Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{8}{-7}\right) +\left(\frac{9}{3}\right) -\left(\frac{-6}{-10}\right)\\= \frac{-8}{7}+ \frac{9}{3}-\frac{6}{10}\\=\frac{-8}{7}+\frac{3}{1}-\frac{3}{5}\\=\frac{-40}{35}+\frac{105}{35}-\frac{21}{35}\\=\frac{-40+105-21}{35}\\=\frac{44}{35}\)
2. \(-\left(\frac{-10}{-7}\right) -\left(\frac{8}{10}\right) -\left(\frac{-2}{8}\right)\\= \frac{-10}{7}- \frac{8}{10}+\frac{2}{8}\\=\frac{-10}{7}-\frac{4}{5}+\frac{1}{4}\\=\frac{-200}{140}-\frac{112}{140}+\frac{35}{140}\\=\frac{-200-112+35}{140}\\=\frac{-277}{140}\)
3. \(+\left(\frac{-7}{2}\right) -\left(\frac{-9}{7}\right) +\left(\frac{4}{8}\right)\\= \frac{-7}{2}+ \frac{9}{7}+\frac{4}{8}\\=\frac{-7}{2}+\frac{9}{7}+\frac{1}{2}\\=\frac{-49}{14}+\frac{18}{14}+\frac{7}{14}\\=\frac{-49+18+7}{14}\\=\frac{-24}{14}\\=\frac{-12}{7}\)
4. \(-\left(\frac{-6}{5}\right) -\left(\frac{7}{7}\right) -\left(\frac{-10}{8}\right)\\= \frac{6}{5}- \frac{7}{7}+\frac{10}{8}\\=\frac{6}{5}-\frac{1}{1}+\frac{5}{4}\\=\frac{24}{20}-\frac{20}{20}+\frac{25}{20}\\=\frac{24-20+25}{20}\\=\frac{29}{20}\)
5. \(+\left(\frac{-5}{-7}\right) +\left(\frac{5}{-3}\right) -\left(\frac{8}{8}\right)\\= \frac{5}{7}- \frac{5}{3}-\frac{8}{8}\\=\frac{5}{7}-\frac{5}{3}-\frac{1}{1}\\=\frac{15}{21}-\frac{35}{21}-\frac{21}{21}\\=\frac{15-35-21}{21}\\=\frac{-41}{21}\)
6. \(+\left(\frac{6}{7}\right) +\left(\frac{-10}{10}\right) +\left(\frac{-3}{-6}\right)\\= \frac{6}{7}- \frac{10}{10}+\frac{3}{6}\\=\frac{6}{7}-\frac{1}{1}+\frac{1}{2}\\=\frac{12}{14}-\frac{14}{14}+\frac{7}{14}\\=\frac{12-14+7}{14}\\=\frac{5}{14}\)
7. \(+\left(\frac{-3}{-8}\right) +\left(\frac{8}{-4}\right) -\left(\frac{-9}{6}\right)\\= \frac{3}{8}- \frac{8}{4}+\frac{9}{6}\\=\frac{3}{8}-\frac{2}{1}+\frac{3}{2}\\=\frac{3-2+3}{8}\\=\frac{4}{8}\\=\frac{1}{2}\)
8. \(-\left(\frac{4}{-5}\right) -\left(\frac{-10}{5}\right) +\left(\frac{-3}{3}\right)\\= \frac{4}{5}+ \frac{10}{5}-\frac{3}{3}\\=\frac{4}{5}+\frac{2}{1}-\frac{1}{1}\\=\frac{4+2-1}{5}\\=\frac{5}{5}\\=\frac{1}{1}\)
9. \(-\left(\frac{-3}{2}\right) -\left(\frac{-5}{7}\right) -\left(\frac{7}{-10}\right)\\= \frac{3}{2}+ \frac{5}{7}+\frac{7}{10}\\=\frac{105}{70}+\frac{50}{70}+\frac{49}{70}\\=\frac{105+50+49}{70}\\=\frac{204}{70}\\=\frac{102}{35}\)
10. \(+\left(\frac{-10}{-7}\right) -\left(\frac{10}{9}\right) +\left(\frac{-6}{-6}\right)\\= \frac{10}{7}- \frac{10}{9}+\frac{6}{6}\\=\frac{10}{7}-\frac{10}{9}+\frac{1}{1}\\=\frac{90}{63}-\frac{70}{63}+\frac{63}{63}\\=\frac{90-70+63}{63}\\=\frac{83}{63}\)
11. \(+\left(\frac{7}{5}\right) -\left(\frac{-3}{-8}\right) +\left(\frac{12}{-3}\right)\\= \frac{7}{5}- \frac{3}{8}-\frac{12}{3}\\=\frac{7}{5}-\frac{3}{8}-\frac{4}{1}\\=\frac{56}{40}-\frac{15}{40}-\frac{160}{40}\\=\frac{56-15-160}{40}\\=\frac{-119}{40}\)
12. \(+\left(\frac{-6}{5}\right) -\left(\frac{-5}{-4}\right) +\left(\frac{8}{5}\right)\\= \frac{-6}{5}- \frac{5}{4}+\frac{8}{5}\\=\frac{-24}{20}-\frac{25}{20}+\frac{32}{20}\\=\frac{-24-25+32}{20}\\=\frac{-17}{20}\)