Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-8}{7}\right) +\left(\frac{4}{4}\right) +\left(\frac{-7}{-8}\right)\\= \frac{-8}{7}+ \frac{4}{4}+\frac{7}{8}\\=\frac{-8}{7}+\frac{1}{1}+\frac{7}{8}\\=\frac{-64}{56}+\frac{56}{56}+\frac{49}{56}\\=\frac{-64+56+49}{56}\\=\frac{41}{56}\)
2. \(+\left(\frac{5}{3}\right) -\left(\frac{-10}{-2}\right) +\left(\frac{6}{5}\right)\\= \frac{5}{3}- \frac{10}{2}+\frac{6}{5}\\=\frac{5}{3}-\frac{5}{1}+\frac{6}{5}\\=\frac{25}{15}-\frac{75}{15}+\frac{18}{15}\\=\frac{25-75+18}{15}\\=\frac{-32}{15}\)
3. \(+\left(\frac{-6}{7}\right) -\left(\frac{10}{7}\right) -\left(\frac{-10}{-12}\right)\\= \frac{-6}{7}- \frac{10}{7}-\frac{10}{12}\\=\frac{-6}{7}-\frac{10}{7}-\frac{5}{6}\\=\frac{-36}{42}-\frac{60}{42}-\frac{35}{42}\\=\frac{-36-60-35}{42}\\=\frac{-131}{42}\)
4. \(+\left(\frac{8}{-3}\right) +\left(\frac{6}{8}\right) +\left(\frac{9}{-10}\right)\\= \frac{-8}{3}+ \frac{6}{8}-\frac{9}{10}\\=\frac{-8}{3}+\frac{3}{4}-\frac{9}{10}\\=\frac{-160}{60}+\frac{45}{60}-\frac{54}{60}\\=\frac{-160+45-54}{60}\\=\frac{-169}{60}\)
5. \(+\left(\frac{3}{-2}\right) -\left(\frac{-10}{10}\right) +\left(\frac{-5}{-10}\right)\\= \frac{-3}{2}+ \frac{10}{10}+\frac{5}{10}\\=\frac{-3}{2}+\frac{1}{1}+\frac{1}{2}\\=\frac{-3+1+1}{2}\\=\frac{-1}{2}\)
6. \(+\left(\frac{6}{-5}\right) -\left(\frac{-2}{-2}\right) +\left(\frac{-5}{-11}\right)\\= \frac{-6}{5}- \frac{2}{2}+\frac{5}{11}\\=\frac{-6}{5}-\frac{1}{1}+\frac{5}{11}\\=\frac{-66}{55}-\frac{55}{55}+\frac{25}{55}\\=\frac{-66-55+25}{55}\\=\frac{-96}{55}\)
7. \(-\left(\frac{9}{-4}\right) -\left(\frac{-6}{7}\right) -\left(\frac{5}{10}\right)\\= \frac{9}{4}+ \frac{6}{7}-\frac{5}{10}\\=\frac{9}{4}+\frac{6}{7}-\frac{1}{2}\\=\frac{63}{28}+\frac{24}{28}-\frac{14}{28}\\=\frac{63+24-14}{28}\\=\frac{73}{28}\)
8. \(-\left(\frac{10}{-3}\right) +\left(\frac{7}{4}\right) +\left(\frac{5}{-5}\right)\\= \frac{10}{3}+ \frac{7}{4}-\frac{5}{5}\\=\frac{10}{3}+\frac{7}{4}-\frac{1}{1}\\=\frac{40}{12}+\frac{21}{12}-\frac{12}{12}\\=\frac{40+21-12}{12}\\=\frac{49}{12}\)
9. \(-\left(\frac{-7}{-5}\right) -\left(\frac{3}{-7}\right) -\left(\frac{-3}{6}\right)\\= \frac{-7}{5}+ \frac{3}{7}+\frac{3}{6}\\=\frac{-7}{5}+\frac{3}{7}+\frac{1}{2}\\=\frac{-98}{70}+\frac{30}{70}+\frac{35}{70}\\=\frac{-98+30+35}{70}\\=\frac{-33}{70}\)
10. \(+\left(\frac{9}{-4}\right) +\left(\frac{-5}{-8}\right) -\left(\frac{-5}{-9}\right)\\= \frac{-9}{4}+ \frac{5}{8}-\frac{5}{9}\\=\frac{-162}{72}+\frac{45}{72}-\frac{40}{72}\\=\frac{-162+45-40}{72}\\=\frac{-157}{72}\)
11. \(-\left(\frac{-4}{-7}\right) -\left(\frac{8}{10}\right) -\left(\frac{-6}{-7}\right)\\= \frac{-4}{7}- \frac{8}{10}-\frac{6}{7}\\=\frac{-4}{7}-\frac{4}{5}-\frac{6}{7}\\=\frac{-20}{35}-\frac{28}{35}-\frac{30}{35}\\=\frac{-20-28-30}{35}\\=\frac{-78}{35}\)
12. \(+\left(\frac{-6}{5}\right) +\left(\frac{9}{3}\right) -\left(\frac{-5}{-10}\right)\\= \frac{-6}{5}+ \frac{9}{3}-\frac{5}{10}\\=\frac{-6}{5}+\frac{3}{1}-\frac{1}{2}\\=\frac{-12}{10}+\frac{30}{10}-\frac{5}{10}\\=\frac{-12+30-5}{10}\\=\frac{13}{10}\)