Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(+\left(\frac{3}{-7}\right) -\left(\frac{5}{-4}\right) -\left(\frac{7}{-11}\right)\\= \frac{-3}{7}+ \frac{5}{4}+\frac{7}{11}\\=\frac{-132}{308}+\frac{385}{308}+\frac{196}{308}\\=\frac{-132+385+196}{308}\\=\frac{449}{308}\)
2. \(-\left(\frac{7}{6}\right) +\left(\frac{5}{6}\right) +\left(\frac{12}{2}\right)\\= \frac{-7}{6}+ \frac{5}{6}+\frac{12}{2}\\=\frac{-7}{6}+\frac{5}{6}+\frac{6}{1}\\=\frac{-7+5+6}{6}\\=\frac{4}{6}\\=\frac{2}{3}\)
3. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-4}{-8}\right) -\left(\frac{2}{-4}\right)\\= \frac{-6}{5}- \frac{4}{8}+\frac{2}{4}\\=\frac{-6}{5}-\frac{1}{2}+\frac{1}{2}\\=\frac{-12}{10}-\frac{5}{10}+\frac{5}{10}\\=\frac{-12-5+5}{10}\\=\frac{-12}{10}\\=\frac{-6}{5}\)
4. \(-\left(\frac{-2}{5}\right) +\left(\frac{-8}{-5}\right) -\left(\frac{9}{7}\right)\\= \frac{2}{5}+ \frac{8}{5}-\frac{9}{7}\\=\frac{14}{35}+\frac{56}{35}-\frac{45}{35}\\=\frac{14+56-45}{35}\\=\frac{25}{35}\\=\frac{5}{7}\)
5. \(-\left(\frac{9}{-2}\right) +\left(\frac{8}{-3}\right) +\left(\frac{6}{-12}\right)\\= \frac{9}{2}- \frac{8}{3}-\frac{6}{12}\\=\frac{9}{2}-\frac{8}{3}-\frac{1}{2}\\=\frac{27}{6}-\frac{16}{6}-\frac{3}{6}\\=\frac{27-16-3}{6}\\=\frac{8}{6}\\=\frac{4}{3}\)
6. \(-\left(\frac{-8}{5}\right) -\left(\frac{9}{6}\right) +\left(\frac{-11}{6}\right)\\= \frac{8}{5}- \frac{9}{6}-\frac{11}{6}\\=\frac{8}{5}-\frac{3}{2}-\frac{11}{6}\\=\frac{48}{30}-\frac{45}{30}-\frac{55}{30}\\=\frac{48-45-55}{30}\\=\frac{-52}{30}\\=\frac{-26}{15}\)
7. \(+\left(\frac{-7}{9}\right) -\left(\frac{-6}{-6}\right) +\left(\frac{-5}{4}\right)\\= \frac{-7}{9}- \frac{6}{6}-\frac{5}{4}\\=\frac{-7}{9}-\frac{1}{1}-\frac{5}{4}\\=\frac{-28}{36}-\frac{36}{36}-\frac{45}{36}\\=\frac{-28-36-45}{36}\\=\frac{-109}{36}\)
8. \(+\left(\frac{5}{7}\right) +\left(\frac{-7}{9}\right) -\left(\frac{11}{11}\right)\\= \frac{5}{7}- \frac{7}{9}-\frac{11}{11}\\=\frac{5}{7}-\frac{7}{9}-\frac{1}{1}\\=\frac{45}{63}-\frac{49}{63}-\frac{63}{63}\\=\frac{45-49-63}{63}\\=\frac{-67}{63}\)
9. \(-\left(\frac{-4}{9}\right) +\left(\frac{-6}{-3}\right) -\left(\frac{7}{-11}\right)\\= \frac{4}{9}+ \frac{6}{3}+\frac{7}{11}\\=\frac{4}{9}+\frac{2}{1}+\frac{7}{11}\\=\frac{44}{99}+\frac{198}{99}+\frac{63}{99}\\=\frac{44+198+63}{99}\\=\frac{305}{99}\)
10. \(-\left(\frac{3}{-5}\right) -\left(\frac{-10}{-6}\right) +\left(\frac{6}{6}\right)\\= \frac{3}{5}- \frac{10}{6}+\frac{6}{6}\\=\frac{3}{5}-\frac{5}{3}+\frac{1}{1}\\=\frac{9}{15}-\frac{25}{15}+\frac{15}{15}\\=\frac{9-25+15}{15}\\=\frac{-1}{15}\)
11. \(+\left(\frac{-8}{5}\right) +\left(\frac{6}{7}\right) +\left(\frac{5}{-2}\right)\\= \frac{-8}{5}+ \frac{6}{7}-\frac{5}{2}\\=\frac{-112}{70}+\frac{60}{70}-\frac{175}{70}\\=\frac{-112+60-175}{70}\\=\frac{-227}{70}\)
12. \(-\left(\frac{10}{3}\right) -\left(\frac{-9}{-2}\right) +\left(\frac{-3}{-2}\right)\\= \frac{-10}{3}- \frac{9}{2}+\frac{3}{2}\\=\frac{-20}{6}-\frac{27}{6}+\frac{9}{6}\\=\frac{-20-27+9}{6}\\=\frac{-38}{6}\\=\frac{-19}{3}\)