Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{3}\right) -\left(\frac{4}{7}\right) -\left(\frac{2}{-7}\right)\\= \frac{-2}{3}- \frac{4}{7}+\frac{2}{7}\\=\frac{-14}{21}-\frac{12}{21}+\frac{6}{21}\\=\frac{-14-12+6}{21}\\=\frac{-20}{21}\)
2. \(+\left(\frac{-7}{-4}\right) -\left(\frac{8}{4}\right) -\left(\frac{6}{-11}\right)\\= \frac{7}{4}- \frac{8}{4}+\frac{6}{11}\\=\frac{7}{4}-\frac{2}{1}+\frac{6}{11}\\=\frac{77}{44}-\frac{88}{44}+\frac{24}{44}\\=\frac{77-88+24}{44}\\=\frac{13}{44}\)
3. \(+\left(\frac{2}{5}\right) +\left(\frac{10}{7}\right) -\left(\frac{-3}{4}\right)\\= \frac{2}{5}+ \frac{10}{7}+\frac{3}{4}\\=\frac{56}{140}+\frac{200}{140}+\frac{105}{140}\\=\frac{56+200+105}{140}\\=\frac{361}{140}\)
4. \(-\left(\frac{5}{9}\right) +\left(\frac{-3}{4}\right) -\left(\frac{3}{-3}\right)\\= \frac{-5}{9}- \frac{3}{4}+\frac{3}{3}\\=\frac{-5}{9}-\frac{3}{4}+\frac{1}{1}\\=\frac{-20}{36}-\frac{27}{36}+\frac{36}{36}\\=\frac{-20-27+36}{36}\\=\frac{-11}{36}\)
5. \(+\left(\frac{4}{3}\right) -\left(\frac{8}{3}\right) -\left(\frac{9}{-12}\right)\\= \frac{4}{3}- \frac{8}{3}+\frac{9}{12}\\=\frac{4}{3}-\frac{8}{3}+\frac{3}{4}\\=\frac{16}{12}-\frac{32}{12}+\frac{9}{12}\\=\frac{16-32+9}{12}\\=\frac{-7}{12}\)
6. \(-\left(\frac{-2}{5}\right) +\left(\frac{-6}{-9}\right) -\left(\frac{7}{-5}\right)\\= \frac{2}{5}+ \frac{6}{9}+\frac{7}{5}\\=\frac{2}{5}+\frac{2}{3}+\frac{7}{5}\\=\frac{6}{15}+\frac{10}{15}+\frac{21}{15}\\=\frac{6+10+21}{15}\\=\frac{37}{15}\)
7. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-9}{4}\right) -\left(\frac{7}{6}\right)\\= \frac{-10}{7}- \frac{9}{4}-\frac{7}{6}\\=\frac{-120}{84}-\frac{189}{84}-\frac{98}{84}\\=\frac{-120-189-98}{84}\\=\frac{-407}{84}\)
8. \(+\left(\frac{-2}{-3}\right) -\left(\frac{-9}{2}\right) +\left(\frac{10}{-5}\right)\\= \frac{2}{3}+ \frac{9}{2}-\frac{10}{5}\\=\frac{2}{3}+\frac{9}{2}-\frac{2}{1}\\=\frac{4}{6}+\frac{27}{6}-\frac{12}{6}\\=\frac{4+27-12}{6}\\=\frac{19}{6}\)
9. \(-\left(\frac{-3}{-5}\right) +\left(\frac{-4}{8}\right) +\left(\frac{3}{-3}\right)\\= \frac{-3}{5}- \frac{4}{8}-\frac{3}{3}\\=\frac{-3}{5}-\frac{1}{2}-\frac{1}{1}\\=\frac{-6}{10}-\frac{5}{10}-\frac{10}{10}\\=\frac{-6-5-10}{10}\\=\frac{-21}{10}\)
10. \(-\left(\frac{-5}{-2}\right) +\left(\frac{-8}{5}\right) +\left(\frac{11}{-5}\right)\\= \frac{-5}{2}- \frac{8}{5}-\frac{11}{5}\\=\frac{-25}{10}-\frac{16}{10}-\frac{22}{10}\\=\frac{-25-16-22}{10}\\=\frac{-63}{10}\)
11. \(-\left(\frac{9}{4}\right) +\left(\frac{5}{-5}\right) -\left(\frac{-10}{7}\right)\\= \frac{-9}{4}- \frac{5}{5}+\frac{10}{7}\\=\frac{-9}{4}-\frac{1}{1}+\frac{10}{7}\\=\frac{-63}{28}-\frac{28}{28}+\frac{40}{28}\\=\frac{-63-28+40}{28}\\=\frac{-51}{28}\)
12. \(-\left(\frac{4}{9}\right) +\left(\frac{4}{10}\right) -\left(\frac{-2}{-5}\right)\\= \frac{-4}{9}+ \frac{4}{10}-\frac{2}{5}\\=\frac{-4}{9}+\frac{2}{5}-\frac{2}{5}\\=\frac{-20}{45}+\frac{18}{45}-\frac{18}{45}\\=\frac{-20+18-18}{45}\\=\frac{-20}{45}\\=\frac{-4}{9}\)