Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-10}{7}\right) +\left(\frac{-5}{-8}\right) +\left(\frac{2}{6}\right)\\= \frac{10}{7}+ \frac{5}{8}+\frac{2}{6}\\=\frac{10}{7}+\frac{5}{8}+\frac{1}{3}\\=\frac{240}{168}+\frac{105}{168}+\frac{56}{168}\\=\frac{240+105+56}{168}\\=\frac{401}{168}\)
2. \(-\left(\frac{-10}{3}\right) -\left(\frac{-6}{-10}\right) -\left(\frac{4}{11}\right)\\= \frac{10}{3}- \frac{6}{10}-\frac{4}{11}\\=\frac{10}{3}-\frac{3}{5}-\frac{4}{11}\\=\frac{550}{165}-\frac{99}{165}-\frac{60}{165}\\=\frac{550-99-60}{165}\\=\frac{391}{165}\)
3. \(-\left(\frac{4}{-3}\right) -\left(\frac{8}{4}\right) +\left(\frac{11}{-5}\right)\\= \frac{4}{3}- \frac{8}{4}-\frac{11}{5}\\=\frac{4}{3}-\frac{2}{1}-\frac{11}{5}\\=\frac{20}{15}-\frac{30}{15}-\frac{33}{15}\\=\frac{20-30-33}{15}\\=\frac{-43}{15}\)
4. \(+\left(\frac{6}{5}\right) +\left(\frac{-5}{-2}\right) -\left(\frac{11}{5}\right)\\= \frac{6}{5}+ \frac{5}{2}-\frac{11}{5}\\=\frac{12}{10}+\frac{25}{10}-\frac{22}{10}\\=\frac{12+25-22}{10}\\=\frac{15}{10}\\=\frac{3}{2}\)
5. \(-\left(\frac{-8}{3}\right) -\left(\frac{8}{-5}\right) -\left(\frac{2}{-9}\right)\\= \frac{8}{3}+ \frac{8}{5}+\frac{2}{9}\\=\frac{120}{45}+\frac{72}{45}+\frac{10}{45}\\=\frac{120+72+10}{45}\\=\frac{202}{45}\)
6. \(+\left(\frac{6}{5}\right) +\left(\frac{-5}{-2}\right) -\left(\frac{2}{7}\right)\\= \frac{6}{5}+ \frac{5}{2}-\frac{2}{7}\\=\frac{84}{70}+\frac{175}{70}-\frac{20}{70}\\=\frac{84+175-20}{70}\\=\frac{239}{70}\)
7. \(+\left(\frac{10}{3}\right) +\left(\frac{2}{-2}\right) +\left(\frac{12}{-2}\right)\\= \frac{10}{3}- \frac{2}{2}-\frac{12}{2}\\=\frac{10}{3}-\frac{1}{1}-\frac{6}{1}\\=\frac{10-1-6}{3}\\=\frac{3}{3}\\=\frac{1}{1}\)
8. \(-\left(\frac{8}{3}\right) -\left(\frac{-7}{-9}\right) +\left(\frac{5}{10}\right)\\= \frac{-8}{3}- \frac{7}{9}+\frac{5}{10}\\=\frac{-8}{3}-\frac{7}{9}+\frac{1}{2}\\=\frac{-48}{18}-\frac{14}{18}+\frac{9}{18}\\=\frac{-48-14+9}{18}\\=\frac{-53}{18}\)
9. \(+\left(\frac{-8}{-3}\right) -\left(\frac{2}{3}\right) +\left(\frac{4}{-3}\right)\\= \frac{8}{3}- \frac{2}{3}-\frac{4}{3}\\=\frac{8-2-4}{3}\\=\frac{2}{3}\)
10. \(+\left(\frac{-5}{8}\right) +\left(\frac{-5}{-9}\right) -\left(\frac{-9}{-11}\right)\\= \frac{-5}{8}+ \frac{5}{9}-\frac{9}{11}\\=\frac{-495}{792}+\frac{440}{792}-\frac{648}{792}\\=\frac{-495+440-648}{792}\\=\frac{-703}{792}\)
11. \(-\left(\frac{7}{-8}\right) -\left(\frac{-9}{2}\right) +\left(\frac{-8}{6}\right)\\= \frac{7}{8}+ \frac{9}{2}-\frac{8}{6}\\=\frac{7}{8}+\frac{9}{2}-\frac{4}{3}\\=\frac{21}{24}+\frac{108}{24}-\frac{32}{24}\\=\frac{21+108-32}{24}\\=\frac{97}{24}\)
12. \(+\left(\frac{5}{6}\right) +\left(\frac{6}{-7}\right) +\left(\frac{-3}{3}\right)\\= \frac{5}{6}- \frac{6}{7}-\frac{3}{3}\\=\frac{5}{6}-\frac{6}{7}-\frac{1}{1}\\=\frac{35}{42}-\frac{36}{42}-\frac{42}{42}\\=\frac{35-36-42}{42}\\=\frac{-43}{42}\)