Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-5}{-4}\right) -\left(\frac{-8}{10}\right) +\left(\frac{10}{-7}\right)\\= \frac{5}{4}+ \frac{8}{10}-\frac{10}{7}\\=\frac{5}{4}+\frac{4}{5}-\frac{10}{7}\\=\frac{175}{140}+\frac{112}{140}-\frac{200}{140}\\=\frac{175+112-200}{140}\\=\frac{87}{140}\)
2. \(+\left(\frac{2}{-5}\right) +\left(\frac{10}{-10}\right) -\left(\frac{4}{12}\right)\\= \frac{-2}{5}- \frac{10}{10}-\frac{4}{12}\\=\frac{-2}{5}-\frac{1}{1}-\frac{1}{3}\\=\frac{-6}{15}-\frac{15}{15}-\frac{5}{15}\\=\frac{-6-15-5}{15}\\=\frac{-26}{15}\)
3. \(+\left(\frac{-9}{2}\right) +\left(\frac{-6}{2}\right) -\left(\frac{8}{-9}\right)\\= \frac{-9}{2}- \frac{6}{2}+\frac{8}{9}\\=\frac{-9}{2}-\frac{3}{1}+\frac{8}{9}\\=\frac{-81}{18}-\frac{54}{18}+\frac{16}{18}\\=\frac{-81-54+16}{18}\\=\frac{-119}{18}\)
4. \(-\left(\frac{5}{2}\right) +\left(\frac{-5}{4}\right) +\left(\frac{10}{-2}\right)\\= \frac{-5}{2}- \frac{5}{4}-\frac{10}{2}\\=\frac{-5}{2}-\frac{5}{4}-\frac{5}{1}\\=\frac{-10}{4}-\frac{5}{4}-\frac{20}{4}\\=\frac{-10-5-20}{4}\\=\frac{-35}{4}\)
5. \(-\left(\frac{3}{4}\right) +\left(\frac{-3}{-8}\right) +\left(\frac{-8}{5}\right)\\= \frac{-3}{4}+ \frac{3}{8}-\frac{8}{5}\\=\frac{-30}{40}+\frac{15}{40}-\frac{64}{40}\\=\frac{-30+15-64}{40}\\=\frac{-79}{40}\)
6. \(-\left(\frac{9}{4}\right) -\left(\frac{10}{10}\right) -\left(\frac{-9}{-6}\right)\\= \frac{-9}{4}- \frac{10}{10}-\frac{9}{6}\\=\frac{-9}{4}-\frac{1}{1}-\frac{3}{2}\\=\frac{-9-1-3}{4}\\=\frac{-13}{4}\)
7. \(+\left(\frac{-5}{8}\right) -\left(\frac{6}{-3}\right) -\left(\frac{-2}{-11}\right)\\= \frac{-5}{8}+ \frac{6}{3}-\frac{2}{11}\\=\frac{-5}{8}+\frac{2}{1}-\frac{2}{11}\\=\frac{-55}{88}+\frac{176}{88}-\frac{16}{88}\\=\frac{-55+176-16}{88}\\=\frac{105}{88}\)
8. \(+\left(\frac{-3}{5}\right) -\left(\frac{-5}{-10}\right) +\left(\frac{-8}{-5}\right)\\= \frac{-3}{5}- \frac{5}{10}+\frac{8}{5}\\=\frac{-3}{5}-\frac{1}{2}+\frac{8}{5}\\=\frac{-6}{10}-\frac{5}{10}+\frac{16}{10}\\=\frac{-6-5+16}{10}\\=\frac{5}{10}\\=\frac{1}{2}\)
9. \(+\left(\frac{4}{5}\right) +\left(\frac{3}{9}\right) -\left(\frac{3}{-5}\right)\\= \frac{4}{5}+ \frac{3}{9}+\frac{3}{5}\\=\frac{4}{5}+\frac{1}{3}+\frac{3}{5}\\=\frac{12}{15}+\frac{5}{15}+\frac{9}{15}\\=\frac{12+5+9}{15}\\=\frac{26}{15}\)
10. \(-\left(\frac{-7}{-2}\right) +\left(\frac{10}{7}\right) +\left(\frac{4}{-3}\right)\\= \frac{-7}{2}+ \frac{10}{7}-\frac{4}{3}\\=\frac{-147}{42}+\frac{60}{42}-\frac{56}{42}\\=\frac{-147+60-56}{42}\\=\frac{-143}{42}\)
11. \(-\left(\frac{-7}{8}\right) +\left(\frac{6}{-5}\right) +\left(\frac{8}{6}\right)\\= \frac{7}{8}- \frac{6}{5}+\frac{8}{6}\\=\frac{7}{8}-\frac{6}{5}+\frac{4}{3}\\=\frac{105}{120}-\frac{144}{120}+\frac{160}{120}\\=\frac{105-144+160}{120}\\=\frac{121}{120}\)
12. \(-\left(\frac{-5}{-6}\right) -\left(\frac{-10}{3}\right) -\left(\frac{8}{-4}\right)\\= \frac{-5}{6}+ \frac{10}{3}+\frac{8}{4}\\=\frac{-5}{6}+\frac{10}{3}+\frac{2}{1}\\=\frac{-5+10+2}{6}\\=\frac{7}{6}\)