Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{8}\right) +\left(\frac{8}{-7}\right) +\left(\frac{4}{8}\right)\\= \frac{-5}{8}- \frac{8}{7}+\frac{4}{8}\\=\frac{-5}{8}-\frac{8}{7}+\frac{1}{2}\\=\frac{-35}{56}-\frac{64}{56}+\frac{28}{56}\\=\frac{-35-64+28}{56}\\=\frac{-71}{56}\)
2. \(+\left(\frac{-4}{-9}\right) +\left(\frac{-3}{4}\right) +\left(\frac{-7}{9}\right)\\= \frac{4}{9}- \frac{3}{4}-\frac{7}{9}\\=\frac{16}{36}-\frac{27}{36}-\frac{28}{36}\\=\frac{16-27-28}{36}\\=\frac{-39}{36}\\=\frac{-13}{12}\)
3. \(-\left(\frac{-8}{-3}\right) +\left(\frac{8}{5}\right) -\left(\frac{-5}{-8}\right)\\= \frac{-8}{3}+ \frac{8}{5}-\frac{5}{8}\\=\frac{-320}{120}+\frac{192}{120}-\frac{75}{120}\\=\frac{-320+192-75}{120}\\=\frac{-203}{120}\)
4. \(-\left(\frac{5}{-2}\right) +\left(\frac{-9}{10}\right) -\left(\frac{9}{11}\right)\\= \frac{5}{2}- \frac{9}{10}-\frac{9}{11}\\=\frac{275}{110}-\frac{99}{110}-\frac{90}{110}\\=\frac{275-99-90}{110}\\=\frac{86}{110}\\=\frac{43}{55}\)
5. \(+\left(\frac{-4}{-7}\right) -\left(\frac{-6}{2}\right) +\left(\frac{3}{-5}\right)\\= \frac{4}{7}+ \frac{6}{2}-\frac{3}{5}\\=\frac{4}{7}+\frac{3}{1}-\frac{3}{5}\\=\frac{20}{35}+\frac{105}{35}-\frac{21}{35}\\=\frac{20+105-21}{35}\\=\frac{104}{35}\)
6. \(+\left(\frac{-4}{3}\right) +\left(\frac{6}{2}\right) -\left(\frac{10}{-11}\right)\\= \frac{-4}{3}+ \frac{6}{2}+\frac{10}{11}\\=\frac{-4}{3}+\frac{3}{1}+\frac{10}{11}\\=\frac{-44}{33}+\frac{99}{33}+\frac{30}{33}\\=\frac{-44+99+30}{33}\\=\frac{85}{33}\)
7. \(+\left(\frac{4}{-3}\right) +\left(\frac{-3}{-8}\right) -\left(\frac{7}{4}\right)\\= \frac{-4}{3}+ \frac{3}{8}-\frac{7}{4}\\=\frac{-32}{24}+\frac{9}{24}-\frac{42}{24}\\=\frac{-32+9-42}{24}\\=\frac{-65}{24}\)
8. \(-\left(\frac{3}{2}\right) -\left(\frac{2}{-6}\right) +\left(\frac{-5}{-4}\right)\\= \frac{-3}{2}+ \frac{2}{6}+\frac{5}{4}\\=\frac{-3}{2}+\frac{1}{3}+\frac{5}{4}\\=\frac{-18}{12}+\frac{4}{12}+\frac{15}{12}\\=\frac{-18+4+15}{12}\\=\frac{1}{12}\)
9. \(-\left(\frac{-8}{9}\right) +\left(\frac{6}{6}\right) -\left(\frac{6}{9}\right)\\= \frac{8}{9}+ \frac{6}{6}-\frac{6}{9}\\=\frac{8}{9}+\frac{1}{1}-\frac{2}{3}\\=\frac{8+1-2}{9}\\=\frac{7}{9}\)
10. \(-\left(\frac{-5}{-6}\right) -\left(\frac{9}{4}\right) -\left(\frac{5}{-7}\right)\\= \frac{-5}{6}- \frac{9}{4}+\frac{5}{7}\\=\frac{-70}{84}-\frac{189}{84}+\frac{60}{84}\\=\frac{-70-189+60}{84}\\=\frac{-199}{84}\)
11. \(+\left(\frac{10}{7}\right) -\left(\frac{-7}{-9}\right) +\left(\frac{-7}{-2}\right)\\= \frac{10}{7}- \frac{7}{9}+\frac{7}{2}\\=\frac{180}{126}-\frac{98}{126}+\frac{441}{126}\\=\frac{180-98+441}{126}\\=\frac{523}{126}\)
12. \(-\left(\frac{2}{-9}\right) -\left(\frac{-9}{-10}\right) -\left(\frac{11}{-4}\right)\\= \frac{2}{9}- \frac{9}{10}+\frac{11}{4}\\=\frac{40}{180}-\frac{162}{180}+\frac{495}{180}\\=\frac{40-162+495}{180}\\=\frac{373}{180}\)