frac{-10}{15}+\frac{6}{15}-\frac{20}{15}\\=\frac{-10+6-20}{15}\\=\frac{-24}{15}\\=\frac{-8}{5}\)
9. \(+\left(\frac{-8}{-5}\right) -\left(\frac{8}{-7}\right) +\left(\frac{-12}{-3}\right)\\= \frac{8}{5}+ \frac{8}{7}+\frac{12}{3}\\=\frac{8}{5}+\frac{8}{7}+\frac{4}{1}\\=\frac{56}{35}+\frac{40}{35}+\frac{140}{35}\\=\frac{56+40+140}{35}\\=\frac{236}{35}\)
10. \(-\left(\frac{2}{3}\right) -\left(\frac{5}{-10}\right) +\left(\frac{-10}{11}\right)\\= \frac{-2}{3}+ \frac{5}{10}-\frac{10}{11}\\=\frac{-2}{3}+\frac{1}{2}-\frac{10}{11}\\=\frac{-44}{66}+\frac{33}{66}-\frac{60}{66}\\=\frac{-44+33-60}{66}\\=\frac{-71}{66}\)
11. \(+\left(\frac{10}{9}\right) +\left(\frac{4}{-4}\right) -\left(\frac{12}{2}\right)\\= \frac{10}{9}- \frac{4}{4}-\frac{12}{2}\\=\frac{10}{9}-\frac{1}{1}-\frac{6}{1}\\=\frac{10-1-6}{9}\\=\frac{3}{9}\\=\frac{1}{3}\)
12. \(-\left(\frac{5}{-2}\right) -\left(\frac{-4}{4}\right) +\left(\frac{8}{-5}\right)\\= \frac{5}{2}+ \frac{4}{4}-\frac{8}{5}\\=\frac{5}{2}+\frac{1}{1}-\frac{8}{5}\\=\frac{25}{10}+\frac{10}{10}-\frac{16}{10}\\=\frac{25+10-16}{10}\\=\frac{19}{10}\)