Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{7}{8}\right) +\left(\frac{-10}{2}\right) -\left(\frac{-11}{-4}\right)\\= \frac{7}{8}- \frac{10}{2}-\frac{11}{4}\\=\frac{7}{8}-\frac{5}{1}-\frac{11}{4}\\=\frac{7-5-11}{8}\\=\frac{-9}{8}\)
2. \(-\left(\frac{-4}{-7}\right) +\left(\frac{2}{7}\right) -\left(\frac{10}{-6}\right)\\= \frac{-4}{7}+ \frac{2}{7}+\frac{10}{6}\\=\frac{-4}{7}+\frac{2}{7}+\frac{5}{3}\\=\frac{-12}{21}+\frac{6}{21}+\frac{35}{21}\\=\frac{-12+6+35}{21}\\=\frac{29}{21}\)
3. \(+\left(\frac{5}{-6}\right) -\left(\frac{-10}{9}\right) +\left(\frac{-3}{12}\right)\\= \frac{-5}{6}+ \frac{10}{9}-\frac{3}{12}\\=\frac{-5}{6}+\frac{10}{9}-\frac{1}{4}\\=\frac{-30}{36}+\frac{40}{36}-\frac{9}{36}\\=\frac{-30+40-9}{36}\\=\frac{1}{36}\)
4. \(-\left(\frac{10}{9}\right) -\left(\frac{5}{8}\right) +\left(\frac{-5}{3}\right)\\= \frac{-10}{9}- \frac{5}{8}-\frac{5}{3}\\=\frac{-80}{72}-\frac{45}{72}-\frac{120}{72}\\=\frac{-80-45-120}{72}\\=\frac{-245}{72}\)
5. \(+\left(\frac{6}{7}\right) -\left(\frac{-7}{7}\right) -\left(\frac{-4}{7}\right)\\= \frac{6}{7}+ \frac{7}{7}+\frac{4}{7}\\=\frac{6}{7}+\frac{1}{1}+\frac{4}{7}\\=\frac{6+1+4}{7}\\=\frac{11}{7}\)
6. \(+\left(\frac{4}{5}\right) -\left(\frac{-9}{8}\right) -\left(\frac{-6}{6}\right)\\= \frac{4}{5}+ \frac{9}{8}+\frac{6}{6}\\=\frac{4}{5}+\frac{9}{8}+\frac{1}{1}\\=\frac{32}{40}+\frac{45}{40}+\frac{40}{40}\\=\frac{32+45+40}{40}\\=\frac{117}{40}\)
7. \(+\left(\frac{-5}{-4}\right) -\left(\frac{7}{-7}\right) -\left(\frac{9}{-10}\right)\\= \frac{5}{4}+ \frac{7}{7}+\frac{9}{10}\\=\frac{5}{4}+\frac{1}{1}+\frac{9}{10}\\=\frac{25}{20}+\frac{20}{20}+\frac{18}{20}\\=\frac{25+20+18}{20}\\=\frac{63}{20}\)
8. \(-\left(\frac{-9}{7}\right) -\left(\frac{-8}{-9}\right) +\left(\frac{4}{-11}\right)\\= \frac{9}{7}- \frac{8}{9}-\frac{4}{11}\\=\frac{891}{693}-\frac{616}{693}-\frac{252}{693}\\=\frac{891-616-252}{693}\\=\frac{23}{693}\)
9. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-3}{-8}\right) +\left(\frac{10}{5}\right)\\= \frac{6}{5}+ \frac{3}{8}+\frac{10}{5}\\=\frac{6}{5}+\frac{3}{8}+\frac{2}{1}\\=\frac{48}{40}+\frac{15}{40}+\frac{80}{40}\\=\frac{48+15+80}{40}\\=\frac{143}{40}\)
10. \(+\left(\frac{-4}{-3}\right) -\left(\frac{-2}{-9}\right) -\left(\frac{7}{-6}\right)\\= \frac{4}{3}- \frac{2}{9}+\frac{7}{6}\\=\frac{24}{18}-\frac{4}{18}+\frac{21}{18}\\=\frac{24-4+21}{18}\\=\frac{41}{18}\)
11. \(+\left(\frac{9}{-8}\right) -\left(\frac{4}{-9}\right) +\left(\frac{9}{-3}\right)\\= \frac{-9}{8}+ \frac{4}{9}-\frac{9}{3}\\=\frac{-9}{8}+\frac{4}{9}-\frac{3}{1}\\=\frac{-81}{72}+\frac{32}{72}-\frac{216}{72}\\=\frac{-81+32-216}{72}\\=\frac{-265}{72}\)
12. \(+\left(\frac{-9}{-7}\right) +\left(\frac{-6}{-7}\right) -\left(\frac{6}{-5}\right)\\= \frac{9}{7}+ \frac{6}{7}+\frac{6}{5}\\=\frac{45}{35}+\frac{30}{35}+\frac{42}{35}\\=\frac{45+30+42}{35}\\=\frac{117}{35}\)