Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-6}{5}\right) +\left(\frac{9}{-5}\right) +\left(\frac{-2}{-10}\right)\\= \frac{-6}{5}- \frac{9}{5}+\frac{2}{10}\\=\frac{-6}{5}-\frac{9}{5}+\frac{1}{5}\\=\frac{-6-9+1}{5}\\=\frac{-14}{5}\)
2. \(+\left(\frac{-10}{-3}\right) +\left(\frac{5}{5}\right) -\left(\frac{-2}{-3}\right)\\= \frac{10}{3}+ \frac{5}{5}-\frac{2}{3}\\=\frac{10}{3}+\frac{1}{1}-\frac{2}{3}\\=\frac{10+1-2}{3}\\=\frac{9}{3}\\=\frac{3}{1}\)
3. \(+\left(\frac{-10}{3}\right) +\left(\frac{5}{5}\right) -\left(\frac{-6}{-8}\right)\\= \frac{-10}{3}+ \frac{5}{5}-\frac{6}{8}\\=\frac{-10}{3}+\frac{1}{1}-\frac{3}{4}\\=\frac{-40}{12}+\frac{12}{12}-\frac{9}{12}\\=\frac{-40+12-9}{12}\\=\frac{-37}{12}\)
4. \(-\left(\frac{10}{3}\right) -\left(\frac{-8}{4}\right) -\left(\frac{2}{10}\right)\\= \frac{-10}{3}+ \frac{8}{4}-\frac{2}{10}\\=\frac{-10}{3}+\frac{2}{1}-\frac{1}{5}\\=\frac{-50}{15}+\frac{30}{15}-\frac{3}{15}\\=\frac{-50+30-3}{15}\\=\frac{-23}{15}\)
5. \(+\left(\frac{-2}{-3}\right) +\left(\frac{3}{3}\right) +\left(\frac{11}{-6}\right)\\= \frac{2}{3}+ \frac{3}{3}-\frac{11}{6}\\=\frac{2}{3}+\frac{1}{1}-\frac{11}{6}\\=\frac{4}{6}+\frac{6}{6}-\frac{11}{6}\\=\frac{4+6-11}{6}\\=\frac{-1}{6}\)
6. \(-\left(\frac{3}{7}\right) -\left(\frac{10}{-9}\right) -\left(\frac{8}{-5}\right)\\= \frac{-3}{7}+ \frac{10}{9}+\frac{8}{5}\\=\frac{-135}{315}+\frac{350}{315}+\frac{504}{315}\\=\frac{-135+350+504}{315}\\=\frac{719}{315}\)
7. \(+\left(\frac{-10}{-7}\right) -\left(\frac{-2}{-7}\right) -\left(\frac{-9}{-4}\right)\\= \frac{10}{7}- \frac{2}{7}-\frac{9}{4}\\=\frac{40}{28}-\frac{8}{28}-\frac{63}{28}\\=\frac{40-8-63}{28}\\=\frac{-31}{28}\)
8. \(+\left(\frac{4}{3}\right) +\left(\frac{-7}{-7}\right) -\left(\frac{-12}{-8}\right)\\= \frac{4}{3}+ \frac{7}{7}-\frac{12}{8}\\=\frac{4}{3}+\frac{1}{1}-\frac{3}{2}\\=\frac{8}{6}+\frac{6}{6}-\frac{9}{6}\\=\frac{8+6-9}{6}\\=\frac{5}{6}\)
9. \(+\left(\frac{-3}{-2}\right) -\left(\frac{-10}{7}\right) +\left(\frac{-12}{7}\right)\\= \frac{3}{2}+ \frac{10}{7}-\frac{12}{7}\\=\frac{21}{14}+\frac{20}{14}-\frac{24}{14}\\=\frac{21+20-24}{14}\\=\frac{17}{14}\)
10. \(+\left(\frac{-4}{-3}\right) -\left(\frac{7}{-8}\right) -\left(\frac{11}{3}\right)\\= \frac{4}{3}+ \frac{7}{8}-\frac{11}{3}\\=\frac{32}{24}+\frac{21}{24}-\frac{88}{24}\\=\frac{32+21-88}{24}\\=\frac{-35}{24}\)
11. \(+\left(\frac{-8}{-7}\right) +\left(\frac{9}{4}\right) -\left(\frac{12}{-4}\right)\\= \frac{8}{7}+ \frac{9}{4}+\frac{12}{4}\\=\frac{8}{7}+\frac{9}{4}+\frac{3}{1}\\=\frac{32}{28}+\frac{63}{28}+\frac{84}{28}\\=\frac{32+63+84}{28}\\=\frac{179}{28}\)
12. \(-\left(\frac{-7}{6}\right) -\left(\frac{4}{-2}\right) +\left(\frac{7}{-10}\right)\\= \frac{7}{6}+ \frac{4}{2}-\frac{7}{10}\\=\frac{7}{6}+\frac{2}{1}-\frac{7}{10}\\=\frac{35}{30}+\frac{60}{30}-\frac{21}{30}\\=\frac{35+60-21}{30}\\=\frac{74}{30}\\=\frac{37}{15}\)