Breuken haakjesregel (reeks 2)

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Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{5}{3}\right) -\left(\frac{4}{-8}\right) +\left(\frac{-6}{6}\right)\\= \frac{-5}{3}+ \frac{4}{8}-\frac{6}{6}\\=\frac{-5}{3}+\frac{1}{2}-\frac{1}{1}\\=\frac{-10}{6}+\frac{3}{6}-\frac{6}{6}\\=\frac{-10+3-6}{6}\\=\frac{-13}{6}\)
2. \(-\left(\frac{-6}{7}\right) -\left(\frac{-2}{-4}\right) +\left(\frac{11}{-10}\right)\\= \frac{6}{7}- \frac{2}{4}-\frac{11}{10}\\=\frac{6}{7}-\frac{1}{2}-\frac{11}{10}\\=\frac{60}{70}-\frac{35}{70}-\frac{77}{70}\\=\frac{60-35-77}{70}\\=\frac{-52}{70}\\=\frac{-26}{35}\)
3. \(-\left(\frac{6}{5}\right) -\left(\frac{7}{4}\right) +\left(\frac{11}{5}\right)\\= \frac{-6}{5}- \frac{7}{4}+\frac{11}{5}\\=\frac{-24}{20}-\frac{35}{20}+\frac{44}{20}\\=\frac{-24-35+44}{20}\\=\frac{-15}{20}\\=\frac{-3}{4}\)
4. \(+\left(\frac{-10}{-7}\right) -\left(\frac{-3}{5}\right) -\left(\frac{2}{-10}\right)\\= \frac{10}{7}+ \frac{3}{5}+\frac{2}{10}\\=\frac{10}{7}+\frac{3}{5}+\frac{1}{5}\\=\frac{50}{35}+\frac{21}{35}+\frac{7}{35}\\=\frac{50+21+7}{35}\\=\frac{78}{35}\)
5. \(+\left(\frac{4}{7}\right) -\left(\frac{9}{-10}\right) -\left(\frac{-12}{-2}\right)\\= \frac{4}{7}+ \frac{9}{10}-\frac{12}{2}\\=\frac{4}{7}+\frac{9}{10}-\frac{6}{1}\\=\frac{40}{70}+\frac{63}{70}-\frac{420}{70}\\=\frac{40+63-420}{70}\\=\frac{-317}{70}\)
6. \(+\left(\frac{5}{6}\right) +\left(\frac{-4}{4}\right) +\left(\frac{3}{-10}\right)\\= \frac{5}{6}- \frac{4}{4}-\frac{3}{10}\\=\frac{5}{6}-\frac{1}{1}-\frac{3}{10}\\=\frac{25}{30}-\frac{30}{30}-\frac{9}{30}\\=\frac{25-30-9}{30}\\=\frac{-14}{30}\\=\frac{-7}{15}\)
7. \(-\left(\frac{7}{-3}\right) +\left(\frac{4}{2}\right) +\left(\frac{12}{-5}\right)\\= \frac{7}{3}+ \frac{4}{2}-\frac{12}{5}\\=\frac{7}{3}+\frac{2}{1}-\frac{12}{5}\\=\frac{35}{15}+\frac{30}{15}-\frac{36}{15}\\=\frac{35+30-36}{15}\\=\frac{29}{15}\)
8. \(-\left(\frac{10}{7}\right) -\left(\frac{-8}{8}\right) -\left(\frac{-4}{2}\right)\\= \frac{-10}{7}+ \frac{8}{8}+\frac{4}{2}\\=\frac{-10}{7}+\frac{1}{1}+\frac{2}{1}\\=\frac{-10+1+2}{7}\\=\frac{-7}{7}\\=\frac{-1}{1}\)
9. \(-\left(\frac{9}{5}\right) -\left(\frac{8}{10}\right) +\left(\frac{-2}{-12}\right)\\= \frac{-9}{5}- \frac{8}{10}+\frac{2}{12}\\=\frac{-9}{5}-\frac{4}{5}+\frac{1}{6}\\=\frac{-54}{30}-\frac{24}{30}+\frac{5}{30}\\=\frac{-54-24+5}{30}\\=\frac{-73}{30}\)
10. \(-\left(\frac{5}{-6}\right) +\left(\frac{3}{10}\right) +\left(\frac{8}{3}\right)\\= \frac{5}{6}+ \frac{3}{10}+\frac{8}{3}\\=\frac{25}{30}+\frac{9}{30}+\frac{80}{30}\\=\frac{25+9+80}{30}\\=\frac{114}{30}\\=\frac{19}{5}\)
11. \(-\left(\frac{3}{-2}\right) -\left(\frac{3}{-10}\right) -\left(\frac{2}{11}\right)\\= \frac{3}{2}+ \frac{3}{10}-\frac{2}{11}\\=\frac{165}{110}+\frac{33}{110}-\frac{20}{110}\\=\frac{165+33-20}{110}\\=\frac{178}{110}\\=\frac{89}{55}\)
12. \(+\left(\frac{-8}{3}\right) -\left(\frac{6}{-3}\right) +\left(\frac{9}{-3}\right)\\= \frac{-8}{3}+ \frac{6}{3}-\frac{9}{3}\\=\frac{-8}{3}+\frac{2}{1}-\frac{3}{1}\\=\frac{-8+2-3}{3}\\=\frac{-9}{3}\\=\frac{-3}{1}\)