Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-2}{7}\right) -\left(\frac{-8}{7}\right) +\left(\frac{12}{-5}\right)\\= \frac{-2}{7}+ \frac{8}{7}-\frac{12}{5}\\=\frac{-10}{35}+\frac{40}{35}-\frac{84}{35}\\=\frac{-10+40-84}{35}\\=\frac{-54}{35}\)
2. \(+\left(\frac{-2}{-3}\right) -\left(\frac{-7}{5}\right) -\left(\frac{-12}{-3}\right)\\= \frac{2}{3}+ \frac{7}{5}-\frac{12}{3}\\=\frac{2}{3}+\frac{7}{5}-\frac{4}{1}\\=\frac{10}{15}+\frac{21}{15}-\frac{60}{15}\\=\frac{10+21-60}{15}\\=\frac{-29}{15}\)
3. \(+\left(\frac{4}{5}\right) +\left(\frac{9}{9}\right) -\left(\frac{-8}{-9}\right)\\= \frac{4}{5}+ \frac{9}{9}-\frac{8}{9}\\=\frac{4}{5}+\frac{1}{1}-\frac{8}{9}\\=\frac{36}{45}+\frac{45}{45}-\frac{40}{45}\\=\frac{36+45-40}{45}\\=\frac{41}{45}\)
4. \(-\left(\frac{10}{3}\right) +\left(\frac{7}{8}\right) +\left(\frac{-3}{9}\right)\\= \frac{-10}{3}+ \frac{7}{8}-\frac{3}{9}\\=\frac{-10}{3}+\frac{7}{8}-\frac{1}{3}\\=\frac{-80}{24}+\frac{21}{24}-\frac{8}{24}\\=\frac{-80+21-8}{24}\\=\frac{-67}{24}\)
5. \(-\left(\frac{8}{7}\right) -\left(\frac{6}{-6}\right) -\left(\frac{-4}{12}\right)\\= \frac{-8}{7}+ \frac{6}{6}+\frac{4}{12}\\=\frac{-8}{7}+\frac{1}{1}+\frac{1}{3}\\=\frac{-24}{21}+\frac{21}{21}+\frac{7}{21}\\=\frac{-24+21+7}{21}\\=\frac{4}{21}\)
6. \(-\left(\frac{3}{-2}\right) -\left(\frac{-3}{7}\right) +\left(\frac{7}{-5}\right)\\= \frac{3}{2}+ \frac{3}{7}-\frac{7}{5}\\=\frac{105}{70}+\frac{30}{70}-\frac{98}{70}\\=\frac{105+30-98}{70}\\=\frac{37}{70}\)
7. \(-\left(\frac{5}{6}\right) +\left(\frac{-10}{7}\right) +\left(\frac{8}{11}\right)\\= \frac{-5}{6}- \frac{10}{7}+\frac{8}{11}\\=\frac{-385}{462}-\frac{660}{462}+\frac{336}{462}\\=\frac{-385-660+336}{462}\\=\frac{-709}{462}\)
8. \(-\left(\frac{9}{4}\right) -\left(\frac{6}{-6}\right) -\left(\frac{9}{8}\right)\\= \frac{-9}{4}+ \frac{6}{6}-\frac{9}{8}\\=\frac{-9}{4}+\frac{1}{1}-\frac{9}{8}\\=\frac{-18}{8}+\frac{8}{8}-\frac{9}{8}\\=\frac{-18+8-9}{8}\\=\frac{-19}{8}\)
9. \(-\left(\frac{-10}{-3}\right) -\left(\frac{-10}{2}\right) -\left(\frac{-2}{9}\right)\\= \frac{-10}{3}+ \frac{10}{2}+\frac{2}{9}\\=\frac{-10}{3}+\frac{5}{1}+\frac{2}{9}\\=\frac{-30}{9}+\frac{45}{9}+\frac{2}{9}\\=\frac{-30+45+2}{9}\\=\frac{17}{9}\)
10. \(+\left(\frac{-9}{-7}\right) -\left(\frac{-3}{4}\right) -\left(\frac{-6}{-7}\right)\\= \frac{9}{7}+ \frac{3}{4}-\frac{6}{7}\\=\frac{36}{28}+\frac{21}{28}-\frac{24}{28}\\=\frac{36+21-24}{28}\\=\frac{33}{28}\)
11. \(+\left(\frac{5}{-9}\right) -\left(\frac{-6}{-5}\right) -\left(\frac{-11}{-12}\right)\\= \frac{-5}{9}- \frac{6}{5}-\frac{11}{12}\\=\frac{-100}{180}-\frac{216}{180}-\frac{165}{180}\\=\frac{-100-216-165}{180}\\=\frac{-481}{180}\)
12. \(+\left(\frac{-7}{-8}\right) -\left(\frac{7}{-8}\right) -\left(\frac{3}{4}\right)\\= \frac{7}{8}+ \frac{7}{8}-\frac{3}{4}\\=\frac{7+7-3}{8}\\=\frac{11}{8}\)