Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{8}{-5}\right) +\left(\frac{-3}{10}\right) +\left(\frac{-11}{-7}\right)\\= \frac{8}{5}- \frac{3}{10}+\frac{11}{7}\\=\frac{112}{70}-\frac{21}{70}+\frac{110}{70}\\=\frac{112-21+110}{70}\\=\frac{201}{70}\)
2. \(+\left(\frac{-3}{4}\right) +\left(\frac{10}{9}\right) -\left(\frac{-5}{-7}\right)\\= \frac{-3}{4}+ \frac{10}{9}-\frac{5}{7}\\=\frac{-189}{252}+\frac{280}{252}-\frac{180}{252}\\=\frac{-189+280-180}{252}\\=\frac{-89}{252}\)
3. \(-\left(\frac{4}{-7}\right) -\left(\frac{10}{-9}\right) +\left(\frac{4}{9}\right)\\= \frac{4}{7}+ \frac{10}{9}+\frac{4}{9}\\=\frac{36}{63}+\frac{70}{63}+\frac{28}{63}\\=\frac{36+70+28}{63}\\=\frac{134}{63}\)
4. \(-\left(\frac{-8}{-7}\right) -\left(\frac{6}{10}\right) +\left(\frac{-12}{6}\right)\\= \frac{-8}{7}- \frac{6}{10}-\frac{12}{6}\\=\frac{-8}{7}-\frac{3}{5}-\frac{2}{1}\\=\frac{-40}{35}-\frac{21}{35}-\frac{70}{35}\\=\frac{-40-21-70}{35}\\=\frac{-131}{35}\)
5. \(-\left(\frac{-6}{-5}\right) +\left(\frac{3}{8}\right) -\left(\frac{4}{-8}\right)\\= \frac{-6}{5}+ \frac{3}{8}+\frac{4}{8}\\=\frac{-6}{5}+\frac{3}{8}+\frac{1}{2}\\=\frac{-48}{40}+\frac{15}{40}+\frac{20}{40}\\=\frac{-48+15+20}{40}\\=\frac{-13}{40}\)
6. \(-\left(\frac{-4}{-3}\right) -\left(\frac{-3}{3}\right) +\left(\frac{-3}{-10}\right)\\= \frac{-4}{3}+ \frac{3}{3}+\frac{3}{10}\\=\frac{-4}{3}+\frac{1}{1}+\frac{3}{10}\\=\frac{-40}{30}+\frac{30}{30}+\frac{9}{30}\\=\frac{-40+30+9}{30}\\=\frac{-1}{30}\)
7. \(-\left(\frac{-3}{8}\right) -\left(\frac{2}{5}\right) -\left(\frac{-11}{7}\right)\\= \frac{3}{8}- \frac{2}{5}+\frac{11}{7}\\=\frac{105}{280}-\frac{112}{280}+\frac{440}{280}\\=\frac{105-112+440}{280}\\=\frac{433}{280}\)
8. \(+\left(\frac{6}{-5}\right) -\left(\frac{8}{4}\right) +\left(\frac{9}{-7}\right)\\= \frac{-6}{5}- \frac{8}{4}-\frac{9}{7}\\=\frac{-6}{5}-\frac{2}{1}-\frac{9}{7}\\=\frac{-42}{35}-\frac{70}{35}-\frac{45}{35}\\=\frac{-42-70-45}{35}\\=\frac{-157}{35}\)
9. \(-\left(\frac{-4}{3}\right) -\left(\frac{9}{4}\right) +\left(\frac{11}{6}\right)\\= \frac{4}{3}- \frac{9}{4}+\frac{11}{6}\\=\frac{16}{12}-\frac{27}{12}+\frac{22}{12}\\=\frac{16-27+22}{12}\\=\frac{11}{12}\)
10. \(+\left(\frac{-8}{-9}\right) +\left(\frac{2}{9}\right) +\left(\frac{-4}{7}\right)\\= \frac{8}{9}+ \frac{2}{9}-\frac{4}{7}\\=\frac{56}{63}+\frac{14}{63}-\frac{36}{63}\\=\frac{56+14-36}{63}\\=\frac{34}{63}\)
11. \(-\left(\frac{4}{3}\right) +\left(\frac{-7}{6}\right) +\left(\frac{-12}{2}\right)\\= \frac{-4}{3}- \frac{7}{6}-\frac{12}{2}\\=\frac{-4}{3}-\frac{7}{6}-\frac{6}{1}\\=\frac{-8}{6}-\frac{7}{6}-\frac{36}{6}\\=\frac{-8-7-36}{6}\\=\frac{-51}{6}\\=\frac{-17}{2}\)
12. \(+\left(\frac{-6}{-5}\right) +\left(\frac{4}{7}\right) +\left(\frac{-5}{7}\right)\\= \frac{6}{5}+ \frac{4}{7}-\frac{5}{7}\\=\frac{42}{35}+\frac{20}{35}-\frac{25}{35}\\=\frac{42+20-25}{35}\\=\frac{37}{35}\)