Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{6}\right) -\left(\frac{-8}{-3}\right) -\left(\frac{-12}{-10}\right)\\= \frac{-5}{6}- \frac{8}{3}-\frac{12}{10}\\=\frac{-5}{6}-\frac{8}{3}-\frac{6}{5}\\=\frac{-25}{30}-\frac{80}{30}-\frac{36}{30}\\=\frac{-25-80-36}{30}\\=\frac{-141}{30}\\=\frac{-47}{10}\)
2. \(-\left(\frac{-7}{-6}\right) -\left(\frac{7}{-10}\right) +\left(\frac{8}{10}\right)\\= \frac{-7}{6}+ \frac{7}{10}+\frac{8}{10}\\=\frac{-7}{6}+\frac{7}{10}+\frac{4}{5}\\=\frac{-35}{30}+\frac{21}{30}+\frac{24}{30}\\=\frac{-35+21+24}{30}\\=\frac{10}{30}\\=\frac{1}{3}\)
3. \(-\left(\frac{-4}{5}\right) -\left(\frac{10}{8}\right) +\left(\frac{-5}{-2}\right)\\= \frac{4}{5}- \frac{10}{8}+\frac{5}{2}\\=\frac{4}{5}-\frac{5}{4}+\frac{5}{2}\\=\frac{16}{20}-\frac{25}{20}+\frac{50}{20}\\=\frac{16-25+50}{20}\\=\frac{41}{20}\)
4. \(-\left(\frac{4}{-7}\right) -\left(\frac{-7}{-9}\right) -\left(\frac{-11}{7}\right)\\= \frac{4}{7}- \frac{7}{9}+\frac{11}{7}\\=\frac{36}{63}-\frac{49}{63}+\frac{99}{63}\\=\frac{36-49+99}{63}\\=\frac{86}{63}\)
5. \(-\left(\frac{6}{5}\right) -\left(\frac{-8}{6}\right) -\left(\frac{-6}{2}\right)\\= \frac{-6}{5}+ \frac{8}{6}+\frac{6}{2}\\=\frac{-6}{5}+\frac{4}{3}+\frac{3}{1}\\=\frac{-18}{15}+\frac{20}{15}+\frac{45}{15}\\=\frac{-18+20+45}{15}\\=\frac{47}{15}\)
6. \(+\left(\frac{-9}{-4}\right) -\left(\frac{10}{7}\right) +\left(\frac{11}{6}\right)\\= \frac{9}{4}- \frac{10}{7}+\frac{11}{6}\\=\frac{189}{84}-\frac{120}{84}+\frac{154}{84}\\=\frac{189-120+154}{84}\\=\frac{223}{84}\)
7. \(+\left(\frac{-10}{3}\right) +\left(\frac{-10}{10}\right) +\left(\frac{-4}{2}\right)\\= \frac{-10}{3}- \frac{10}{10}-\frac{4}{2}\\=\frac{-10}{3}-\frac{1}{1}-\frac{2}{1}\\=\frac{-10-1-2}{3}\\=\frac{-13}{3}\)
8. \(+\left(\frac{2}{9}\right) +\left(\frac{-2}{-8}\right) -\left(\frac{-2}{10}\right)\\= \frac{2}{9}+ \frac{2}{8}+\frac{2}{10}\\=\frac{2}{9}+\frac{1}{4}+\frac{1}{5}\\=\frac{40}{180}+\frac{45}{180}+\frac{36}{180}\\=\frac{40+45+36}{180}\\=\frac{121}{180}\)
9. \(+\left(\frac{10}{-9}\right) +\left(\frac{4}{-7}\right) +\left(\frac{9}{-11}\right)\\= \frac{-10}{9}- \frac{4}{7}-\frac{9}{11}\\=\frac{-770}{693}-\frac{396}{693}-\frac{567}{693}\\=\frac{-770-396-567}{693}\\=\frac{-1733}{693}\)
10. \(-\left(\frac{-4}{-7}\right) +\left(\frac{-9}{-6}\right) +\left(\frac{5}{10}\right)\\= \frac{-4}{7}+ \frac{9}{6}+\frac{5}{10}\\=\frac{-4}{7}+\frac{3}{2}+\frac{1}{2}\\=\frac{-8}{14}+\frac{21}{14}+\frac{7}{14}\\=\frac{-8+21+7}{14}\\=\frac{20}{14}\\=\frac{10}{7}\)
11. \(+\left(\frac{-7}{-4}\right) -\left(\frac{-3}{9}\right) +\left(\frac{9}{8}\right)\\= \frac{7}{4}+ \frac{3}{9}+\frac{9}{8}\\=\frac{7}{4}+\frac{1}{3}+\frac{9}{8}\\=\frac{42}{24}+\frac{8}{24}+\frac{27}{24}\\=\frac{42+8+27}{24}\\=\frac{77}{24}\)
12. \(-\left(\frac{2}{-3}\right) -\left(\frac{-6}{2}\right) +\left(\frac{11}{-5}\right)\\= \frac{2}{3}+ \frac{6}{2}-\frac{11}{5}\\=\frac{2}{3}+\frac{3}{1}-\frac{11}{5}\\=\frac{10}{15}+\frac{45}{15}-\frac{33}{15}\\=\frac{10+45-33}{15}\\=\frac{22}{15}\)