Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-8}{5}\right) +\left(\frac{8}{-8}\right) +\left(\frac{2}{-3}\right)\\= \frac{8}{5}- \frac{8}{8}-\frac{2}{3}\\=\frac{8}{5}-\frac{1}{1}-\frac{2}{3}\\=\frac{24}{15}-\frac{15}{15}-\frac{10}{15}\\=\frac{24-15-10}{15}\\=\frac{-1}{15}\)
2. \(+\left(\frac{-6}{5}\right) +\left(\frac{-3}{4}\right) +\left(\frac{-11}{10}\right)\\= \frac{-6}{5}- \frac{3}{4}-\frac{11}{10}\\=\frac{-24}{20}-\frac{15}{20}-\frac{22}{20}\\=\frac{-24-15-22}{20}\\=\frac{-61}{20}\)
3. \(-\left(\frac{3}{5}\right) +\left(\frac{-6}{3}\right) -\left(\frac{7}{-6}\right)\\= \frac{-3}{5}- \frac{6}{3}+\frac{7}{6}\\=\frac{-3}{5}-\frac{2}{1}+\frac{7}{6}\\=\frac{-18}{30}-\frac{60}{30}+\frac{35}{30}\\=\frac{-18-60+35}{30}\\=\frac{-43}{30}\)
4. \(-\left(\frac{-4}{-5}\right) +\left(\frac{10}{4}\right) +\left(\frac{5}{8}\right)\\= \frac{-4}{5}+ \frac{10}{4}+\frac{5}{8}\\=\frac{-4}{5}+\frac{5}{2}+\frac{5}{8}\\=\frac{-32}{40}+\frac{100}{40}+\frac{25}{40}\\=\frac{-32+100+25}{40}\\=\frac{93}{40}\)
5. \(+\left(\frac{7}{2}\right) -\left(\frac{3}{-2}\right) +\left(\frac{6}{-12}\right)\\= \frac{7}{2}+ \frac{3}{2}-\frac{6}{12}\\=\frac{7}{2}+\frac{3}{2}-\frac{1}{2}\\=\frac{7+3-1}{2}\\=\frac{9}{2}\)
6. \(-\left(\frac{-3}{8}\right) +\left(\frac{-6}{-8}\right) -\left(\frac{10}{-4}\right)\\= \frac{3}{8}+ \frac{6}{8}+\frac{10}{4}\\=\frac{3}{8}+\frac{3}{4}+\frac{5}{2}\\=\frac{3+3+5}{8}\\=\frac{11}{8}\)
7. \(-\left(\frac{9}{-4}\right) +\left(\frac{2}{-7}\right) -\left(\frac{-11}{-12}\right)\\= \frac{9}{4}- \frac{2}{7}-\frac{11}{12}\\=\frac{189}{84}-\frac{24}{84}-\frac{77}{84}\\=\frac{189-24-77}{84}\\=\frac{88}{84}\\=\frac{22}{21}\)
8. \(-\left(\frac{-9}{-4}\right) +\left(\frac{10}{-5}\right) -\left(\frac{-2}{-11}\right)\\= \frac{-9}{4}- \frac{10}{5}-\frac{2}{11}\\=\frac{-9}{4}-\frac{2}{1}-\frac{2}{11}\\=\frac{-99}{44}-\frac{88}{44}-\frac{8}{44}\\=\frac{-99-88-8}{44}\\=\frac{-195}{44}\)
9. \(-\left(\frac{9}{8}\right) +\left(\frac{10}{-8}\right) -\left(\frac{2}{3}\right)\\= \frac{-9}{8}- \frac{10}{8}-\frac{2}{3}\\=\frac{-9}{8}-\frac{5}{4}-\frac{2}{3}\\=\frac{-27}{24}-\frac{30}{24}-\frac{16}{24}\\=\frac{-27-30-16}{24}\\=\frac{-73}{24}\)
10. \(-\left(\frac{10}{9}\right) +\left(\frac{-2}{2}\right) +\left(\frac{-9}{-9}\right)\\= \frac{-10}{9}- \frac{2}{2}+\frac{9}{9}\\=\frac{-10}{9}-\frac{1}{1}+\frac{1}{1}\\=\frac{-10-1+1}{9}\\=\frac{-10}{9}\)
11. \(+\left(\frac{5}{7}\right) +\left(\frac{10}{-7}\right) -\left(\frac{-5}{5}\right)\\= \frac{5}{7}- \frac{10}{7}+\frac{5}{5}\\=\frac{5}{7}-\frac{10}{7}+\frac{1}{1}\\=\frac{5-10+1}{7}\\=\frac{-4}{7}\)
12. \(+\left(\frac{-7}{4}\right) +\left(\frac{-7}{-8}\right) +\left(\frac{-10}{-4}\right)\\= \frac{-7}{4}+ \frac{7}{8}+\frac{10}{4}\\=\frac{-7}{4}+\frac{7}{8}+\frac{5}{2}\\=\frac{-14}{8}+\frac{7}{8}+\frac{20}{8}\\=\frac{-14+7+20}{8}\\=\frac{13}{8}\)