Breuken haakjesregel (reeks 2)

Hoofdmenu Eentje per keer  🖨

Bereken

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

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Bereken

Verbetersleutel

1. \(-\left(\frac{-8}{3}\right) +\left(\frac{-3}{-10}\right) +\left(\frac{-11}{9}\right)\\= \frac{8}{3}+ \frac{3}{10}-\frac{11}{9}\\=\frac{240}{90}+\frac{27}{90}-\frac{110}{90}\\=\frac{240+27-110}{90}\\=\frac{157}{90}\)
2. \(+\left(\frac{-6}{-5}\right) +\left(\frac{-5}{8}\right) +\left(\frac{-7}{-12}\right)\\= \frac{6}{5}- \frac{5}{8}+\frac{7}{12}\\=\frac{144}{120}-\frac{75}{120}+\frac{70}{120}\\=\frac{144-75+70}{120}\\=\frac{139}{120}\)
3. \(+\left(\frac{-4}{-9}\right) -\left(\frac{-3}{7}\right) +\left(\frac{12}{-8}\right)\\= \frac{4}{9}+ \frac{3}{7}-\frac{12}{8}\\=\frac{4}{9}+\frac{3}{7}-\frac{3}{2}\\=\frac{56}{126}+\frac{54}{126}-\frac{189}{126}\\=\frac{56+54-189}{126}\\=\frac{-79}{126}\)
4. \(-\left(\frac{-4}{5}\right) +\left(\frac{-8}{2}\right) -\left(\frac{6}{-7}\right)\\= \frac{4}{5}- \frac{8}{2}+\frac{6}{7}\\=\frac{4}{5}-\frac{4}{1}+\frac{6}{7}\\=\frac{28}{35}-\frac{140}{35}+\frac{30}{35}\\=\frac{28-140+30}{35}\\=\frac{-82}{35}\)
5. \(-\left(\frac{-10}{9}\right) -\left(\frac{-9}{7}\right) +\left(\frac{4}{5}\right)\\= \frac{10}{9}+ \frac{9}{7}+\frac{4}{5}\\=\frac{350}{315}+\frac{405}{315}+\frac{252}{315}\\=\frac{350+405+252}{315}\\=\frac{1007}{315}\)
6. \(-\left(\frac{4}{-5}\right) +\left(\frac{-6}{-4}\right) +\left(\frac{-5}{-3}\right)\\= \frac{4}{5}+ \frac{6}{4}+\frac{5}{3}\\=\frac{4}{5}+\frac{3}{2}+\frac{5}{3}\\=\frac{24}{30}+\frac{45}{30}+\frac{50}{30}\\=\frac{24+45+50}{30}\\=\frac{119}{30}\)
7. \(-\left(\frac{5}{6}\right) +\left(\frac{-10}{-10}\right) -\left(\frac{-10}{5}\right)\\= \frac{-5}{6}+ \frac{10}{10}+\frac{10}{5}\\=\frac{-5}{6}+\frac{1}{1}+\frac{2}{1}\\=\frac{-5+1+2}{6}\\=\frac{-2}{6}\\=\frac{-1}{3}\)
8. \(-\left(\frac{-3}{-4}\right) +\left(\frac{-10}{-7}\right) -\left(\frac{-9}{-6}\right)\\= \frac{-3}{4}+ \frac{10}{7}-\frac{9}{6}\\=\frac{-3}{4}+\frac{10}{7}-\frac{3}{2}\\=\frac{-21}{28}+\frac{40}{28}-\frac{42}{28}\\=\frac{-21+40-42}{28}\\=\frac{-23}{28}\)
9. \(-\left(\frac{7}{3}\right) +\left(\frac{2}{-7}\right) +\left(\frac{-10}{6}\right)\\= \frac{-7}{3}- \frac{2}{7}-\frac{10}{6}\\=\frac{-7}{3}-\frac{2}{7}-\frac{5}{3}\\=\frac{-49}{21}-\frac{6}{21}-\frac{35}{21}\\=\frac{-49-6-35}{21}\\=\frac{-90}{21}\\=\frac{-30}{7}\)
10. \(-\left(\frac{5}{2}\right) +\left(\frac{-5}{5}\right) -\left(\frac{-10}{6}\right)\\= \frac{-5}{2}- \frac{5}{5}+\frac{10}{6}\\=\frac{-5}{2}-\frac{1}{1}+\frac{5}{3}\\=\frac{-15}{6}-\frac{6}{6}+\frac{10}{6}\\=\frac{-15-6+10}{6}\\=\frac{-11}{6}\)
11. \(+\left(\frac{10}{-3}\right) +\left(\frac{-4}{2}\right) +\left(\frac{-9}{-9}\right)\\= \frac{-10}{3}- \frac{4}{2}+\frac{9}{9}\\=\frac{-10}{3}-\frac{2}{1}+\frac{1}{1}\\=\frac{-10-2+1}{3}\\=\frac{-11}{3}\)
12. \(+\left(\frac{-4}{7}\right) +\left(\frac{4}{-3}\right) -\left(\frac{4}{11}\right)\\= \frac{-4}{7}- \frac{4}{3}-\frac{4}{11}\\=\frac{-132}{231}-\frac{308}{231}-\frac{84}{231}\\=\frac{-132-308-84}{231}\\=\frac{-524}{231}\)