Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-5}{-3}\right) +\left(\frac{-4}{8}\right) -\left(\frac{4}{-8}\right)\\= \frac{-5}{3}- \frac{4}{8}+\frac{4}{8}\\=\frac{-5}{3}-\frac{1}{2}+\frac{1}{2}\\=\frac{-10}{6}-\frac{3}{6}+\frac{3}{6}\\=\frac{-10-3+3}{6}\\=\frac{-10}{6}\\=\frac{-5}{3}\)
2. \(+\left(\frac{10}{-7}\right) -\left(\frac{-2}{2}\right) +\left(\frac{7}{5}\right)\\= \frac{-10}{7}+ \frac{2}{2}+\frac{7}{5}\\=\frac{-10}{7}+\frac{1}{1}+\frac{7}{5}\\=\frac{-50}{35}+\frac{35}{35}+\frac{49}{35}\\=\frac{-50+35+49}{35}\\=\frac{34}{35}\)
3. \(+\left(\frac{-5}{-3}\right) +\left(\frac{-3}{-3}\right) -\left(\frac{10}{7}\right)\\= \frac{5}{3}+ \frac{3}{3}-\frac{10}{7}\\=\frac{5}{3}+\frac{1}{1}-\frac{10}{7}\\=\frac{35}{21}+\frac{21}{21}-\frac{30}{21}\\=\frac{35+21-30}{21}\\=\frac{26}{21}\)
4. \(+\left(\frac{8}{-9}\right) -\left(\frac{4}{7}\right) -\left(\frac{9}{8}\right)\\= \frac{-8}{9}- \frac{4}{7}-\frac{9}{8}\\=\frac{-448}{504}-\frac{288}{504}-\frac{567}{504}\\=\frac{-448-288-567}{504}\\=\frac{-1303}{504}\)
5. \(-\left(\frac{-10}{-7}\right) -\left(\frac{7}{-9}\right) -\left(\frac{-12}{-9}\right)\\= \frac{-10}{7}+ \frac{7}{9}-\frac{12}{9}\\=\frac{-10}{7}+\frac{7}{9}-\frac{4}{3}\\=\frac{-90}{63}+\frac{49}{63}-\frac{84}{63}\\=\frac{-90+49-84}{63}\\=\frac{-125}{63}\)
6. \(+\left(\frac{-5}{-8}\right) +\left(\frac{3}{7}\right) -\left(\frac{6}{2}\right)\\= \frac{5}{8}+ \frac{3}{7}-\frac{6}{2}\\=\frac{5}{8}+\frac{3}{7}-\frac{3}{1}\\=\frac{35}{56}+\frac{24}{56}-\frac{168}{56}\\=\frac{35+24-168}{56}\\=\frac{-109}{56}\)
7. \(+\left(\frac{-4}{-3}\right) +\left(\frac{-9}{6}\right) +\left(\frac{2}{12}\right)\\= \frac{4}{3}- \frac{9}{6}+\frac{2}{12}\\=\frac{4}{3}-\frac{3}{2}+\frac{1}{6}\\=\frac{8}{6}-\frac{9}{6}+\frac{1}{6}\\=\frac{8-9+1}{6}\\=\frac{0}{6}\\=\frac{0}{1}\)
8. \(+\left(\frac{-5}{7}\right) -\left(\frac{7}{8}\right) +\left(\frac{4}{-7}\right)\\= \frac{-5}{7}- \frac{7}{8}-\frac{4}{7}\\=\frac{-40}{56}-\frac{49}{56}-\frac{32}{56}\\=\frac{-40-49-32}{56}\\=\frac{-121}{56}\)
9. \(-\left(\frac{3}{2}\right) +\left(\frac{-4}{-5}\right) +\left(\frac{6}{5}\right)\\= \frac{-3}{2}+ \frac{4}{5}+\frac{6}{5}\\=\frac{-15}{10}+\frac{8}{10}+\frac{12}{10}\\=\frac{-15+8+12}{10}\\=\frac{5}{10}\\=\frac{1}{2}\)
10. \(-\left(\frac{-2}{5}\right) -\left(\frac{-10}{-5}\right) -\left(\frac{-12}{2}\right)\\= \frac{2}{5}- \frac{10}{5}+\frac{12}{2}\\=\frac{2}{5}-\frac{2}{1}+\frac{6}{1}\\=\frac{2-2+6}{5}\\=\frac{6}{5}\)
11. \(-\left(\frac{-7}{-4}\right) +\left(\frac{-10}{6}\right) -\left(\frac{-5}{9}\right)\\= \frac{-7}{4}- \frac{10}{6}+\frac{5}{9}\\=\frac{-7}{4}-\frac{5}{3}+\frac{5}{9}\\=\frac{-63}{36}-\frac{60}{36}+\frac{20}{36}\\=\frac{-63-60+20}{36}\\=\frac{-103}{36}\)
12. \(-\left(\frac{-5}{2}\right) +\left(\frac{-2}{-9}\right) -\left(\frac{4}{-7}\right)\\= \frac{5}{2}+ \frac{2}{9}+\frac{4}{7}\\=\frac{315}{126}+\frac{28}{126}+\frac{72}{126}\\=\frac{315+28+72}{126}\\=\frac{415}{126}\)