Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{-7}\right) +\left(\frac{-5}{3}\right) +\left(\frac{6}{8}\right)\\= \frac{5}{7}- \frac{5}{3}+\frac{6}{8}\\=\frac{5}{7}-\frac{5}{3}+\frac{3}{4}\\=\frac{60}{84}-\frac{140}{84}+\frac{63}{84}\\=\frac{60-140+63}{84}\\=\frac{-17}{84}\)
2. \(-\left(\frac{2}{7}\right) -\left(\frac{8}{4}\right) -\left(\frac{-12}{5}\right)\\= \frac{-2}{7}- \frac{8}{4}+\frac{12}{5}\\=\frac{-2}{7}-\frac{2}{1}+\frac{12}{5}\\=\frac{-10}{35}-\frac{70}{35}+\frac{84}{35}\\=\frac{-10-70+84}{35}\\=\frac{4}{35}\)
3. \(-\left(\frac{-3}{-8}\right) +\left(\frac{-10}{-8}\right) +\left(\frac{12}{-8}\right)\\= \frac{-3}{8}+ \frac{10}{8}-\frac{12}{8}\\=\frac{-3}{8}+\frac{5}{4}-\frac{3}{2}\\=\frac{-3+5-3}{8}\\=\frac{-1}{8}\)
4. \(+\left(\frac{-8}{-7}\right) -\left(\frac{7}{2}\right) +\left(\frac{6}{9}\right)\\= \frac{8}{7}- \frac{7}{2}+\frac{6}{9}\\=\frac{8}{7}-\frac{7}{2}+\frac{2}{3}\\=\frac{48}{42}-\frac{147}{42}+\frac{28}{42}\\=\frac{48-147+28}{42}\\=\frac{-71}{42}\)
5. \(-\left(\frac{-5}{-3}\right) +\left(\frac{5}{-8}\right) -\left(\frac{-9}{3}\right)\\= \frac{-5}{3}- \frac{5}{8}+\frac{9}{3}\\=\frac{-5}{3}-\frac{5}{8}+\frac{3}{1}\\=\frac{-40}{24}-\frac{15}{24}+\frac{72}{24}\\=\frac{-40-15+72}{24}\\=\frac{17}{24}\)
6. \(+\left(\frac{3}{-2}\right) +\left(\frac{-8}{3}\right) -\left(\frac{2}{-3}\right)\\= \frac{-3}{2}- \frac{8}{3}+\frac{2}{3}\\=\frac{-9}{6}-\frac{16}{6}+\frac{4}{6}\\=\frac{-9-16+4}{6}\\=\frac{-21}{6}\\=\frac{-7}{2}\)
7. \(+\left(\frac{-4}{-5}\right) +\left(\frac{8}{8}\right) +\left(\frac{-8}{8}\right)\\= \frac{4}{5}+ \frac{8}{8}-\frac{8}{8}\\=\frac{4}{5}+\frac{1}{1}-\frac{1}{1}\\=\frac{4+1-1}{5}\\=\frac{4}{5}\)
8. \(-\left(\frac{-9}{5}\right) +\left(\frac{-6}{-7}\right) +\left(\frac{-2}{8}\right)\\= \frac{9}{5}+ \frac{6}{7}-\frac{2}{8}\\=\frac{9}{5}+\frac{6}{7}-\frac{1}{4}\\=\frac{252}{140}+\frac{120}{140}-\frac{35}{140}\\=\frac{252+120-35}{140}\\=\frac{337}{140}\)
9. \(-\left(\frac{-3}{5}\right) -\left(\frac{10}{6}\right) +\left(\frac{2}{-10}\right)\\= \frac{3}{5}- \frac{10}{6}-\frac{2}{10}\\=\frac{3}{5}-\frac{5}{3}-\frac{1}{5}\\=\frac{9}{15}-\frac{25}{15}-\frac{3}{15}\\=\frac{9-25-3}{15}\\=\frac{-19}{15}\)
10. \(+\left(\frac{-6}{5}\right) -\left(\frac{6}{10}\right) +\left(\frac{4}{8}\right)\\= \frac{-6}{5}- \frac{6}{10}+\frac{4}{8}\\=\frac{-6}{5}-\frac{3}{5}+\frac{1}{2}\\=\frac{-12}{10}-\frac{6}{10}+\frac{5}{10}\\=\frac{-12-6+5}{10}\\=\frac{-13}{10}\)
11. \(-\left(\frac{-10}{-7}\right) +\left(\frac{4}{8}\right) +\left(\frac{2}{11}\right)\\= \frac{-10}{7}+ \frac{4}{8}+\frac{2}{11}\\=\frac{-10}{7}+\frac{1}{2}+\frac{2}{11}\\=\frac{-220}{154}+\frac{77}{154}+\frac{28}{154}\\=\frac{-220+77+28}{154}\\=\frac{-115}{154}\)
12. \(-\left(\frac{4}{-5}\right) +\left(\frac{-8}{6}\right) +\left(\frac{5}{-8}\right)\\= \frac{4}{5}- \frac{8}{6}-\frac{5}{8}\\=\frac{4}{5}-\frac{4}{3}-\frac{5}{8}\\=\frac{96}{120}-\frac{160}{120}-\frac{75}{120}\\=\frac{96-160-75}{120}\\=\frac{-139}{120}\)