Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{10}{9}\right) -\left(\frac{2}{6}\right) +\left(\frac{7}{8}\right)\\= \frac{10}{9}- \frac{2}{6}+\frac{7}{8}\\=\frac{10}{9}-\frac{1}{3}+\frac{7}{8}\\=\frac{80}{72}-\frac{24}{72}+\frac{63}{72}\\=\frac{80-24+63}{72}\\=\frac{119}{72}\)
2. \(-\left(\frac{-10}{-7}\right) +\left(\frac{-8}{6}\right) +\left(\frac{-12}{8}\right)\\= \frac{-10}{7}- \frac{8}{6}-\frac{12}{8}\\=\frac{-10}{7}-\frac{4}{3}-\frac{3}{2}\\=\frac{-60}{42}-\frac{56}{42}-\frac{63}{42}\\=\frac{-60-56-63}{42}\\=\frac{-179}{42}\)
3. \(-\left(\frac{-8}{-5}\right) +\left(\frac{10}{-5}\right) -\left(\frac{-8}{-6}\right)\\= \frac{-8}{5}- \frac{10}{5}-\frac{8}{6}\\=\frac{-8}{5}-\frac{2}{1}-\frac{4}{3}\\=\frac{-24}{15}-\frac{30}{15}-\frac{20}{15}\\=\frac{-24-30-20}{15}\\=\frac{-74}{15}\)
4. \(+\left(\frac{-5}{6}\right) +\left(\frac{5}{-10}\right) +\left(\frac{12}{10}\right)\\= \frac{-5}{6}- \frac{5}{10}+\frac{12}{10}\\=\frac{-5}{6}-\frac{1}{2}+\frac{6}{5}\\=\frac{-25}{30}-\frac{15}{30}+\frac{36}{30}\\=\frac{-25-15+36}{30}\\=\frac{-4}{30}\\=\frac{-2}{15}\)
5. \(+\left(\frac{-8}{-3}\right) -\left(\frac{-3}{5}\right) -\left(\frac{-6}{-2}\right)\\= \frac{8}{3}+ \frac{3}{5}-\frac{6}{2}\\=\frac{8}{3}+\frac{3}{5}-\frac{3}{1}\\=\frac{40}{15}+\frac{9}{15}-\frac{45}{15}\\=\frac{40+9-45}{15}\\=\frac{4}{15}\)
6. \(-\left(\frac{-2}{7}\right) +\left(\frac{-7}{-10}\right) +\left(\frac{3}{-2}\right)\\= \frac{2}{7}+ \frac{7}{10}-\frac{3}{2}\\=\frac{20}{70}+\frac{49}{70}-\frac{105}{70}\\=\frac{20+49-105}{70}\\=\frac{-36}{70}\\=\frac{-18}{35}\)
7. \(+\left(\frac{-4}{7}\right) +\left(\frac{6}{4}\right) -\left(\frac{-8}{10}\right)\\= \frac{-4}{7}+ \frac{6}{4}+\frac{8}{10}\\=\frac{-4}{7}+\frac{3}{2}+\frac{4}{5}\\=\frac{-40}{70}+\frac{105}{70}+\frac{56}{70}\\=\frac{-40+105+56}{70}\\=\frac{121}{70}\)
8. \(+\left(\frac{3}{2}\right) +\left(\frac{-9}{2}\right) -\left(\frac{-8}{6}\right)\\= \frac{3}{2}- \frac{9}{2}+\frac{8}{6}\\=\frac{3}{2}-\frac{9}{2}+\frac{4}{3}\\=\frac{9}{6}-\frac{27}{6}+\frac{8}{6}\\=\frac{9-27+8}{6}\\=\frac{-10}{6}\\=\frac{-5}{3}\)
9. \(+\left(\frac{8}{-7}\right) -\left(\frac{8}{6}\right) +\left(\frac{4}{-11}\right)\\= \frac{-8}{7}- \frac{8}{6}-\frac{4}{11}\\=\frac{-8}{7}-\frac{4}{3}-\frac{4}{11}\\=\frac{-264}{231}-\frac{308}{231}-\frac{84}{231}\\=\frac{-264-308-84}{231}\\=\frac{-656}{231}\)
10. \(+\left(\frac{7}{-8}\right) -\left(\frac{-7}{-5}\right) +\left(\frac{-10}{11}\right)\\= \frac{-7}{8}- \frac{7}{5}-\frac{10}{11}\\=\frac{-385}{440}-\frac{616}{440}-\frac{400}{440}\\=\frac{-385-616-400}{440}\\=\frac{-1401}{440}\)
11. \(+\left(\frac{-8}{5}\right) -\left(\frac{10}{-7}\right) -\left(\frac{-2}{10}\right)\\= \frac{-8}{5}+ \frac{10}{7}+\frac{2}{10}\\=\frac{-8}{5}+\frac{10}{7}+\frac{1}{5}\\=\frac{-56}{35}+\frac{50}{35}+\frac{7}{35}\\=\frac{-56+50+7}{35}\\=\frac{1}{35}\)
12. \(-\left(\frac{7}{-8}\right) -\left(\frac{-9}{3}\right) +\left(\frac{11}{-7}\right)\\= \frac{7}{8}+ \frac{9}{3}-\frac{11}{7}\\=\frac{7}{8}+\frac{3}{1}-\frac{11}{7}\\=\frac{49}{56}+\frac{168}{56}-\frac{88}{56}\\=\frac{49+168-88}{56}\\=\frac{129}{56}\)