Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{-9}{-4}\right) -\left(\frac{-9}{8}\right) -\left(\frac{-4}{-11}\right)\\= \frac{9}{4}+ \frac{9}{8}-\frac{4}{11}\\=\frac{198}{88}+\frac{99}{88}-\frac{32}{88}\\=\frac{198+99-32}{88}\\=\frac{265}{88}\)
2. \(-\left(\frac{9}{-7}\right) -\left(\frac{8}{-4}\right) +\left(\frac{-2}{6}\right)\\= \frac{9}{7}+ \frac{8}{4}-\frac{2}{6}\\=\frac{9}{7}+\frac{2}{1}-\frac{1}{3}\\=\frac{27}{21}+\frac{42}{21}-\frac{7}{21}\\=\frac{27+42-7}{21}\\=\frac{62}{21}\)
3. \(-\left(\frac{-3}{-4}\right) +\left(\frac{6}{-10}\right) -\left(\frac{10}{-2}\right)\\= \frac{-3}{4}- \frac{6}{10}+\frac{10}{2}\\=\frac{-3}{4}-\frac{3}{5}+\frac{5}{1}\\=\frac{-15}{20}-\frac{12}{20}+\frac{100}{20}\\=\frac{-15-12+100}{20}\\=\frac{73}{20}\)
4. \(-\left(\frac{10}{-9}\right) +\left(\frac{-6}{-10}\right) +\left(\frac{-11}{12}\right)\\= \frac{10}{9}+ \frac{6}{10}-\frac{11}{12}\\=\frac{10}{9}+\frac{3}{5}-\frac{11}{12}\\=\frac{200}{180}+\frac{108}{180}-\frac{165}{180}\\=\frac{200+108-165}{180}\\=\frac{143}{180}\)
5. \(+\left(\frac{-4}{-9}\right) +\left(\frac{4}{-5}\right) +\left(\frac{11}{-7}\right)\\= \frac{4}{9}- \frac{4}{5}-\frac{11}{7}\\=\frac{140}{315}-\frac{252}{315}-\frac{495}{315}\\=\frac{140-252-495}{315}\\=\frac{-607}{315}\)
6. \(-\left(\frac{8}{-5}\right) -\left(\frac{5}{4}\right) +\left(\frac{10}{6}\right)\\= \frac{8}{5}- \frac{5}{4}+\frac{10}{6}\\=\frac{8}{5}-\frac{5}{4}+\frac{5}{3}\\=\frac{96}{60}-\frac{75}{60}+\frac{100}{60}\\=\frac{96-75+100}{60}\\=\frac{121}{60}\)
7. \(+\left(\frac{-4}{5}\right) +\left(\frac{-9}{-10}\right) +\left(\frac{-2}{6}\right)\\= \frac{-4}{5}+ \frac{9}{10}-\frac{2}{6}\\=\frac{-4}{5}+\frac{9}{10}-\frac{1}{3}\\=\frac{-24}{30}+\frac{27}{30}-\frac{10}{30}\\=\frac{-24+27-10}{30}\\=\frac{-7}{30}\)
8. \(+\left(\frac{-3}{-2}\right) +\left(\frac{-6}{9}\right) -\left(\frac{-8}{-8}\right)\\= \frac{3}{2}- \frac{6}{9}-\frac{8}{8}\\=\frac{3}{2}-\frac{2}{3}-\frac{1}{1}\\=\frac{9}{6}-\frac{4}{6}-\frac{6}{6}\\=\frac{9-4-6}{6}\\=\frac{-1}{6}\)
9. \(-\left(\frac{-2}{9}\right) -\left(\frac{-10}{-6}\right) +\left(\frac{4}{-7}\right)\\= \frac{2}{9}- \frac{10}{6}-\frac{4}{7}\\=\frac{2}{9}-\frac{5}{3}-\frac{4}{7}\\=\frac{14}{63}-\frac{105}{63}-\frac{36}{63}\\=\frac{14-105-36}{63}\\=\frac{-127}{63}\)
10. \(-\left(\frac{-6}{-5}\right) -\left(\frac{10}{-3}\right) +\left(\frac{12}{3}\right)\\= \frac{-6}{5}+ \frac{10}{3}+\frac{12}{3}\\=\frac{-6}{5}+\frac{10}{3}+\frac{4}{1}\\=\frac{-18}{15}+\frac{50}{15}+\frac{60}{15}\\=\frac{-18+50+60}{15}\\=\frac{92}{15}\)
11. \(-\left(\frac{-6}{5}\right) +\left(\frac{9}{8}\right) +\left(\frac{12}{8}\right)\\= \frac{6}{5}+ \frac{9}{8}+\frac{12}{8}\\=\frac{6}{5}+\frac{9}{8}+\frac{3}{2}\\=\frac{48}{40}+\frac{45}{40}+\frac{60}{40}\\=\frac{48+45+60}{40}\\=\frac{153}{40}\)
12. \(-\left(\frac{-5}{4}\right) -\left(\frac{-2}{9}\right) -\left(\frac{-2}{-12}\right)\\= \frac{5}{4}+ \frac{2}{9}-\frac{2}{12}\\=\frac{5}{4}+\frac{2}{9}-\frac{1}{6}\\=\frac{45}{36}+\frac{8}{36}-\frac{6}{36}\\=\frac{45+8-6}{36}\\=\frac{47}{36}\)