Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{5}\right) +\left(\frac{-4}{-5}\right) -\left(\frac{-5}{10}\right)\\= \frac{-8}{5}+ \frac{4}{5}+\frac{5}{10}\\=\frac{-8}{5}+\frac{4}{5}+\frac{1}{2}\\=\frac{-16}{10}+\frac{8}{10}+\frac{5}{10}\\=\frac{-16+8+5}{10}\\=\frac{-3}{10}\)
2. \(+\left(\frac{6}{-5}\right) -\left(\frac{2}{8}\right) -\left(\frac{-6}{-3}\right)\\= \frac{-6}{5}- \frac{2}{8}-\frac{6}{3}\\=\frac{-6}{5}-\frac{1}{4}-\frac{2}{1}\\=\frac{-24}{20}-\frac{5}{20}-\frac{40}{20}\\=\frac{-24-5-40}{20}\\=\frac{-69}{20}\)
3. \(+\left(\frac{-9}{2}\right) +\left(\frac{2}{10}\right) +\left(\frac{-2}{7}\right)\\= \frac{-9}{2}+ \frac{2}{10}-\frac{2}{7}\\=\frac{-9}{2}+\frac{1}{5}-\frac{2}{7}\\=\frac{-315}{70}+\frac{14}{70}-\frac{20}{70}\\=\frac{-315+14-20}{70}\\=\frac{-321}{70}\)
4. \(-\left(\frac{4}{7}\right) +\left(\frac{-6}{-8}\right) -\left(\frac{8}{7}\right)\\= \frac{-4}{7}+ \frac{6}{8}-\frac{8}{7}\\=\frac{-4}{7}+\frac{3}{4}-\frac{8}{7}\\=\frac{-16}{28}+\frac{21}{28}-\frac{32}{28}\\=\frac{-16+21-32}{28}\\=\frac{-27}{28}\)
5. \(-\left(\frac{8}{9}\right) +\left(\frac{-3}{7}\right) +\left(\frac{5}{5}\right)\\= \frac{-8}{9}- \frac{3}{7}+\frac{5}{5}\\=\frac{-8}{9}-\frac{3}{7}+\frac{1}{1}\\=\frac{-56}{63}-\frac{27}{63}+\frac{63}{63}\\=\frac{-56-27+63}{63}\\=\frac{-20}{63}\)
6. \(-\left(\frac{4}{5}\right) +\left(\frac{8}{6}\right) +\left(\frac{-2}{2}\right)\\= \frac{-4}{5}+ \frac{8}{6}-\frac{2}{2}\\=\frac{-4}{5}+\frac{4}{3}-\frac{1}{1}\\=\frac{-12}{15}+\frac{20}{15}-\frac{15}{15}\\=\frac{-12+20-15}{15}\\=\frac{-7}{15}\)
7. \(-\left(\frac{-10}{-7}\right) -\left(\frac{-10}{-3}\right) +\left(\frac{9}{-6}\right)\\= \frac{-10}{7}- \frac{10}{3}-\frac{9}{6}\\=\frac{-10}{7}-\frac{10}{3}-\frac{3}{2}\\=\frac{-60}{42}-\frac{140}{42}-\frac{63}{42}\\=\frac{-60-140-63}{42}\\=\frac{-263}{42}\)
8. \(+\left(\frac{-10}{-7}\right) -\left(\frac{-6}{7}\right) +\left(\frac{-4}{4}\right)\\= \frac{10}{7}+ \frac{6}{7}-\frac{4}{4}\\=\frac{10}{7}+\frac{6}{7}-\frac{1}{1}\\=\frac{10+6-1}{7}\\=\frac{15}{7}\)
9. \(+\left(\frac{3}{-7}\right) -\left(\frac{-4}{2}\right) -\left(\frac{5}{-9}\right)\\= \frac{-3}{7}+ \frac{4}{2}+\frac{5}{9}\\=\frac{-3}{7}+\frac{2}{1}+\frac{5}{9}\\=\frac{-27}{63}+\frac{126}{63}+\frac{35}{63}\\=\frac{-27+126+35}{63}\\=\frac{134}{63}\)
10. \(-\left(\frac{-9}{2}\right) +\left(\frac{8}{-10}\right) -\left(\frac{-10}{-12}\right)\\= \frac{9}{2}- \frac{8}{10}-\frac{10}{12}\\=\frac{9}{2}-\frac{4}{5}-\frac{5}{6}\\=\frac{135}{30}-\frac{24}{30}-\frac{25}{30}\\=\frac{135-24-25}{30}\\=\frac{86}{30}\\=\frac{43}{15}\)
11. \(-\left(\frac{4}{-9}\right) -\left(\frac{7}{-2}\right) +\left(\frac{-10}{-11}\right)\\= \frac{4}{9}+ \frac{7}{2}+\frac{10}{11}\\=\frac{88}{198}+\frac{693}{198}+\frac{180}{198}\\=\frac{88+693+180}{198}\\=\frac{961}{198}\)
12. \(-\left(\frac{9}{8}\right) +\left(\frac{2}{8}\right) -\left(\frac{-2}{3}\right)\\= \frac{-9}{8}+ \frac{2}{8}+\frac{2}{3}\\=\frac{-9}{8}+\frac{1}{4}+\frac{2}{3}\\=\frac{-27}{24}+\frac{6}{24}+\frac{16}{24}\\=\frac{-27+6+16}{24}\\=\frac{-5}{24}\)