Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-4}{-3}\right) -\left(\frac{2}{2}\right) +\left(\frac{-4}{-7}\right)\\= \frac{-4}{3}- \frac{2}{2}+\frac{4}{7}\\=\frac{-4}{3}-\frac{1}{1}+\frac{4}{7}\\=\frac{-28}{21}-\frac{21}{21}+\frac{12}{21}\\=\frac{-28-21+12}{21}\\=\frac{-37}{21}\)
2. \(+\left(\frac{-7}{5}\right) -\left(\frac{-10}{-5}\right) -\left(\frac{-4}{7}\right)\\= \frac{-7}{5}- \frac{10}{5}+\frac{4}{7}\\=\frac{-7}{5}-\frac{2}{1}+\frac{4}{7}\\=\frac{-49}{35}-\frac{70}{35}+\frac{20}{35}\\=\frac{-49-70+20}{35}\\=\frac{-99}{35}\)
3. \(+\left(\frac{7}{-8}\right) -\left(\frac{-8}{6}\right) -\left(\frac{10}{5}\right)\\= \frac{-7}{8}+ \frac{8}{6}-\frac{10}{5}\\=\frac{-7}{8}+\frac{4}{3}-\frac{2}{1}\\=\frac{-21}{24}+\frac{32}{24}-\frac{48}{24}\\=\frac{-21+32-48}{24}\\=\frac{-37}{24}\)
4. \(-\left(\frac{-10}{7}\right) -\left(\frac{-5}{7}\right) -\left(\frac{-2}{-3}\right)\\= \frac{10}{7}+ \frac{5}{7}-\frac{2}{3}\\=\frac{30}{21}+\frac{15}{21}-\frac{14}{21}\\=\frac{30+15-14}{21}\\=\frac{31}{21}\)
5. \(-\left(\frac{5}{-8}\right) -\left(\frac{-10}{8}\right) +\left(\frac{8}{-8}\right)\\= \frac{5}{8}+ \frac{10}{8}-\frac{8}{8}\\=\frac{5}{8}+\frac{5}{4}-\frac{1}{1}\\=\frac{5+5-1}{8}\\=\frac{9}{8}\)
6. \(+\left(\frac{8}{-5}\right) -\left(\frac{-9}{-7}\right) -\left(\frac{12}{-9}\right)\\= \frac{-8}{5}- \frac{9}{7}+\frac{12}{9}\\=\frac{-8}{5}-\frac{9}{7}+\frac{4}{3}\\=\frac{-168}{105}-\frac{135}{105}+\frac{140}{105}\\=\frac{-168-135+140}{105}\\=\frac{-163}{105}\)
7. \(-\left(\frac{-4}{3}\right) +\left(\frac{2}{8}\right) -\left(\frac{-5}{3}\right)\\= \frac{4}{3}+ \frac{2}{8}+\frac{5}{3}\\=\frac{4}{3}+\frac{1}{4}+\frac{5}{3}\\=\frac{16}{12}+\frac{3}{12}+\frac{20}{12}\\=\frac{16+3+20}{12}\\=\frac{39}{12}\\=\frac{13}{4}\)
8. \(+\left(\frac{-5}{-2}\right) -\left(\frac{7}{-10}\right) -\left(\frac{-6}{9}\right)\\= \frac{5}{2}+ \frac{7}{10}+\frac{6}{9}\\=\frac{5}{2}+\frac{7}{10}+\frac{2}{3}\\=\frac{75}{30}+\frac{21}{30}+\frac{20}{30}\\=\frac{75+21+20}{30}\\=\frac{116}{30}\\=\frac{58}{15}\)
9. \(-\left(\frac{6}{5}\right) -\left(\frac{9}{6}\right) -\left(\frac{-9}{6}\right)\\= \frac{-6}{5}- \frac{9}{6}+\frac{9}{6}\\=\frac{-6}{5}-\frac{3}{2}+\frac{3}{2}\\=\frac{-12}{10}-\frac{15}{10}+\frac{15}{10}\\=\frac{-12-15+15}{10}\\=\frac{-12}{10}\\=\frac{-6}{5}\)
10. \(-\left(\frac{-6}{-7}\right) -\left(\frac{-6}{-9}\right) +\left(\frac{-2}{-4}\right)\\= \frac{-6}{7}- \frac{6}{9}+\frac{2}{4}\\=\frac{-6}{7}-\frac{2}{3}+\frac{1}{2}\\=\frac{-36}{42}-\frac{28}{42}+\frac{21}{42}\\=\frac{-36-28+21}{42}\\=\frac{-43}{42}\)
11. \(-\left(\frac{4}{-7}\right) +\left(\frac{-9}{-9}\right) -\left(\frac{-3}{-9}\right)\\= \frac{4}{7}+ \frac{9}{9}-\frac{3}{9}\\=\frac{4}{7}+\frac{1}{1}-\frac{1}{3}\\=\frac{12}{21}+\frac{21}{21}-\frac{7}{21}\\=\frac{12+21-7}{21}\\=\frac{26}{21}\)
12. \(-\left(\frac{8}{9}\right) -\left(\frac{-9}{2}\right) +\left(\frac{3}{-4}\right)\\= \frac{-8}{9}+ \frac{9}{2}-\frac{3}{4}\\=\frac{-32}{36}+\frac{162}{36}-\frac{27}{36}\\=\frac{-32+162-27}{36}\\=\frac{103}{36}\)