Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{9}{5}\right) -\left(\frac{-9}{-9}\right) -\left(\frac{-4}{3}\right)\\= \frac{9}{5}- \frac{9}{9}+\frac{4}{3}\\=\frac{9}{5}-\frac{1}{1}+\frac{4}{3}\\=\frac{27}{15}-\frac{15}{15}+\frac{20}{15}\\=\frac{27-15+20}{15}\\=\frac{32}{15}\)
2. \(+\left(\frac{-10}{-9}\right) -\left(\frac{5}{-4}\right) +\left(\frac{-6}{6}\right)\\= \frac{10}{9}+ \frac{5}{4}-\frac{6}{6}\\=\frac{10}{9}+\frac{5}{4}-\frac{1}{1}\\=\frac{40}{36}+\frac{45}{36}-\frac{36}{36}\\=\frac{40+45-36}{36}\\=\frac{49}{36}\)
3. \(-\left(\frac{-6}{5}\right) -\left(\frac{-7}{-5}\right) -\left(\frac{-3}{-8}\right)\\= \frac{6}{5}- \frac{7}{5}-\frac{3}{8}\\=\frac{48}{40}-\frac{56}{40}-\frac{15}{40}\\=\frac{48-56-15}{40}\\=\frac{-23}{40}\)
4. \(+\left(\frac{7}{9}\right) -\left(\frac{2}{10}\right) -\left(\frac{-4}{6}\right)\\= \frac{7}{9}- \frac{2}{10}+\frac{4}{6}\\=\frac{7}{9}-\frac{1}{5}+\frac{2}{3}\\=\frac{35}{45}-\frac{9}{45}+\frac{30}{45}\\=\frac{35-9+30}{45}\\=\frac{56}{45}\)
5. \(+\left(\frac{-9}{5}\right) -\left(\frac{5}{-5}\right) -\left(\frac{-4}{-11}\right)\\= \frac{-9}{5}+ \frac{5}{5}-\frac{4}{11}\\=\frac{-9}{5}+\frac{1}{1}-\frac{4}{11}\\=\frac{-99}{55}+\frac{55}{55}-\frac{20}{55}\\=\frac{-99+55-20}{55}\\=\frac{-64}{55}\)
6. \(-\left(\frac{-9}{4}\right) -\left(\frac{8}{-7}\right) -\left(\frac{-2}{-11}\right)\\= \frac{9}{4}+ \frac{8}{7}-\frac{2}{11}\\=\frac{693}{308}+\frac{352}{308}-\frac{56}{308}\\=\frac{693+352-56}{308}\\=\frac{989}{308}\)
7. \(-\left(\frac{-9}{-2}\right) +\left(\frac{2}{-2}\right) +\left(\frac{-7}{6}\right)\\= \frac{-9}{2}- \frac{2}{2}-\frac{7}{6}\\=\frac{-9}{2}-\frac{1}{1}-\frac{7}{6}\\=\frac{-27}{6}-\frac{6}{6}-\frac{7}{6}\\=\frac{-27-6-7}{6}\\=\frac{-40}{6}\\=\frac{-20}{3}\)
8. \(+\left(\frac{-10}{7}\right) +\left(\frac{-3}{-9}\right) -\left(\frac{8}{-9}\right)\\= \frac{-10}{7}+ \frac{3}{9}+\frac{8}{9}\\=\frac{-10}{7}+\frac{1}{3}+\frac{8}{9}\\=\frac{-90}{63}+\frac{21}{63}+\frac{56}{63}\\=\frac{-90+21+56}{63}\\=\frac{-13}{63}\)
9. \(-\left(\frac{-6}{-7}\right) +\left(\frac{8}{-3}\right) -\left(\frac{3}{5}\right)\\= \frac{-6}{7}- \frac{8}{3}-\frac{3}{5}\\=\frac{-90}{105}-\frac{280}{105}-\frac{63}{105}\\=\frac{-90-280-63}{105}\\=\frac{-433}{105}\)
10. \(-\left(\frac{-2}{7}\right) +\left(\frac{6}{10}\right) +\left(\frac{5}{10}\right)\\= \frac{2}{7}+ \frac{6}{10}+\frac{5}{10}\\=\frac{2}{7}+\frac{3}{5}+\frac{1}{2}\\=\frac{20}{70}+\frac{42}{70}+\frac{35}{70}\\=\frac{20+42+35}{70}\\=\frac{97}{70}\)
11. \(+\left(\frac{-7}{-8}\right) -\left(\frac{-10}{-6}\right) +\left(\frac{9}{-3}\right)\\= \frac{7}{8}- \frac{10}{6}-\frac{9}{3}\\=\frac{7}{8}-\frac{5}{3}-\frac{3}{1}\\=\frac{21}{24}-\frac{40}{24}-\frac{72}{24}\\=\frac{21-40-72}{24}\\=\frac{-91}{24}\)
12. \(+\left(\frac{-9}{2}\right) -\left(\frac{6}{6}\right) +\left(\frac{5}{5}\right)\\= \frac{-9}{2}- \frac{6}{6}+\frac{5}{5}\\=\frac{-9}{2}-\frac{1}{1}+\frac{1}{1}\\=\frac{-9-1+1}{2}\\=\frac{-9}{2}\)