Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-2}{-5}\right) -\left(\frac{6}{4}\right) +\left(\frac{2}{-4}\right)\\= \frac{-2}{5}- \frac{6}{4}-\frac{2}{4}\\=\frac{-2}{5}-\frac{3}{2}-\frac{1}{2}\\=\frac{-4}{10}-\frac{15}{10}-\frac{5}{10}\\=\frac{-4-15-5}{10}\\=\frac{-24}{10}\\=\frac{-12}{5}\)
2. \(-\left(\frac{9}{-8}\right) -\left(\frac{-7}{-3}\right) -\left(\frac{-8}{11}\right)\\= \frac{9}{8}- \frac{7}{3}+\frac{8}{11}\\=\frac{297}{264}-\frac{616}{264}+\frac{192}{264}\\=\frac{297-616+192}{264}\\=\frac{-127}{264}\)
3. \(-\left(\frac{7}{-3}\right) -\left(\frac{2}{-2}\right) -\left(\frac{-12}{-7}\right)\\= \frac{7}{3}+ \frac{2}{2}-\frac{12}{7}\\=\frac{7}{3}+\frac{1}{1}-\frac{12}{7}\\=\frac{49}{21}+\frac{21}{21}-\frac{36}{21}\\=\frac{49+21-36}{21}\\=\frac{34}{21}\)
4. \(+\left(\frac{2}{-3}\right) +\left(\frac{10}{-9}\right) -\left(\frac{11}{-11}\right)\\= \frac{-2}{3}- \frac{10}{9}+\frac{11}{11}\\=\frac{-2}{3}-\frac{10}{9}+\frac{1}{1}\\=\frac{-6}{9}-\frac{10}{9}+\frac{9}{9}\\=\frac{-6-10+9}{9}\\=\frac{-7}{9}\)
5. \(-\left(\frac{4}{7}\right) -\left(\frac{-7}{3}\right) +\left(\frac{2}{-10}\right)\\= \frac{-4}{7}+ \frac{7}{3}-\frac{2}{10}\\=\frac{-4}{7}+\frac{7}{3}-\frac{1}{5}\\=\frac{-60}{105}+\frac{245}{105}-\frac{21}{105}\\=\frac{-60+245-21}{105}\\=\frac{164}{105}\)
6. \(-\left(\frac{3}{-5}\right) +\left(\frac{-10}{-7}\right) +\left(\frac{11}{-7}\right)\\= \frac{3}{5}+ \frac{10}{7}-\frac{11}{7}\\=\frac{21}{35}+\frac{50}{35}-\frac{55}{35}\\=\frac{21+50-55}{35}\\=\frac{16}{35}\)
7. \(+\left(\frac{9}{7}\right) -\left(\frac{-10}{-9}\right) +\left(\frac{-9}{2}\right)\\= \frac{9}{7}- \frac{10}{9}-\frac{9}{2}\\=\frac{162}{126}-\frac{140}{126}-\frac{567}{126}\\=\frac{162-140-567}{126}\\=\frac{-545}{126}\)
8. \(+\left(\frac{9}{8}\right) -\left(\frac{-4}{-4}\right) +\left(\frac{-6}{9}\right)\\= \frac{9}{8}- \frac{4}{4}-\frac{6}{9}\\=\frac{9}{8}-\frac{1}{1}-\frac{2}{3}\\=\frac{27}{24}-\frac{24}{24}-\frac{16}{24}\\=\frac{27-24-16}{24}\\=\frac{-13}{24}\)
9. \(+\left(\frac{-4}{-3}\right) -\left(\frac{4}{7}\right) +\left(\frac{-12}{-8}\right)\\= \frac{4}{3}- \frac{4}{7}+\frac{12}{8}\\=\frac{4}{3}-\frac{4}{7}+\frac{3}{2}\\=\frac{56}{42}-\frac{24}{42}+\frac{63}{42}\\=\frac{56-24+63}{42}\\=\frac{95}{42}\)
10. \(-\left(\frac{-9}{7}\right) -\left(\frac{-7}{-8}\right) +\left(\frac{3}{12}\right)\\= \frac{9}{7}- \frac{7}{8}+\frac{3}{12}\\=\frac{9}{7}-\frac{7}{8}+\frac{1}{4}\\=\frac{72}{56}-\frac{49}{56}+\frac{14}{56}\\=\frac{72-49+14}{56}\\=\frac{37}{56}\)
11. \(+\left(\frac{-10}{-7}\right) -\left(\frac{-5}{7}\right) +\left(\frac{-2}{8}\right)\\= \frac{10}{7}+ \frac{5}{7}-\frac{2}{8}\\=\frac{10}{7}+\frac{5}{7}-\frac{1}{4}\\=\frac{40}{28}+\frac{20}{28}-\frac{7}{28}\\=\frac{40+20-7}{28}\\=\frac{53}{28}\)
12. \(+\left(\frac{5}{2}\right) -\left(\frac{10}{-2}\right) -\left(\frac{8}{-10}\right)\\= \frac{5}{2}+ \frac{10}{2}+\frac{8}{10}\\=\frac{5}{2}+\frac{5}{1}+\frac{4}{5}\\=\frac{25}{10}+\frac{50}{10}+\frac{8}{10}\\=\frac{25+50+8}{10}\\=\frac{83}{10}\)