Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-6}{-5}\right) -\left(\frac{-2}{-3}\right) -\left(\frac{-11}{-6}\right)\\= \frac{-6}{5}- \frac{2}{3}-\frac{11}{6}\\=\frac{-36}{30}-\frac{20}{30}-\frac{55}{30}\\=\frac{-36-20-55}{30}\\=\frac{-111}{30}\\=\frac{-37}{10}\)
2. \(+\left(\frac{-2}{3}\right) +\left(\frac{6}{10}\right) -\left(\frac{-9}{11}\right)\\= \frac{-2}{3}+ \frac{6}{10}+\frac{9}{11}\\=\frac{-2}{3}+\frac{3}{5}+\frac{9}{11}\\=\frac{-110}{165}+\frac{99}{165}+\frac{135}{165}\\=\frac{-110+99+135}{165}\\=\frac{124}{165}\)
3. \(-\left(\frac{6}{5}\right) -\left(\frac{-3}{2}\right) -\left(\frac{12}{-11}\right)\\= \frac{-6}{5}+ \frac{3}{2}+\frac{12}{11}\\=\frac{-132}{110}+\frac{165}{110}+\frac{120}{110}\\=\frac{-132+165+120}{110}\\=\frac{153}{110}\)
4. \(+\left(\frac{2}{-7}\right) +\left(\frac{-4}{7}\right) -\left(\frac{3}{12}\right)\\= \frac{-2}{7}- \frac{4}{7}-\frac{3}{12}\\=\frac{-2}{7}-\frac{4}{7}-\frac{1}{4}\\=\frac{-8}{28}-\frac{16}{28}-\frac{7}{28}\\=\frac{-8-16-7}{28}\\=\frac{-31}{28}\)
5. \(-\left(\frac{-2}{7}\right) +\left(\frac{-6}{7}\right) +\left(\frac{-7}{5}\right)\\= \frac{2}{7}- \frac{6}{7}-\frac{7}{5}\\=\frac{10}{35}-\frac{30}{35}-\frac{49}{35}\\=\frac{10-30-49}{35}\\=\frac{-69}{35}\)
6. \(-\left(\frac{4}{-9}\right) -\left(\frac{-7}{-10}\right) -\left(\frac{-10}{-3}\right)\\= \frac{4}{9}- \frac{7}{10}-\frac{10}{3}\\=\frac{40}{90}-\frac{63}{90}-\frac{300}{90}\\=\frac{40-63-300}{90}\\=\frac{-323}{90}\)
7. \(+\left(\frac{4}{-7}\right) +\left(\frac{-5}{10}\right) -\left(\frac{8}{-8}\right)\\= \frac{-4}{7}- \frac{5}{10}+\frac{8}{8}\\=\frac{-4}{7}-\frac{1}{2}+\frac{1}{1}\\=\frac{-8}{14}-\frac{7}{14}+\frac{14}{14}\\=\frac{-8-7+14}{14}\\=\frac{-1}{14}\)
8. \(-\left(\frac{10}{3}\right) -\left(\frac{-6}{-4}\right) +\left(\frac{7}{-2}\right)\\= \frac{-10}{3}- \frac{6}{4}-\frac{7}{2}\\=\frac{-10}{3}-\frac{3}{2}-\frac{7}{2}\\=\frac{-20}{6}-\frac{9}{6}-\frac{21}{6}\\=\frac{-20-9-21}{6}\\=\frac{-50}{6}\\=\frac{-25}{3}\)
9. \(-\left(\frac{-5}{-3}\right) +\left(\frac{3}{-5}\right) -\left(\frac{8}{8}\right)\\= \frac{-5}{3}- \frac{3}{5}-\frac{8}{8}\\=\frac{-5}{3}-\frac{3}{5}-\frac{1}{1}\\=\frac{-25}{15}-\frac{9}{15}-\frac{15}{15}\\=\frac{-25-9-15}{15}\\=\frac{-49}{15}\)
10. \(-\left(\frac{4}{-9}\right) -\left(\frac{-10}{-5}\right) -\left(\frac{-11}{2}\right)\\= \frac{4}{9}- \frac{10}{5}+\frac{11}{2}\\=\frac{4}{9}-\frac{2}{1}+\frac{11}{2}\\=\frac{8}{18}-\frac{36}{18}+\frac{99}{18}\\=\frac{8-36+99}{18}\\=\frac{71}{18}\)
11. \(+\left(\frac{-10}{7}\right) +\left(\frac{3}{3}\right) +\left(\frac{-8}{11}\right)\\= \frac{-10}{7}+ \frac{3}{3}-\frac{8}{11}\\=\frac{-10}{7}+\frac{1}{1}-\frac{8}{11}\\=\frac{-110}{77}+\frac{77}{77}-\frac{56}{77}\\=\frac{-110+77-56}{77}\\=\frac{-89}{77}\)
12. \(+\left(\frac{-6}{5}\right) -\left(\frac{-6}{7}\right) -\left(\frac{3}{-2}\right)\\= \frac{-6}{5}+ \frac{6}{7}+\frac{3}{2}\\=\frac{-84}{70}+\frac{60}{70}+\frac{105}{70}\\=\frac{-84+60+105}{70}\\=\frac{81}{70}\)